Juan Luis Vázquez. Publications 2000-2017

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2000
Quenching for a one-dimensional fully nonlinear parabolic equation in detonation theory (authors: Victor A. Galaktionov, Stéphane Gerbi, J. L. V.), SIAM J. Appl. Math. 61 (2000/01), no. 4, 1253–1285.     pdf
Behaviour of interfaces in a diffusion-absorption equation with critical exponents (authors: Victor A. Galaktionov, Sergei I. Shmarev, J. L. V.), Interfaces Free Bound. 2 (2000), no. 4, 425–448.     pdf
The Hardy inequality and the asymptotic behaviour of the heat equation with an inverse-square potential (authors: J. L. V., Enrike Zuazua), J. Funct. Anal. 173 (2000), no. 1, 103–153.     pdf
Asymptotics of the fast-diffusion equation with critical exponent (authors: Victor A. Galaktionov, Lambertus A. Peletier, J. L. V.), SIAM J. Math. Anal. 31 (2000), no. 5, 1157–1174.     pdf
Very intense pulse in the ground­wa­ter flow in fissurized porous stratum (authors: Grigori I. Barenblatt, E. A. Ingerman, H. Shvetz, J. L. V.), Proc. Natl. Acad. Sci. USA 97 (2000), no. 4, pp. 1366-1369.     pdf
 
2001
Uniqueness of solution to a free boundary problem from combustion (authors: Claudia Lederman, J. L. V., Noemi I. Wolanski), Trans. Amer. Math. Soc. 353 (2001), no. 2, 655–692.     pdf
Asymptotic convergence of the Stefan problem to Hele-Shaw (authors: Fernando Quirós, J. L. V.), Trans. Amer. Math. Soc. 353 (2001), no. 2, 609–634.     pdf
Solutions of nonlinear parabolic equations without growth restrictions on the data. (authors: Lucio Boccardo, Thierry Gallouët,, J. L. V.), Electron. J. Differential Equations 2001, No. 60, 20 pp.     pdf
Extinction behaviour for fast diffusion equations with absorption (authors: Raúl Ferreira, J. L. V.), Nonlinear Anal. 43 (2001), no. 8, Ser. A: Theory Methods, 943–985.     pdf
Uniqueness in a two-phase free-boundary problem (authors: Claudia Lederman, J. L. V., Noemi I. Wolanski), Adv. Differential Equations 6 (2001), no. 12, 1409–1442.     pdf
A mixed semilinear parabolic problem in a noncylindrical space-time domain. (authors: Claudia Lederman, J. L. V., Noemi I. Wolanski), Differential Integral Equations 14 (2001), no. 4, 385–404.     pdf
 
2002
Theory of extended solutions for fast-diffusion equations in optimal classes of data. Radiation from singularities (authors: Emmanuel Chasseigne, J. L. V.), Arch. Ration. Mech. Anal. 164 (2002), no. 2, 133–187.     pdf
Complete blow-up and thermal avalanche for heat equations with nonlinear boundary conditions (authors: Quirós, Fernando; Rossi, Julio D.; J. L. V.), Comm. Partial Differential Equations 27 (2002), no. 1-2, 395–424.     pdf
Sets of admissible initial data for porous-medium equations with absorption (authors: Emmanuel Chasseigne, J. L. V.), Proceedings of the 2001 Luminy Conference on Quasilinear Elliptic and Parabolic Equations and System, 53–83, Electron. J. Differ. Equ. Conf., 8 , Southwest Texas State Univ., San Marcos, TX, 2002.     pdf
Obstructions to existence in fast-diffusion equations (authors: Ana Rodríguez, J. L. V.), J. Differential Equations 184 (2002), no. 2, 348–385.     pdf
Complexity of large time behaviour of evolution equations with bounded data (authors: J. L. V., Enrike Zuazua), Dedicated to the memory of Jacques-Louis Lions. Chinese Ann. Math. Ser. B 23 (2002), no. 2, 293–310.     pdf
Uniqueness of asymptotic profiles for an extinction problem (authors: Ferreira, R.; Galaktionov, V. A., J. L. V.), Nonlinear Anal. 50 (2002), no. 4, Ser. A: Theory Methods, 495–507.     pdf
The problem of blow-up in nonlinear parabolic equations (authors: Galaktionov, Victor A.; J. L. V.), Current developments in partial differential equations (Temuco, 1999). Discrete Contin. Dyn. Syst. 8 (2002), no. 2, 399–433.     pdf
Ignition and propagation in an integro-differential model for spherical flames (authors: Roquejoffre, Jean-Michel, J. L. V.), Discrete Contin. Dyn. Syst. Ser. B 2 (2002), no. 3, 379–387     pdf
 
2003
Asymptotic behaviour for the porous medium equation posed in the whole space (author: J. L. V.), Dedicated to Philippe Bénilan. J. Evol. Equ. 3 (2003), no. 1, 67–118.     pdf
The pressure equation in the fast diffusion range (authors: Emmanuel Chasseigne, J. L. V.), Rev. Mat. Iberoamericana 19 (2003), no. 3, 873–917.     pdf
Introduction. Dedicated to Philippe Bénilan (authors: Haïm Brézis, Wolfgang Arendt, Louise Barthélemy, Michael Crandall, Jose Carrillo, J. Ildefonso Diaz, Jerome A. Goldstein, Michel Pierre, J. L. V.), J. Evol. Equ. 3 (2003), no. 1, 1–9.     pdf
The nonlinearly damped oscillator (author: J. L. V.), ESAIM Control Optim. Calc. Var. 9 (2003), 231–246.     pdf
Darcy's law and the theory of shrinking solutions of fast diffusion equations (author: J. L. V.), SIAM J. Math. Anal. 35 (2003), no. 4, 1005–1028.     pdf
Geometrical properties of solutions of the porous medium equation for large times (authors: Ki-Ahm Lee, J. L. V.), Indiana Univ. Math. J. 52 (2003), no. 4, 991–1016.     pdf
Fine asymptotics for fast diffusion equations (authors: José A. Carrillo, J. L. V.), Comm. Partial Differential Equations 28 (2003), no. 5-6, 1023–1056.     pdf
Intermediate asymptotics for a nonhomogeneous nonlinear heat equation (authors: V. A. Galaktionov, Sh. Kamin, R. Kershner, Kh. L. Vaskez= J. L. V.), (Russian) Tr. Semin. im. I. G. Petrovskogo No. 23 (2003), 61-92, 409; translation in J. Math. Sci. (N. Y.) 120 (2004), no. 3, 1277–1294.     pdf
Mathematics, science and technology: a deep and enduring connection (author: J. L. V.), (Portuguese) Bol. Soc. Port. Mat. No. 49 (2003), 19–70.     pdf
Large time behavior for a simplified 1D model of fluid-solid interaction (authors: J. L. V., Enrique Zuazua), Comm. Partial Differential Equations 28 (2003), no. 9-10, 1705–1738.     pdf
Study of self-similarity for the fast-diffusion equation (authors: Raúl Ferreira, J. L. V.), Adv. Differential Equations 8 (2003), no. 9, 1125–1152.     pdf
 
2004
The Dirichlet problem for the porous medium equation in bounded domains. Asymptotic behavior (authors: J. L. V.), Monatsh. Math. 142 (2004), no. 1-2, 81–111.     pdf
Thermal avalanche for blowup solutions of semilinear heat equations (authors: Quirós, Fernando; Rossi, Julio D.;, J. L. V.), Comm. Pure Appl. Math. 57 (2004), no. 1, 59–98.     pdf
Nonlinear diffusion and image contour enhancement (authors: G. I. Barenblatt, J. L. V.), Interfaces Free Bound. 6 (2004), no. 1, 31–54.     pdf
Intermediate asymptotics for a nonhomogeneous nonlinear heat equation (authors: V. A. Galaktionov, Sh. Kamin, R. Kershner, Vaskez, Kh. L= J. L. V.), (Russian) Tr. Semin. im. I. G. Petrovskogo No. 23 (2003), 61--92, 409; translation in J. Math. Sci. (N. Y.) 120 (2004), no. 3, 1277–1294.     pdf
Complexity of large time behaviour of evolution equations with bounded data (authors: J. L. V., Enrike Zuazua), "Frontiers in mathematical analysis and numerical methods", 267–295, World Sci. Publ., River Edge, NJ, 2004.     pdf
 
2005
Symmetrization and mass comparison for degenerate nonlinear parabolic and related elliptic equations. (author: J. L. V.), Adv. Nonlinear Stud. 5 (2005), no. 1, 87–131.     pdf
Failure of the strong maximum principle in nonlinear diffusion. Existence of needles. (author: J. L. V.), Comm. Partial Differential Equations 30 (2005), no. 7-9, 1263–1303.     pdf
The porous medium equation. New contractivity results (author: J. L. V.), in "Elliptic and parabolic problems", 433–451, Progr. Nonlinear Differential Equations Appl., 63, Birkhäuser, Basel, 2005.     pdf
Mathematical blowup for reaction-diffusion equations and systems (authors: de Pablo, A.; Ferreira, R.; Quirós, F. , J. L. V.), (Spanish) Bol. Soc. Esp. Mat. Apl. Se⃗MA No. 32 (2005), 75–111.     pdf
Viscosity solutions for quasilinear degenerate parabolic equations of porous medium type (authors: Brändle, Cristina , J. L. V.), Indiana Univ. Math. J. 54 (2005), no. 3, 817–860.     pdf
Singular free boundary problem from image processing (authors: A. L. Amadori, , J. L. V.), Math. Models Methods Appl. Sci. 15 (2005), no. 5, 689–715.     pdf
The diffusive limit for Carleman-type kinetic models (authors: Francesco Salvarani, J. L. V.), Nonlinearity 18 (2005), no. 3, 1223–1248.     pdf
 
2006
Large-time geometric properties of solutions of the evolution p-Laplacian equation (authors: Ki-ahm Lee, Arshak Petrosyan, J. L. V.), J. Differential Equations 229 (2006), no. 2, 389–411.     pdf
Global positivity estimates and Harnack inequalities for the fast diffusion equation (authors: Matteo Bonforte, J. L. V.), J. Funct. Anal. 240 (2006), no. 2, 399–428.     pdf
Classification of blow-up with nonlinear diffusion and localized reaction (authors: Raúl Ferreira, Arturo de Pablo, J. L. V.), J. Differential Equations 231 (2006), no. 1, 195–211.     pdf
A weighted symmetrization for nonlinear elliptic and parabolic equations in inhomogeneous media (authors: Guillermo Reyes, J. L. V.), J. Eur. Math. Soc. (JEMS) 8 (2006), no. 3, 531–554.     pdf
The Cauchy problem for the inhomogeneous porous medium equation (authors: Guillermo Reyes, J. L. V.), Netw. Heterog. Media 1 (2006), no. 2, 337–351.     pdf
Extended solutions for general fast diffusion equations with optimal measure data (authors: Emmanuel Chasseigne, J. L. V.), Adv. Differential Equations 11 (2006), no. 6, 627–646.     pdf
Lack of collision in a simplified 1D model for fluid-solid interaction (authors: J. L. V., Enrique Zuazua), Math. Models Methods Appl. Sci. 16 (2006), no. 5, 637–678.     pdf
Dirichlet boundary conditions can prevent blow-up reaction-diffusion equations and systems (authors: Marek Fila, Hirokazu Ninomiya, J. L. V.), Discrete Contin. Dyn. Syst. 14 (2006), no. 1, 63–74.     pdf
Stabilization towards a singular steady state with gradient blow-up for a diffusion-convection problem. (authors: Philippe Souplet, J. L. V.), Discrete Contin. Dyn. Syst. 14 (2006), no. 1, 221–234.     pdf
 
2007
Perspectives in nonlinear diffusion: between analysis, physics and geometry (author: J. L. V.), International Congress of Mathematicians. Vol. I, 609–634, Eur. Math. Soc., Zürich, 2007. ICM2006 Plenary speaker.     pdf
Multiple blowup for nonlinear heat equations at different places and different times (authors: Noriko Mizoguchi, J. L. V.), Indiana Univ. Math. J. 56 (2007), no. 6, 2859–2886.     pdf
Porous medium flow in a tube. Traveling waves and KPP behavior (author: J. L. V.), Commun. Contemp. Math. 9 (2007), no. 5, 731–751.     pdf
Localized non-diffusive asymptotic patterns for nonlinear parabolic equations with gradient absorption (authors: Philippe Laurençot. J. L. V.), J. Dynam. Differential Equations 19 (2007), no. 4, 985–1005.     pdf
Viscosity solutions for elliptic-parabolic problems (authors: Paola Mannucci, J. L. V.), NoDEA Nonlinear Differential Equations Appl. 14 (2007), no. 1-2, 75–90.     pdf
Asymptotic complexity in filtration equations (authors: José A. Carrillo, J. L. V.), J. Evol. Equ. 7 (2007), no. 3, 471–495.     pdf
Asymptotic behaviour of the porous media equation in domains with holes (authors: Cristina Brändle, Fernando Quirós, J. L. V.), Interfaces Free Bound. 9 (2007), no. 2, 211–232.     pdf
Finite-time blow-down in the evolution of point masses by planar logarithmic diffusion (authors: J. L. V.), Discrete Contin. Dyn. Syst. 19 (2007), no. 1, 1–35     pdf
Heat equation with dynamical boundary conditions of locally reactive type (authors: J. L. V., Enzo Vitillaro), Semigroup Forum 74 (2007), no. 1, 1–40.     pdf
Reverse smoothing effects, fine asymptotics, and Harnack inequalities for fast diffusion equations (authors: Matteo Bonforte, J. L. V.), Bound. Value Probl. 2007, Art. ID 21425, 31 pp.     pdf
Some new kernel functions for real-valued data (authors: J. L. V., Lluis Belanche, Miguel Vázquez), International Journal of Computer, Mathematical Sciences and Applications (Int. J. Comput. Math. Sci. Appl.), Vol. 1, no. 2 (2007), 149-160.     pdf
Hardy-Poincaré inequalities and applications to nonlinear diffusions (authors: Adrien Blanchet, Matteo Bonforte, Jean Dolbeault, Gabriele Grillo, J. L. V.), C. R. Math. Acad. Sci. Paris 344 (2007) , no. 7, 431–436.     pdf
 
2008
Parabolic approach to Nonlinear Elliptic Eigenvalue Problems (authors: Ki-ahm Lee, J. L. V.), Advances in Mathematics, 219 (2008), 2006-2028.     pdf
Radial equivalence for the two basic nonlinear degenerate diffusion equations (authors: Razvan Iagar, Ariel Sánchez, J. L. V.), J. Math. Pures Appl. (9) 89 (2008), no. 1, 1-24.     pdf
Fast Diffusion Flow on Manifolds of Nonpositive Curvature (authors: Matteo Bonforte, Gabriele Grillo, J. L. V.), J. Evol. Equ. 8 (2008), no. 1, 99-128.     pdf
Heat equation with dynamical boundary conditions of reactive type (authors: J. L. V., Enzo Vitillaro), Comm. Partial Differential Equations 33 4 (2008), no. 4-6, 561-612.     pdf
Wave equation with second-order non-standard dynamical boundary conditions (authors: J. L. V., Enzo Vitillaro), Math. Models Methods Appl. Sci. (M3AS) 18 (2008), no. 12, 2019-205.     pdf
The inhomogeneous PME in several space dimensions. Existence and uniqueness of finite energy solutions (authors: Guillermo Reyes, J. L. V.), Commun. Pure Appl. Anal. 7 (2008), no. 6, 1275-1294.     pdf
Distance-Based Kernels for Real-Valued Data (authors: Lluís Belanche, J. L. V., Miguel Vázquez), in "Data Analysis, Machine Learning and Applications", pp. 3-10, Springer Berlin Heidelberg, 2008. ISBN 978-3-540-78246-9 (Online).     pdf
 
2009
Local Aronson-Bénilan estimates and entropy formulae for porous medium and fast diffusion equations on manifolds (authors: Peng Lu, Lei Ni, J. L. V., Cédric Villani), J. Math. Pures Appl. 91 (2009), no. 1, 1-19.     pdf
Asymptotics of the fast diffusion equation via entropy estimates (authors: Adrien Blanchet, Matteo Bonforte, Jean Dolbeault, Gabriele Grillo, J. L. V.), Arch. Rational Mech. Anal. 191 (2009), no. 2, 347-385.     pdf
Long time behavior for the inhomogeneous PME in a medium with slowly decaying density (authors: Guillermo Reyes, J. L. V.), Commun. Pure Appl. Anal. 8 (2009), no. 2, 493-508.     pdf
Measure-valued solutions and the phenomenon of blow-down in logarithmic diffusion (author: J. L. V.), J. Math. Anal. Appl. 352 (2009), no 1, 515-547.     pdf
Noncoercive convection-diffusion elliptic problems with Neumann boundary conditions (authors: Jérôme Droniou, J. L. V.), Cal. Var. Partial Differential Equations 34, Issue 4 (2009), 413-434.     pdf
Asymptotic analysis for the p-Laplacian Evolution Equation in an Exterior Domain (authors: Razvan G. Iagar, J. L. V.), Ann. Inst. H. Poincaré, Anal. Non Linéaire 26 (2009), no. 2, 497-520.     pdf
On the Laplace equation with dynamical boundary conditions of reactive-diffusive type (authors: J. L. V., Enzo Vitillaro), JMAA 354 (2009), no 2, 674-688.     pdf
 
2010
Sharp rates of decay of solutions to the nonlinear fast diffusion equation via functional inequalities (authors: Matteo Bonforte, J. Dolbeault, G. Grillo, J. L. V.), Proc. Natl. Acad. Sci. USA 107 (2010), no. 38, 16459–16464.     pdf
Local smoothing effects, positivity, and Harnack inequalities for the fast p-Laplacian equation (authors: Matteo Bonforte, Razvan G. Iagar, J. L. V.), Adv. Math. 224 (2010), no. 5, 2151–2215.     pdf
Special fast diffusion with slow asymptotics: entropy method and flow on a Riemann manifold (authors: Matteo Bonforte, Gabriele Grillo, J. L. V.), Arch. Ration. Mech. Anal. 196 (2010), no. 2, 631–680.     pdf
Anomalous large-time behaviour of the p-Laplacian flow in an exterior domain in low dimension (authors: Razvan G. Iagar, J. L. V.), J. Eur. Math. Soc. (JEMS) 12 (2010), no. 1, 249–277.     pdf
Positivity, local smoothing, and Harnack inequalities for very fast diffusion equations (authors: Matteo Bonforte, J. L. V.), Adv. Math. 223 (2010), no. 2, 529–578.     pdf
Long time behavior for the inhomogeneous PME in a medium with rapidly decaying density (authors: Shoshana Kamin, Guillermo Reyes, J. L. V.), Discrete Contin. Dyn. Syst. 26 (2010), no. 2, 521–549.     pdf
 
2011
Nonlinear porous medium flow with fractional potential pressure (authors: Luis A. Caffarelli, J. L. V.), Arch. Ration. Mech. Anal. 202 (2011), no. 2, 537–565.     pdf
Asymptotic behaviour of a porous medium equation with fractional diffusion (authors: Luis A. Caffarelli, J. L. V.), Discrete Contin. Dyn. Syst. 29 (2011), no. 4, 1393–1404.     pdf
A fractional porous medium equation (authors: Arturo de Pablo, Fernando Quirós, Ana Rodríguez, J. L. V.), Adv. Math. 226 (2011), no. 2, 1378–1409.     pdf
Highly time-oscillating solutions for very fast diffusion equations (authors: J. L. V., Winkler, Michael), J. Evol. Equ. 11 (2011), no. 3, 725–742.     pdf
The evolution of singularities in fast diffusion equations: infinite-time blow-down (authors: J. L. V., Winkler, Michael), SIAM J. Math. Anal. 43 (2011), no. 4, 1499–1535.     pdf
Multiple blow-up for a porous medium equation with reaction (authors: Noriko Mizoguchi, Fernando Quirós, J. L. V.), Math. Ann. 350 (2011), no. 4, 801–827.     pdf
Asymptotic behaviour of a nonlinear parabolic equation with gradient absorption and critical exponent (authors: Razvan G. Iagar, Philippe Laurençot, J. L. V.), Interfaces Free Bound. 13 (2011), no. 2, 271–295.     pdf
A continuum of extinction rates for the fast diffusion equation (authors: Marek Fila, J. L. V., , Michael Winkler ), Commun. Pure Appl. Anal. 10 (2011), no. 4, 1129–1147.     pdf
Heat equation with dynamical boundary conditions of reactive-diffusive type (authors: J. L. V., Enzo Vitillaro ), J. Differential Equations 250 (2011), no. 4, 2143–2161.     pdf
 
2012
A general fractional porous medium equation (authors: Arturo de Pablo, Fernando Quirós, Ana Rodríguez, J. L. V.), Comm. Pure Appl. Math. 65 (2012), no. 9, 1242–1284.     pdf
Nonlinear diffusion with fractional Laplacian operators (author: J. L. V.), "Nonlinear partial differential equations", 271–298, Abel Symp., 7, Springer, Heidelberg, 2012.     pdf
Quantitative local bounds for subcritical semilinear elliptic equations (authors: Matteo Bonforte, Gabriele Grillo, J. L. V.), Milan J. Math. 80 (2012), no. 1, 65–118.     pdf
Functional aspects of the Hardy inequality: appearance of a hidden energy (authors: J. L. V., Nikolaos B. Zographopoulos), J. Evol. Equ. 12 (2012), no. 3, 713–739.     pdf
A porous medium equation involving the infinity-Laplacian. Viscosity solutions and asymptotic behavior (authors: Manuel Portilheiro, J. L. V.), Comm. Pure Appl. Math. 65 (2012), no. 9, 1242–1284.     pdf
Rate of convergence to Barenblatt profiles for the fast diffusion equation (authors: Marek Fila, J. L. V., Michael Winkler, Eiji Yanagida), Arch. Ration. Mech. Anal. 204 (2012), no. 2, 599–625.     pdf
Large-time geometrical properties of solutions of the Barenblatt equation of elasto-plastic filtration (authors: Yong Huang, J. L. V.), Differential Equations 252 (2012), no. 7, 4229–4242.     pdf
Behaviour near extinction for the Fast Diffusion Equation on bounded domains (authors: Matteo Bonforte, Gabriele Grillo, J. L. V.), J. Math. Pures Appl. (9) 97 (2012), no. 1, 1–38.     pdf
 
2013
Regularity of solutions of the fractional porous medium flow (authors: Luis Caffarelli, Fernando Soria, J. L. V.), J. Eur. Math. Soc. (JEMS) 15 (2013), no. 5, 1701–1746.     pdf
Classification of radial solutions to the Emden-Fowler equation on the hyperbolic space (authors: Matteo Bonforte, Filippo Gazzola, Gabriele Grillo, J. L. V.), Calc. Var. Partial Differential Equations 46 (2013), no. 1-2, 375–401.     pdf
Hardy type inequalities and hidden energies (authors: J. L. V., Nikolaos B. Zographopoulos), Discrete Contin. Dyn. Syst. 33 (2013), no. 11-12, 5457–5491.     pdf
Functional aspects of the Hardy inequality: appearance of a hidden energy (authors: J. L. V., Nikolaos B. Zographopoulos), Differential and difference equations with applications, 653–665, Springer Proc. Math. Stat., 47, Springer, New York, 2013.     pdf
Quantitative bounds for subcritical semilinear elliptic equations (authors: Matteo Bonforte, Gabriele Grillo, J. L. V.), Recent trends in nonlinear partial differential equations. II. Stationary problems, 63–89, Contemp. Math., 595, Amer. Math. Soc., Providence, RI, 2013.     pdf
Degenerate homogeneous parabolic equations associated with the infinity-Laplacian (authors: Manuel Portilheiro, J. L. V.), Calc. Var. Partial Differential Equations 46 (2013), no. 3-4, 705–724.     pdf
Asymptotic behaviour of the doubly nonlinear diffusion equation utpum on bounded domains (authors: Diana Stan, J. L. V.), Nonlinear Anal. 77 (2013), 1–32.     pdf
 
2014
Classical solutions for a logarithmic fractional diffusion equation (authors: Arturo de Pablo, Fernando Quirós, Ana Rodríguez, J. L. V.), J. Math. Pures Appl. (9) 101 (2014), no. 6, 901–924.     pdf
Symmetrization for linear and nonlinear fractional parabolic equations of porous medium type (authors: J. L. V., Bruno Volzone), J. Math. Pures Appl. (9) 101 (2014), no. 5, 553–582.     pdf
Barenblatt solutions and asymptotic behaviour for a nonlinear fractional heat equation of porous medium type (author: J. L. V.), J. Eur. Math. Soc. (JEMS) 16 (2014), no. 4, 769–803.     pdf
A mean field equation as limit of nonlinear diffusions with fractional Laplacian operators (authors: Sylvia Serfaty, J. L. V.), Calc. Var. Partial Differential Equations 49 (2014), no. 3-4, 1091–1120.     pdf
Recent progress in the theory of nonlinear diffusion with fractional Laplacian operators (author: J. L. V.), Discrete Contin. Dyn. Syst. Ser. S 7 (2014), no. 4, 857–885.     pdf
The Hele-Shaw asymptotics for mechanical models of tumor growth (authors: Benoît Perthame, Fernando Quirós, J. L. V.), Arch. Ration. Mech. Anal. 212 (2014), no. 1, 93–127.     pdf
Quantitative local and global a priori estimates for fractional nonlinear diffusion equations (authors: Matteo Bonforte, J. L. V.), Adv. Math. 250 (2014), 242–284.     pdf
The Fisher-KPP equation with nonlinear fractional diffusion (authors: Diana Stan, J. L. V.), SIAM J. Math. Anal. 46 (2014), no. 5, 3241–3276.     pdf
Finite and infinite speed of propagation for porous medium equations with fractional pressure (authors: Diana Stan, Félix del Teso, J. L. V.), C. R. Math. Acad. Sci. Paris 352 (2014), no. 2, 123–128.     pdf
The Maximum Principle (author: J. L. V.), In "Selected Papers of James Serrin", 2 volumes"(P. Pucci, V. Radulescu, H. Weinberger, Editors). Contemporary Mathematicians, Birkhäuser. Springer Basel, 2014.     pdf
Progress in the theory of Nonlinear Diffusion. Asymptotics via entropy methods (author: J. L. V.), "Trends in Contemporary Mathematics", V. Ancona & E. Strickland eds, Springer INdAM Series vol. 8, Springer, 2014.     pdf
 
2015
Fundamental solution and long time behavior of the porous medium equation in hyperbolic space (author: J. L. V.), J. Math. Pures Appl. (9) 104 (2015), no. 3, 454–484.     pdf
The mesa problem for the fractional porous medium equation (author: J. L. V.), Interfaces Free Bound. 17 (2015), no. 2, 261–286.     pdf
Existence, uniqueness and asymptotic behaviour for fractional porous medium equations on bounded domains (authors: Matteo Bonforte, Yannick Sire, J. L. V.), Discrete Contin. Dyn. Syst. 35 (2015), no. 12, 5725–5767.     pdf
A priori estimates for fractional nonlinear degenerate diffusion equations on bounded domains (authors: Matteo Bonforte, J. L. V.), Arch. Ration. Mech. Anal. 218 (2015), no. 1, 317–362.     pdf
Transformations of self-similar solutions for porous medium equations of fractional type (authors: Diana Stan, Félix del Teso, J. L. V.), Nonlinear Anal. 119 (2015), 62–73.     pdf
Optimal estimates for fractional fast diffusion equations (authors: J. L. V., Bruno Volzone), J. Math. Pures Appl. (9) 103 (2015), no. 2, 535–556.     pdf
Free Boundary Problems: The Forefront of Current and Future Developments (authors: Gui-Qiang Chen, Henrik Shahgholian, J. L. V.), Phil. Trans. R. Soc. A 373 (2015), 20140285. 8 pages.     pdf
Exponential convergence towards stationary states for the 1D porous medium equation with fractional pressure (authors: José Antonio Carrillo, Yanhong Huang, M. C. Santos, J. L. V.), J. Differential Equations 258 (2015), no. 3, 736–763.     pdf
Some Free Boundary Problems involving Nonlocal Diffusion and Aggregation (authors: José Antonio Carrillo, J. L. V.), Phil. Trans. R. Soc. A 373 (2015), Issue 2050 , 20140275, 16 pp.     pdf
Regularity of solutions of the fractional porous medium flow with exponent 1/2 (authors: Luis Caffarelli, J. L. V.), Algebra i Analiz 27 (2015), no 3 [St. Petersburg Math. Journal 27 (2016), no 3, 437-460] (volume in honor of Prof. Nina Uraltseva).     pdf
 
2016
The Dirichlet problem for the fractional p-Laplacian evolution equation (author: J. L. V.), J. Differential Equations 260 (2016), no. 7, 6038–6056.     pdf
Non-existence and instantaneous extinction of solutions for singular nonlinear fractional diffusion equations (authors: Matteo Bonforte, Antonio Segatti, J. L. V.), Calc. Var. Partial Differential Equations 55 (2016), no. 3, 55-68.     pdf
Fractional nonlinear degenerate diffusion equations on bounded domains part I. Existence, uniqueness and upper bounds (authors: Matteo Bonforte, J. L. V.), Nonlinear Anal. 131 (2016), 363–398.     pdf
Finite and infinite speed of propagation for porous medium equations with nonlocal pressure (authors: Diana Stan, Félix del Teso, J. L. V.), J. Differential Equations 260 (2016), no. 2, 1154–1199.     pdf
Existence of maximal solutions for some very singular nonlinear fractional diffusion equations in 1D (author: J. L. V.), J. Evol. Equ. 16 (2016), 723–758.     pdf
2017
Optimal Existence and Uniqueness Theory for the Fractional Heat Equation (authors: M. Bonforte, Y. Sire, J. L. V.), Nonlin. Anal. TMA, 153 (2017), 142-168.     pdf
Symmetrization for fractional elliptic and parabolic equations and an isoperimetric application (authors: Yannick Sire, J. L. V., Bruno Volzone), Chinese Annals of Mathematics Ser. B 38 (2017), no. 2, 661-686. (Volume in honor of H. Brezis).     pdf
Classical solutions and higher regularity for nonlinear fractional diffusion equations (authors: J. L. V., Arturo de Pablo, Fernando Quirós, Ana Rodríguez), J. Eur. Math. Soc. 19 , 7 (2017), 1949-1975.     pdf
The Fisher-KPP problem with doubly nonlinear diffusion (authors: Alessandro Audrito, J. L. V.), J. Differential Equations 263 (2017), no. 11, 7647--7708. ArXiv:1601.05718.     pdf
The Fisher-KPP problem with doubly nonlinear "fast" diffusion (authors: Alessandro Audrito, J. L. V.), Nonlinear Analysis TMA, 157 (2017), 212--248.     pdf
The porous medium equation on Riemannian manifolds with negative curvature. The large-time behaviour (authors: Gabriele Grillo, Matteo Muratori, J. L. V.), Advances in Mathematics 314 (2017), 328-377.     pdf
Weak and smooth solutions for a fractional Yamabe flow: the case of general compact and locally conformally flat manifolds (authors: Panagiota Daskalopoulos, Yannick Sire, J. L. V.), Comm. Partial Differential Equations 42 (2017), no. 9, 1481--1496. ArXiv:1702.05221.     pdf
The mathematical theories of diffusion. Nonlinear and fractional diffusion (author: , J. L. V.), in ``Nonlocal and Nonlinear Diffusions and Interactions: New Methods and Directions'', Springer Lecture Notes in Mathematics, ISBN 978-3-319-61493-9. C.I.M.E. Foundation Subseries, Cetraro, Italy 2016.     pdf
 
        to appear
Asymptotic behaviour for the Fractional Heat Equation in the Euclidean space (author: J. L. V.), To appear in CVEE (``Complex Variables and Elliptic Equations''), Special Volume in honor of Vladimir I. Smirnov's 130th anniversary. ArXiv:1708.00821 [math.AP].     pdf
 
Preprints in arXiv
Flatness implies smoothness for solutions of the porous medium equation (authors: Clemens Kienzler, Herbert Koch, J. L. V.), arXiv:1609.09048v1.     pdf
Existence of weak solutions for a general porous medium equation with nonlocal pressure (authors: Diana Stan, Félix del Teso, J. L. V.), arXiv:1609.05139.     pdf
Sharp global estimates for local and nonlocal porous medium-type equations in bounded domains (authors: M. Bonforte, A. Figalli, J. L. V.), arXiv:1610.09881.     pdf
Asymptotic behaviour methods for the Heat Equation. Convergence to the Gaussian (author: J. L. V.), arXiv:1706.10034 [math.AP].     pdf
Porous medium equation with nonlocal pressure in a bounded domain (authors: Quoc-Hung Nguyen, J. L. V.), arXiv:1708.00660 [math.AP].     pdf
   

Research Books after 2000

The Porous Medium Equation. Mathematical Theory (author: J. L. V.), Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, Oxford, 2007. English, xxii+624 pages. ISBN-10: 0-19-856903-3, ISBN-13: 978-0-19-856903-9.     pdf
Smoothing and Decay Estimates for Nonlinear Diffusion Equations. Equations of Porous Medium Type (author: J. L. V.), Oxford University Press, Oxford Lecture Series, 2006. English, 248 pp. ISBN-10: 0-19-920297-4, ISBN-13: 978-0-19-920297-3.     pdf
A Stability Technique for Evolution Partial Differential Equations. A Dynamical Systems Approach (authors: Victor A. Galaktionov, J. L. V.), Birkhäuser Verlag, PNLDE 56 (Progress in Non-Linear Differential Equations and Their Applications), 2003. English, 391 pages (xxii+377 pp). ISBN 0-8176-4146-7.     pdf
Senderos de la ciencia. Del operador Laplaciano a los procesos difusivos no lineales''} [From the Laplacian Operator to Nonlinear Diffusive Processes] (author: J. L. V.), Discurso de ingreso en la Real Academia de Ciencias Exactas, Físicas y Naturales [Inaugural address as member of the Spanish Royal Academy of Sciences], March 26, 2014. Spanish. ISBN: 978-84-695-9782-8.     pdf
Recent Trends in Partial Differential Equations (authors: J. L. V., Xavier Cabré, José Antonio Carrillo Editors), American Mathematical Society, 123 pages, Series: Contemporary Mathematics, no. 409, 2004. ISBN-10: 0-8218-3891-1 ISBN-13: 978-0-8218-3891-4.     pdf
Free boundary problems: the forefront of current and future developments (authors: Gui-Qiang Chen, Henrik Shahgholian, J. L. V. Editors), Phil. Trans. Royal Soc. A 373: 20140285 (2015, volume 373, issue 2050). http://dx.doi.org/10.1098/rsta.2014.0285.     pdf
   

Conference Proceedings

A two phase free boundary problem from combustion: uniqueness and agreement of solution (authors: Claudia Lederman, J. L. V., Noemi I. Wolanski), Free boundary problems: theory and applications, I (Chiba, 1999), 180–189, GAKUTO Internat. Ser. Math. Sci. Appl., 13, Gakkōtosho, Tokyo, 2000.     pdf
From kinetic systems to diffusion equations (authors: Salvarani, F., J. L. V.), "WASCOM 2003''—12th Conference on Waves and Stability in Continuous Media, 475–481, World Sci. Publ., River Edge, NJ, 2004.     pdf
Partial differential equations and dynamical systems (authors: J. L. V.), (Spanish) Mathematical contributions in honor of Professor Enrique Outerelo Domínguez, 391–406, Homen. Univ. Complut., Editorial Complutense, Madrid, 2004.     pdf
The problems of blow-up for nonlinear heat equations. Complete blow-up and avalanche formation (author: J. L. V.), Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 15 (2004), no. 3-4, 281–300.     pdf
 

Expository papers and other articles

Mathematics and the goals of the Year 2000 Program. A call to Spanish mathematicians (author: J. L. V.), (Las matemáticas y los objetivos del año 2000. Un llamamiento a los matemáticos españoles (Spanish), Gac. R. Soc. Mat. Esp. 3 (2000), no. 1, 9–22.     pdf
 
Mathematical Events in Spain in the Year 2000 (author: J. L. V.), Intelligencer, Springer, July 2000, pp. 12-14.     pdf
Pasar sin rozar. Mecánica de fluidos (author: J. L. V.), en "Fotografiando las Matemáticas" (Spanish), Carroggio SA de Eds, (Spanish) Madrid 2000, pp. 92-95.     pdf
 
The importance of Mathematics in the development of Science and Technology (author: J. L. V.), Boletín Soc. Esp. Mat. Aplicada 9 (2001) 69-112.     pdf
 
Matemáticas, ciencia y tecnología: una relación profunda y duradera (author: J. L. V.), (Spanish) Encuentros Interdisciplinares, no. 11, vol. IV (2002), 22-38. Portuguese version : Matemática, Ciência e Tecnologia: uma relaçao profunda e duradoura. Boletim da Sociedade Portuguesa de Matemática, 49 (2003), 19-70.     pdf
 
Miguel de Guzmán, maestro de matemáticos (author: J. L. V.), (Spanish) SUMA 46 (2004), pp. 17-21.     pdf
The Navier-Stokes equation: a physico-mathematical challenge for the XXIst century (author: J. L. V.), Millennium problems, (Spanish) 31–56, Monogr. Real Acad. Ci. Exact. Fís.-Quím. Nat. Zaragoza, 26 , Zaragoza, 2004.     pdf
 
Volumen dedicado a las Matemáticas Interdisciplinares el siglo XXI (authors: A. Quirós, J. L. V.), (Spanish) Revista Encuentros Multidisciplinares, vol. VIII, no 23, 2006.     pdf
 
Sin matemáticas no hay paraíso. Saber de números y fórmulas está de moda (author: J. L. V.), (Spanish) artículo publicado en el diario La Nueva España de Oviedo, sección Opinión, 4 Feb. 2009.     pdf
 
Article in ``Recalling James Serrin'' (author: J. L. V.), (Howard Levine and Hans Weinberger, Coordinating Editors) Notices of the AMS 60, no. 6 (2013), 709-710.     pdf
 
Las Matemáticas y sus aplicaciones, ayer y hoy. Retos del futuro (author: J. L. V.), (Spanish) Revista Encuentros Multidisciplinares, no. 45, Sept-Dic. 2013. Pp. 2-13.     pdf