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,  Comm. Partial Differential Equations 33 (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, 2006Preprint 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.Eqns2006
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 Vazque
z,  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.
Preprint
Postscript 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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