SOME RESEARCH  PAPERS

 See section of Classic Oldies Papers 2009-2010    “Heat equation with dynamical boundary conditions of reactive--diffusive type”, Juan Luis Vázquez and Enzo Vitillaro. arXiv1001.3642v1 [math.AP] Math. Annalen, to appear.   “On the Laplace equation with dynamical boundary conditions of reactive-diffusive type”,  J. L. Vazquez, E. Vitillaro, JMAA, to appear. Preprint, june 2008 Pdf file    “Positivity, local smoothing, and Harnack inequalities for very fast diffusion equations.” Matteo Bonforte,  Juan Luis Vazquez. Advances in Mathematics 223 (2010) 52--578.   “Positivity, local smoothing, and Harnack inequalities for very fast diffusion equations.” Matteo Bonforte, Razvan Iagar, Juan Luis Vazquez. Preprint 16 Feb 2009; arXiv:0902.2750v1 [math.AP].   Advances in Mathematics, to appear.   “Special fast diffusion with slow asymptotics. Entropy method and flow on a Riemannian manifold" Matteo Bonforte, Gabriele Grillo, Juan Luis Vazquez. Arch. Rational Mech. Anal., to appear, Preprint 2008, arXiv  0805.4750v1 [math.AP]   “Long time behavior for the inhomogeneous PME in a medium with rapidly decaying density”. Shoshana Kamin, G. Reyes, J. L. Vázquez, DCDS-A Special Volume on Parabolic Problems 26, Number 2 (2010), pp. 521–549.   "Asymptotic analysis for the $p$-Laplacian Evolution Equation in an Exterior Domain. The low dimension case." Razvan Iagar, Juan Luis Vazquez. Preprint february 2008, to appear in Journal European Math. Soc.   Pdf file "Asymptotic analysis for the p-Laplacian Evolution Equation in an Exterior Domain (I)." Razvan Iagar, Juan Luis Vazquez. Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire, to appear. Pdf file "Long time behavior for the inhomogeneous PME in a medium with slowly decaying density," G. Reyes, J. L. Vázquez,  Communications on Pure & Applied Analysis, CPAA, Pdf file   “Convection-diffusion elliptic problems with Neumann boundary conditions” Jerome Droniou, Juan Luis Vázquez, Calc. Var. PDE,  24 (2009),  413-434. "Asymptotics of the fast diffusion equation via entropy estimates" Adrien Blanchet, Matteo Bonforte, Jean Dolbeault, Gabriele Grillo, Juan Luis Vazquez. Arch. Rational Mech. Anal. 191 (2009) 347-385  pdf file in arXiv server    “Local Aronson–Bénilan estimates and entropy formulae for porous medium and fast diffusion equations on manifolds”,  Peng Lu, Lei N, Juan-Luis Vázquez, Cédric Villani,   J. Math. Pures Appl. 91 (2009) 1–19, arXiv:0806.1142.   “Measure-valued solutions and the phenomenon of blow-down in logarithmic difusión”, Juan Luis Vázquez,  J. Math. Anal. Appl. 352 (2009) 515–547. 2008 "Wave equation with second-order non-standard dynamical boundary conditions",  J. L. Vázquez, E. Vitillaro, Mathematical Models and Methods in Applied Sciences (M3AS), Vol. 18, No. 12 (2008) 2019–2054. Pdf file “Parabolic approach to Nonlinear  Elliptic Eigenvalue Problems”, Ki-Ahm Lee,  Juan Luis Vazquez, Advances in Mathematics 219 (2008) 2006–2028. Pdf file   "The inhomogeneous PME in several space  dimensions. Existence and uniqueness of finite energy solutions", G. Reyes, J. L. Vázquez,  Commun. Pure Appl. Anal. 7 (2008), no. 6, 1275--1294. Pdf file   “Heat equation with dynamical boundary conditions of reactive type”, J. L. Vázquez, Enzo Vitillaro,  (2008), no. 4-6, 561--612. "Fast Diffusion Flow on Manifolds of Nonpositive Curvature",  Matteo Bonforte, Gabriele Grillo, Juan Luis Vazquez, Journal of Evolution Equations 8 (2008), 99-128 Pdf file "Multiple Blowup for Nonlinear Heat Equations at Different Places and Different Times" N. Mizoguchi (Tokyo) and J.  L. Vázquez, Indiana Univ. Math J..  56, No. 6 (2007), 2859--2886 Pdf file "Radial equivalence for the two basic nonlinear degenerate diffusion equations",  Razvan Iagar, Ariel Sanchez, Juan Luis Vazquez. Journal de Mathématiques Pures Appliquées, vol. 89, no 1 (2008), 1--24.Pdf file 2007 "Localized non-diffusive  asymptotic   equations with gradient absorption" Philippe Laurençot, Juan Luis Vazquez. J. Dynam. Differential Equations  19  (2007),  no. 4,  985--1005. Pdf file "Evolution  of point masses by planar logarithmic diffusion", J. L. Vázquez, DCDS A 19, 1 (September 2007), 1--35.,.   Pdf file (corrected)     solutions of the logarithmic diffusion equation are constructed when the     initial data contain point masses. Contrary to standard  experience in     nonlinear diffusion,  these masses decay into the medium at a fixed     rate given by the magical number, 4 pi. "Asymptotic behaviour of the porous media equation in domains with holes", Cristina Brandle, Fernando Quirós and Juan Luis Vázquez, Interfaces and Free Boundaries Volume 9, Issue 2 (2007), pp. 211–-232., Pdf file "Porous medium flow in a tube. Travelling waves and KPP behaviour", J. L. Vázquez, Comm. Contemporary Math, vol. 9, issue 5 (2007) 731--751.  Pdf file     the travelling wave is constructed and is speed shown to be unique "Asymptotic Complexity in Filtration Equations"  J. A. Carrillo, J. L. Vázquez, Journal Evolution Equations,  7, no 3 (2007), 471--495. Pdf file     we show that the renormalized asymptotic pattern constructed     by means of the Toscani map can be oscillating, even chaotic "Fine Asymptotics near Extinction and Elliptic Harnack Inequalities for the Fast Diffusion Equation",  Matteo Bonforte, Juan Luis Vazquez, Preprint, april  2006. Pdf file "Global Positivity Estimates and Harnack Inequalities for the Fast Diffusion Equation",    Matteo Bonforte and J. L. Vázquez,    Journal of Functional Analysis 240 (2006), 399--428. Pdf file       two papers on the qualitative theory of fast diffusion flows "Hardy-Poincaré inequalities and applications to nonlinear diffusions", Adrien Blanchet, Matteo Bonforte, Jean Dolbeault, Gabriele Grillo, Juan Luis Vázquez, Note CRAS Paris  2007. Pdf file "Viscosity solutions for elliptic-parabolic problems", Paola Mannucci, J. L. Vazquez,  NoDEA, Volume 14, Numbers 1-2 (2007), 75--90. Pdf file "Heat equation with dynamical boundary conditions of of locally reactive type",  J. L. Vázquez, E. Vitillaro,  .Semigroup Forum Vol. 74 (2007) 1—40. Pdf file 2006 "Heat equation with dynamical boundary conditions of reactive type",  J. L. Vázquez, E. Vitillaro, CPDE, 2006.  Preprint UAM, oct 2004. Pdf file "Classification of blow-up with nonlinear diffusion and localized reaction", Raúl Ferreira, Arturo de Pablo, Juan Luis Vázquez, J.Diff.Eqns,  2006 Pdf file "The Cauchy problem for the inhomogeneous porous medium equation",   Guillermo Reyes  and J. L. Vázquez,  Networks and Heterogeneous Media,  2006. Pdf file "Extended solutions for general Fast Diffusion Equations  with optimal measure data",   E. Chasseigne,  J. L. Vázquez, Advances Diff. Eqns.,   2006 . Pdf file "A weighted symmetrization for nonlinear elliptic and parabolic equations in inhomogeneous media", Guillermo Reyes and Juan Luis Vázquez. Preprint, july 2005. J Eur Math Soc,    Pdf file      We establish  symmetrization tehcniques for some non-divergence     operators appearing in flows in inhomogeneous media "Lack of collision in a simplified  $1-d$ model for fluid-solid interaction",  Juan Luis Vázquez and Enrique Zuazua, Mathematical Models and Methods in Applied Sciences Vol. 16, No. 5 (2006) 637-678.. Pdf file    We show that no collsions are admiited in a model for the interaction of solid    masses in a Burgers fluid "Dirichlet boundary conditions can prevent blow-up  in reaction-diffusion equations and systems",  M. Fila, H. Ninomiya, J.L. Vazquez,  DCDS 14, Number 1, (2006), 63--74. Pdf file   Reaction-diffusion  equations are exhibited where   general nonnegative initial  data blow up in finite time   in free space,  but they will never do so if zero boundary conditions   are imposed. "Stabilization towards a singular   steady state with gradient blow-up    for a diffusion-convection problem", Ph. Souplet, J.L. Vazquez  DCDS,  14, Number 1, (2006), 221--234. Pdf file 2005 "Failure of the Strong Maximum Principle in Nonlinear  Diffusion".  Existence of Needles", J. L. Vazquez,  Comm. Partial Diff. Eqns., 30, no 9 (2005), 1263--1303. Pdf file   where it is explained that some nonlinear heat equations break the strong   maximum principle in strange forms (needles) and bounded solutions   need not be continuous "The Porous Medium Equation.  New contractivity results" Juan Luis Vázquez. Progress in Nonlinear Differential Equations and Their Applications, {\bf 63} (205)  (Volume in honor of H. Brezis, Proceedings of Gaeta Congress, June 2004), pp. 433--451  Pdf file "Viscosity solutions for quasilinear degenerate parabolic equations of porous medium type", C. Brandle, J. L. Vazquez,  Indiana University Mathematics Journal,  54 No. 3 (2005), 817–860.to appear. Pdf file "The diffusive limit for Carleman-type kinetic models", Francesco Salvarani, J. L. Vazquez,  Nonlinearity, 18  (2005), 1223--1248. Pdf file "Singular free  boundary problem from image processing",  Anna Lisa Amadori and  Juan Luis Vazquez,  M3AS  Mathematical Models and Methods in the Applied Sciences, 15, No. 5 (May 2005), 689--716. Pdf file "Symmetrization and Mass Comparison for Degenerate Nonlinear Parabolic and  related Elliptic Equations", Juan Luis Vazquez,  Advanced Nonlinear Studies,  5 (2005), 87--131. Pdf file 2004 - "Darcy's Law and the theory of shrinking solutions of  fast diffusion equations,  Juan  Luis Vazquez,  Preprint 2002. SIAM J. Math Anal. 35, no 4 (2004), 1005--1028. .  Postscript file - "Thermal avalanche  for blowing-up solutions of semilinear heat equations'',  F. Quirós,  J. Rossi and J. L. Vazquez, Preprint nov. 2002.  Comm. Pure and Applied Mathematics,  57 (2004), no. 1, 59--98.  Postscript file - "Nonlinear Diffusion and Image Contour Enhancement'', G. I. Barenblatt (University of California at Berkeley) and J. L. Vazquez, Preprint febr 2003, Interfaces and Free Boundaries, 6 (2004), 31-54.  Postscript file 2003 - "Large time behaviour for a simplified 1d model of fluid-solid interaction",  Juan  L. Vázquez and  Enrike Zuazua, Preprint UCM 2001. Comm. Partial Differential Equations  28 (2003), no. 5-6,  1023--1056.  Postscript file - "Fine asymptotics for fast diffusion equations",  José Antonio Carrillo and  J. L. Vázquez,  Preprint UAM 2002. Comm. Partial Differential Equations  28 (2003), no. 5-6,  1023--1056 Postscript file    Pdf  file  -"The pressure equation in the Fast Diffusion range", E. Chasseigne and  J. L. Vazquez, Preprint Univ. Texas 2001. Rev. Mat. Iberoam. 19, 3 (2003), 873-917.  Postscript file - "Geometrical properties of solutions of the porous medium equation for large times",  K. A. Lee and J. Luis Vazquez,  TICAM  Report, Univ. Texas,  2001. Indiana Univ. Math. J. 52 (2003), no. 4, 991--1016.  Postscript file - "Intermediate asymptotics for  inhomogeneous nonlinear heat conduction", V.A. Galaktionov, S. Kamin, R. Kersner and J. L. Vazquez, Preprint may 2002. Article appeared in  volume in honor of Prof. O. A. Oleinik, Trudy Seminara imeni I. G. Petrovskogo, Izd. Moskovskogo Univ., 2003. Pp. 61--92. Postscript file - "The Nonlinearly Damped Oscillator",  Juan Luis Vazquez, Preprint, may 2002. ESAIM Control Optim. Calc. Var. 9 (2003), 231--246.   Postscript file  pdf file 2002 - "Complete blow-up and thermal avalanche for  heat equations with nonlinear boundary conditions'', F. Quirós,  J. Rossi and J. L. Vazquez,  Comm. PDE, 27 (1 and 2) (2002), 395-424.  Preprint Postscript file - "Ignition and propagation in an integro-differential model for spherical flames", Roquejoffre, Jean-Michel and Vázquez, Juan Luis, Discrete Contin. Dyn.  Syst. Ser. B 2 (2002), no. 3, 379--387. Preprint Postscript file - "Complexity of large time behaviour of evolution equations with bounded data",  Juan  L. Vázquez and E. Zuazua,  Chinese Annals of Mathematics,  23, 2, ser. B (2002), 293-310. Special issue in honor of J.L. Lions, Preprint Postscript file - "Obstructions to existence in fast-diffusion equations",  Ana Rodríguez and Juan L. Vazquez, JDE,  184 (2002), 348-385. PreprintPostscript  file   - "Uniqueness of Asymptotic Profiles for an Extinction Problem", R. Ferreira, V. A. Galaktionov and J. L. Vazquez,  Nonlinear Analysis, 50, no 4 (August 2002), 495-507. PreprintPostscript file - "Theory  of extended solutions for Fast Diffusion Equations in Optimal Classes of Data. Radiation from Singularities", E. Chasseigne and J. Luis Vazquez,   Archive Rat. Mech. Anal. 164 (2002), 133-187.  Postscript file 2001 -  "Extinction behaviour for fast diffusion equations with absorption",  R. Ferreira and Juan L. Vazquez, Nonlinear Anal . TMA 43 (2001), no. 8, Ser. A: Theory Methods, 943--985,  Preprint Postscript file - "Uniqueness of solution to a free boundary problem from combustion'',   C. Lederman, J. L. Vazquez and N. Wolanski ,  Trans. Amer. Math. Soc. 353 (2001), no. 2, 655--692,  Preprint  Postscript file 2000 -"Asymptotics of the fast-diffusion equation with critical exponent",  V.A. Galaktionov, L. A. Peletier and J. L. Vazquez,  SIAM J. Math. Anal.,  31, 5 (2000),  1157-1174.  Preprint Postscript file - "The Hardy inequality and the asymptotic behaviour of the heat equation with an inverse square potential", J. L. Vazquez and E. Zuazua,  J. Funct. Anal.  173 (2000), 103-153. Preprint Postscript file - "Quenching for a  one-dimensional fully-nonlinear parabolic equation in detonation theory."  Victor A. Galaktionov (Bath, UK) , Stephane Gerbi (Univ. Savoie, France), and Juan L. Vazquez, SIAM J. Appl. Math.   61 (2000),   no. 4, 1253--1285,  Preprint Postscript file - "Behaviour of interfaces in a diffusion-absorption equation with critical exponents'',  V.A. Galatkionov, S. I. Shmarev and J. L. Vazquez,  Interfaces Free Bound. 2 (2000),  no. 4, 425--448, Preprint Postscript file    Some "CLASSIC OLDIES" "Asymptotic behaviour and propagation properties of the one-dimensional  flow of gas in a porous medium," . Trans. Amer. Math. Soc. 277 (1983), no. 2, 507--527. MR0694373 (84h:35014)  Pdf file

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