Edit Profile (opens in new tab) Vazquez, Juan Luis Co-Author Distance Author ID: vazquez.juan-luis Published as: Vázquez, Juan Luis; Vazquez, Juan Luis; Vazquez, Juan L.; Vazquez, J. L.; Vázquez, J. L.; Vázquez, Juan-Luis; Vázquez, Juan L.; Vazquez, Juan-Luis; Vázquez Suárez, Juan Luis; Vasquez, Juan Luis; Vásquez, Juan Luis; Vazquez, Jean Luis more...less Further Spellings: Vazquez Suárez, Juan Luis Homepage: http://verso.mat.uam.es/~juanluis.vazquez/ External Links: MGP · Wikidata · ResearchGate · IdRef · theses.fr Documents Indexed: 318 Publications since 1979, including 3 Books and 9 Additional arXiv Preprints 3 Contributions as Editor · 1 Further Contribution Co-Authors: 130 Co-Authors with 261 Joint Publications 3,854 Co-Co-Authors all top 5 Co-Authors 60 single-authored 28 Galaktionov, Victor Aleksandrovich 21 Bonforte, Matteo 14 Quirós Gracián, Fernando 12 Gómez-Castro, David 12 Grillo, Gabriele 12 Kamin, Shoshana 11 Alonso Rodríguez, Ana 11 Carrillo de la Plata, José Antonio 11 de Pablo, Arturo 11 del Teso, Félix 11 Peletier, Lambertus Adrianus 8 Caffarelli, Luis Ángel 7 Stan, Diana 7 Wolanski, Noemi I. 7 Zuazua, Enrique 6 Aronson, Donald G. 6 Esteban, Juan Ramón 6 Lederman, Claudia B. 6 Reyes, Guillermo 6 Shmarev, Sergei I. 6 Volzone, Bruno 5 Ferreira, Raúl 5 Herrero, Miguel Ángel 5 Hulshof, Josephus 5 Iagar, Razvan Gabriel 5 Sire, Yannick 5 Véron, Laurent 5 Vitillaro, Enzo 4 Barenblatt, Grigory Isaakovich 4 Boccardo, Lucio 4 Chasseigne, Emmanuel 4 Chaves, Manuela 4 Fila, Marek 4 Lee, Ki-Ahm 4 Winkler, Michael 4 Yarur, Cecilia S. 3 Audrito, Alessandro 3 Chan, Hardy 3 Dolbeault, Jean 3 Endal, Jørgen 3 Escobedo Martínez, Miguel 3 Figalli, Alessio 3 Gallouët, Thierry 3 Lacey, Andrew A. 3 McLeod, John Bryce 3 Muratori, Matteo 3 Zographopoulos, Nikolaos B. 2 Bénilan, Philippe 2 Blanchet, Adrien 2 Brändle, Cristina 2 Díaz Díaz, Jesús Ildefonso 2 Feo, Filomena 2 Gil, Omar 2 Kersner, Robert 2 Laurençot, Philippe 2 Levine, Howard Allen 2 Mizoguchi, Noriko 2 Peral Alonso, Ireneo 2 Perthame, Benoît 2 Portilheiro, Manuel 2 Rossi, Julio Daniel 2 Salvarani, Francesco 2 Sánchez, Ariel 2 Segatti, Antonio 2 Soler, Juan S. 2 Walias, Magdalena 1 Abatangelo, Nicola 1 Álvarez, Gabriel 1 Amadori, Anna Lisa 1 Bernis, Francisco 1 Bertsch, Michiel 1 Brasco, Lorenzo 1 Brézis, Haïm 1 Cabré, Xavier 1 Chen, Gui-Qiang G. 1 Chorin, Alexandre Joel 1 Comparini, Elena 1 Conley, Elizabeth 1 Cortázar, Carmen 1 Daskalopoulos, Panagiota 1 Dold, James W. 1 Droniou, Jérôme 1 Elgueta, Manuel 1 Farina, Alberto 1 Friedman, Avner 1 Garcia-Azorero, Jesús 1 Gariepy, Ron 1 Gazzola, Filippo 1 Gerbi, Stéphane 1 Goldenfeld, Nigel 1 Huang, Yanghong 1 Huang, Yong 1 Ingerman, Eugene A. 1 Jakobsen, Espen Robstad 1 Kienzler, Clemens 1 King, John Robert 1 Koch, Herbert 1 Leoni, Giovanni 1 Liñán, Amable 1 Lions, Pierre-Louis ...and 32 more Co-Authors all top 5 Serials 16 Archive for Rational Mechanics and Analysis 16 Communications in Partial Differential Equations 14 Journal of Differential Equations 12 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 11 Journal de Mathématiques Pures et Appliquées. Neuvième Série 10 Calculus of Variations and Partial Differential Equations 9 Transactions of the American Mathematical Society 9 Comptes Rendus de l’Académie des Sciences. Série I 8 Discrete and Continuous Dynamical Systems 7 Indiana University Mathematics Journal 7 SIAM Journal on Mathematical Analysis 7 Advances in Differential Equations 6 Advances in Mathematics 6 European Journal of Applied Mathematics 6 Journal of Evolution Equations 5 Journal of Functional Analysis 5 Differential and Integral Equations 5 Interfaces and Free Boundaries 5 Journal of the European Mathematical Society (JEMS) 4 Communications on Pure and Applied Mathematics 4 Journal of Mathematical Analysis and Applications 4 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 4 Mathematische Annalen 4 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 4 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 4 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 4 Nonlinear Analysis. Theory, Methods & Applications 3 Manuscripta Mathematica 3 Revista Matemática Iberoamericana 3 Electronic Journal of Differential Equations (EJDE) 3 Advanced Nonlinear Studies 3 Communications on Pure and Applied Analysis 2 Annales de la Faculté des Sciences de Toulouse. Série V. Mathématiques 2 Chinese Annals of Mathematics. Series B 2 Asymptotic Analysis 2 Proceedings of the National Academy of Sciences of the United States of America 2 NoDEA. Nonlinear Differential Equations and Applications 2 Communications in Contemporary Mathematics 2 La Gaceta de la Real Sociedad Matemática Española 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Advances in Nonlinear Analysis 1 Applicable Analysis 1 Communications in Mathematical Physics 1 Israel Journal of Mathematics 1 Journal d’Analyse Mathématique 1 Journal of Mathematical Physics 1 Nonlinearity 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Applied Mathematics and Optimization 1 Collectanea Mathematica 1 Duke Mathematical Journal 1 Journal of the London Mathematical Society. Second Series 1 Journal für die Reine und Angewandte Mathematik 1 Le Matematiche 1 Monatshefte für Mathematik 1 Portugaliae Mathematica 1 Proceedings of the American Mathematical Society 1 Quarterly of Applied Mathematics 1 Revista de la Unión Matemática Argentina 1 Semigroup Forum 1 Soviet Mathematics. Doklady 1 Forum Mathematicum 1 Revista Matemática de la Universidad Complutense de Madrid 1 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 1 SIAM Journal on Applied Mathematics 1 Notices of the American Mathematical Society 1 Journal of Dynamics and Differential Equations 1 Journal of Nonlinear Science 1 Communications in Analysis and Geometry 1 Journal of Mathematical Sciences (New York) 1 St. Petersburg Mathematical Journal 1 European Mathematical Society Newsletter 1 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 1 Fractional Calculus & Applied Analysis 1 Discrete and Continuous Dynamical Systems. Series B 1 Milan Journal of Mathematics 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 1 Boundary Value Problems 1 Complex Variables and Elliptic Equations 1 Contemporary Mathematics 1 The IMA Volumes in Mathematics and its Applications 1 Lecture Notes in Mathematics 1 Oxford Lecture Series in Mathematics and its Applications 1 Pitman Research Notes in Mathematics Series 1 Networks and Heterogeneous Media 1 Discrete and Continuous Dynamical Systems. Series S 1 Analysis & PDE 1 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 1 Boletín de la Sociedad Española de Matemática Aplicada. S\(\vec{\text{e}}\)MA 1 Philosophical Transactions A. Royal Society of London 1 Progress in Nonlinear Differential Equations and Their Applications 1 Oxford Mathematical Monographs all top 5 Fields 305 Partial differential equations (35-XX) 73 Fluid mechanics (76-XX) 13 Classical thermodynamics, heat transfer (80-XX) 12 Real functions (26-XX) 7 Global analysis, analysis on manifolds (58-XX) 6 Operator theory (47-XX) 6 Mechanics of deformable solids (74-XX) 5 Ordinary differential equations (34-XX) 5 Functional analysis (46-XX) 5 Numerical analysis (65-XX) 4 History and biography (01-XX) 4 Differential geometry (53-XX) 4 Statistical mechanics, structure of matter (82-XX) 3 General and overarching topics; collections (00-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Integral equations (45-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 1 Potential theory (31-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Probability theory and stochastic processes (60-XX) 1 Computer science (68-XX) 1 Mechanics of particles and systems (70-XX) 1 Optics, electromagnetic theory (78-XX) 1 Relativity and gravitational theory (83-XX) 1 Geophysics (86-XX) 1 Biology and other natural sciences (92-XX) 1 Information and communication theory, circuits (94-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 278 Publications have been cited 8,362 times in 4,844 Documents Cited by ▼ Year ▼ A strong maximum principle for some quasilinear elliptic equations. Zbl 0561.35003 Vázquez, J. L. 648 1984 An \(L^ 1\)-theory of existence and uniqueness of solutions of nonlinear elliptic equations. Zbl 0866.35037 Bénilan, Philippe; Boccardo, Lucio; Gallouët, Thierry; Gariepy, Ron; Pierre, Michel; Vazquez, Juan Luis 509 1995 The porous medium equation. Mathematical theory. Zbl 1107.35003 Vázquez, Juan Luis 412 2007 Blow-up solutions of some nonlinear elliptic problems. Zbl 0894.35038 Brézis, Haïm; Vázquez, Juan Luis 322 1997 The Hardy inequality and the asymptotic behaviour of the heat equation with an inverse-square potential. Zbl 0953.35053 Vazquez, Juan Luis; Zuazua, Enrike 226 2000 Smoothing and decay estimates for nonlinear diffusion equations. Equations of porous medium type. Zbl 1113.35004 Vázquez, Juan Luis 197 2006 The problem of blow-up in nonlinear parabolic equations. Zbl 1010.35057 Galaktionov, Victor A.; Vázquez, Juan L. 168 2002 Continuation of blowup solutions of nonlinear heat equations in several space dimensions. Zbl 0874.35057 Galaktionov, Victor A.; Vazquez, Juan L. 158 1997 A fractional porous medium equation. Zbl 1208.26016 de Pablo, Arturo; Quirós, Fernando; Rodríguez, Ana; Vázquez, Juan Luis 125 2011 Nonlinear porous medium flow with fractional potential pressure. Zbl 1264.76105 Caffarelli, Luis; Vazquez, Juan Luis 124 2011 A general fractional porous medium equation. Zbl 1248.35220 De Pablo, Arturo; Quirós, Fernando; Rodríguez, Ana; Vázquez, Juan Luis 123 2012 Recent progress in the theory of nonlinear diffusion with fractional Laplacian operators. Zbl 1290.26010 Vázquez, Juan-Luis 119 2014 On the equation of turbulent filtration in one-dimensional porous media. Zbl 0613.76102 Esteban, Juan R.; Vazquez, Juan L. 116 1986 Existence, uniqueness and asymptotic behaviour for fractional porous medium equations on bounded domains. Zbl 1347.35129 Bonforte, Matteo; Sire, Yannick; Vázquez, Juan Luis 116 2015 Nonlinear diffusion with fractional Laplacian operators. Zbl 1248.35223 Vázquez, Juan Luis 97 2012 Fundamental solutions and asymptotic behaviour for the p-Laplacian equations. Zbl 0699.35158 Kamin, S.; Vázquez, J. L. 87 1988 Nonlinear elliptic equations in \(\mathbb{R}^ N\) without growth restrictions on the data. Zbl 0810.35021 Boccardo, Lucio; Gallouët, Thierry; Vazquez, Juan Luis 85 1993 The Hele-Shaw asymptotics for mechanical models of tumor growth. Zbl 1293.35347 Perthame, Benoît; Quirós, Fernando; Vázquez, Juan Luis 82 2014 Asymptotics of the fast diffusion equation via entropy estimates. Zbl 1178.35214 Blanchet, Adrien; Bonforte, Matteo; Dolbeault, Jean; Grillo, Gabriele; Vázquez, Juan Luis 79 2009 Asymptotic behaviour for the porous medium equation posed in the whole space. Zbl 1036.35108 Vázquez, Juan Luis 77 2003 Travelling waves and finite propagation in a reaction-diffusion equation. Zbl 0784.35045 de Pablo, Arturo; Vazquez, Juan Luis 76 1991 Quantitative local and global a priori estimates for fractional nonlinear diffusion equations. Zbl 1288.35127 Bonforte, Matteo; Vázquez, Juan Luis 70 2014 Lipschitz continuity of solutions and interfaces of the N-dimensional porous medium equation. Zbl 0644.35058 Caffarelli, L. A.; Vazquez, J. L.; Wolanski, N. I. 66 1987 A priori estimates for fractional nonlinear degenerate diffusion equations on bounded domains. Zbl 1334.35382 Bonforte, Matteo; Vázquez, Juan Luis 62 2015 Regularity of solutions of the fractional porous medium flow. Zbl 1292.35312 Caffarelli, Luis A.; Soria, Fernando; Vázquez, Juan Luis 60 2013 Asymptotic behaviour and source-type solutions for a diffusion-convection equation. Zbl 0807.35059 Escobedo, Miguel; Vazquez, Juan Luis; Zuazua, Enrike 59 1993 A free-boundary problem for the heat equation arising in flame propagation. Zbl 0814.35149 Caffarelli, Luis A.; Vázquez, Juan L. 58 1995 Optimal existence and uniqueness theory for the fractional heat equation. Zbl 1364.35416 Bonforte, Matteo; Sire, Yannick; Vázquez, Juan Luis 58 2017 The mathematical theories of diffusion: nonlinear and fractional diffusion. Zbl 1492.35151 Vázquez, Juan Luis 56 2017 Barenblatt solutions and asymptotic behaviour for a nonlinear fractional heat equation of porous medium type. Zbl 1297.35279 Vázquez, Juan Luis 56 2014 Homogeneous diffusion in \({\mathbb{R}}\) with power-like nonlinear diffusivity. Zbl 0683.76073 Esteban, Juan R.; Vazquez, Juan L. 55 1988 On the stability or instability of the singular solution of the semilinear heat equation with exponential reaction term. Zbl 0821.35080 Peral, I.; Vazquez, J. L. 54 1995 Sharp rates of decay of solutions to the nonlinear fast diffusion equation via functional inequalities. Zbl 1256.35026 Bonforte, Matteo; Dolbeault, Jean; Grillo, Gabriele; Vázquez, Juan Luis 54 2010 Theory of extended solutions for fast-diffusion equations in optimal classes of data. Radiation from singularities. Zbl 1018.35048 Chasseigne, Emmanuel; Vazquez, Juan Luis 53 2002 A nonlinear heat equation with singular diffusivity. Zbl 0686.35066 Esteban, Juan R.; Rodríguez, Ana; Vázquez, Juan L. 52 1988 Asymptotic behaviour of a porous medium equation with fractional diffusion. Zbl 1211.35043 Caffarelli, Luis; Vázquez, Juan-Luis 52 2011 Positivity, local smoothing, and Harnack inequalities for very fast diffusion equations. Zbl 1184.35083 Bonforte, Matteo; Vázquez, Juan Luis 52 2010 Local Aronson-Bénilan estimates and entropy formulae for porous medium and fast diffusion equations on manifolds. Zbl 1156.58015 Lu, Peng; Ni, Lei; Vázquez, Juan-Luis; Villani, Cédric 51 2009 Nonexistence of solutions for nonlinear heat equations of fast-diffusion type. Zbl 0694.35088 Vazquez, Juan Luis 48 1992 Fine asymptotics for fast diffusion equations. Zbl 1036.35100 Carrillo, José A.; Vázquez, Juan L. 46 2003 On the propagation properties of a nonlinear degenerate parabolic equation. Zbl 0516.35041 Herrero, Miguel A.; Vazquez, Juan Luis 44 1982 Large-time behavior for a simplified 1D model of fluid-solid interaction. Zbl 1071.74017 Vázquez, Juan Luis; Zuazua, Enrique 44 2003 The Dirichlet problem for the fractional \(p\)-Laplacian evolution equation. Zbl 1348.35042 Vázquez, Juan Luis 43 2016 An introduction to the mathematical theory of the porous medium equation. Zbl 0765.76086 Vazquez, Jean Luis 41 1992 Large-time geometric properties of solutions of the evolution \(p\)-Laplacian equation. Zbl 1108.35097 Lee, Ki-Ahm; Petrosyan, Arshak; Vázquez, Juan Luis 40 2006 Global positivity estimates and Harnack inequalities for the fast diffusion equation. Zbl 1107.35063 Bonforte, Matteo; Vazquez, Juan Luis 40 2006 Asymptotic behaviour of nonlinear parabolic equations with critical exponents. A dynamical systems approach. Zbl 0755.35010 Galaktionov, Victor A.; Vazquez, Juan L. 40 1991 Asymptotic behaviour and propagation properties of the one-dimensional flow of gas in a porous medium. Zbl 0528.76096 Vazquez, Juan Luis 39 1983 Asymptotic behaviour and selfsimilarity for the three dimensional Vlasov-Poisson-Fokker-Planck system. Zbl 0873.35066 Carrillo, José A.; Soler, Juan; Vázquez, Juan Luis 39 1996 A diffusion-convection equation in several space dimensions. Zbl 0791.35059 Escobedo, Miguel; Vázquez, Juan Luis; Zuazua, Enrike 38 1993 Asymptotic behaviour of the solutions of a strongly nonlinear parabolic problem. Zbl 0498.35013 Herrero, M. A.; Vazquez, J. L. 37 1981 Classical solutions and higher regularity for nonlinear fractional diffusion equations. Zbl 1371.35331 Vázquez, Juan Luis; de Pablo, Arturo; Quirós, Fernando; Rodríguez, Ana 37 2017 Fast diffusion flow on manifolds of nonpositive curvature. Zbl 1139.35065 Bonforte, Matteo; Grillo, Gabriele; Vazquez, Juan Luis 36 2008 Heat equation with dynamical boundary conditions of reactive-diffusive type. Zbl 1213.35243 Vázquez, Juan Luis; Vitillaro, Enzo 36 2011 A mean field equation as limit of nonlinear diffusions with fractional Laplacian operators. Zbl 1290.35316 Serfaty, Sylvia; Vázquez, Juan Luis 36 2014 Necessary and sufficient conditions for complete blow-up and extinction for one-dimensional quasilinear heat equations. Zbl 0827.35055 Galaktionov, Victor A.; Vazquez, Juan L. 33 1995 Behaviour near extinction for the fast diffusion equation on bounded domains. Zbl 1241.35013 Bonforte, Matteo; Grillo, Gabriele; Vazquez, Juan Luis 33 2012 Rate of approach to a singular steady state in quasilinear reaction-diffusion equations. Zbl 0920.35080 Dold, James W.; Galaktionov, Victor A.; Lacey, Andrew A.; Vázquez, Juan Luis 33 1998 Hardy-Poincaré inequalities and applications to nonlinear diffusions. Zbl 1190.35119 Blanchet, Adrien; Bonforte, Matteo; Dolbeault, Jean; Grillo, Gabriele; Vázquez, Juan-Luis 32 2007 Entropy solutions for diffusion-convection equations with partial diffusivity. Zbl 0803.35084 Escobedo, M.; Vazquez, J. L.; Zuazua, Enrike 32 1994 Fundamental solution and long time behavior of the porous medium equation in hyperbolic space. Zbl 1327.35213 Vázquez, Juan Luis 32 2015 The Dirichlet problem for the porous medium equation in bounded domains. Asymptotic behavior. Zbl 1055.35024 Vazquez, Juan Luis 31 2004 Removable singularities of some strongly nonlinear elliptic equations. Zbl 0452.35034 Vázquez, Juan-Luis; Véron, Laurent 31 1980 Sharp global estimates for local and nonlocal porous medium-type equations in bounded domains. Zbl 1443.35067 Bonforte, Matteo; Figalli, Alessio; Vázquez, Juan Luis 31 2018 Classification of radial solutions to the Emden-Fowler equation on the hyperbolic space. Zbl 1262.35109 Bonforte, Matteo; Gazzola, Filippo; Grillo, Gabriele; Vázquez, Juan Luis 31 2013 The porous medium equation. New contractivity results. Zbl 1147.35050 Vázquez, J. L. 30 2005 The Fisher-KPP equation with nonlinear fractional diffusion. Zbl 1323.35088 Stan, Diana; Vázquez, Juan Luis 30 2014 Symmetrization for linear and nonlinear fractional parabolic equations of porous medium type. Zbl 1290.35317 Vázquez, Juan Luis; Volzone, Bruno 30 2014 The Cauchy problem for the inhomogeneous porous medium equation. Zbl 1124.35035 Reyes, Guillermo; Vazquez, Juan Luis 29 2006 Local smoothing effects, positivity, and Harnack inequalities for the fast \(p\)-Laplacian equation. Zbl 1198.35136 Bonforte, Matteo; Iagar, Razvan Gabriel; Vázquez, Juan Luis 29 2010 The one-dimensional nonlinear heat equation with absorption: Regularity of solutions and interfaces. Zbl 0633.35037 Herrero, Miguel A.; Vázquez, Juan L. 28 1987 Long time behavior for the inhomogeneous PME in a medium with rapidly decaying density. Zbl 1196.35052 Kamin, Shoshana; Reyes, Guillermo; Vázquez, Juan Luis 28 2010 On the Barenblatt equation of elasto-plastic filtration. Zbl 0737.73048 Kamin, S.; Peletier, L. A.; Vazquez, J. L. 28 1991 Geometrical properties of solutions of the porous medium equation for large times. Zbl 1080.35037 Lee, Ki-Ahm; Vázquez, J. L. 28 2003 Heat equation with dynamical boundary conditions of reactive type. Zbl 1168.35375 Vázquez, Juan Luis; Vitillaro, Enzo 28 2008 Domain of existence and blowup for the exponential reaction-diffusion equation. Zbl 0928.35080 Vazquez, Juan Luis 27 1999 Long time behavior for the inhomogeneous PME in a medium with slowly decaying density. Zbl 1169.35313 Reyes, Guillermo; Vázquez, Juan-Luis 27 2009 Fractional nonlinear degenerate diffusion equations on bounded domains. I: Existence, uniqueness and upper bounds. Zbl 1328.35009 Bonforte, Matteo; Vázquez, Juan Luis 27 2016 On a semilinear equation in \({\mathbb{R}}^ 2\) involving bounded measures. Zbl 0536.35025 Vazquez, Juan L. 26 1983 Asymptotics of the fast-diffusion equation with critical exponent. Zbl 0954.35094 Galaktionov, Victor A.; Peletier, Lambertus A.; Vazquez, Juan L. 26 2000 Classification of blow-up with nonlinear diffusion and localized reaction. Zbl 1110.35034 Ferreira, Raúl; De Pablo, Arturo; Vazquez, Juan Luis 26 2006 The Poisson problem for the exterior derivative operator with Dirichlet boundary condition in nonsmooth domains. Zbl 1157.58007 Reyes, Guillermo; Vázquez, Juan-Luis 26 2008 Classification of singular solutions of a nonlinear heat equation. Zbl 0701.35083 Kamin, S.; Peletier, L. A.; Vazquez, J. L. 26 1989 Extinction for a quasilinear heat equation with absorption. I: Technique of intersection comparison. Zbl 0831.35073 Galaktionov, Victor A.; Vazquez, Juan L. 26 1994 The porous medium equation on Riemannian manifolds with negative curvature. the large-time behaviour. Zbl 1437.35428 Grillo, Gabriele; Muratori, Matteo; Vázquez, Juan Luis 26 2017 Special fast diffusion with slow asymptotics: Entropy method and flow on a Riemannian manifold. Zbl 1209.35069 Bonforte, Matteo; Grillo, Gabriele; Vázquez, Juan Luis 26 2010 Asymptotic behaviour of solutions of the porous medium equation with changing sign. Zbl 0755.35011 Kamin, Shoshana; Vazquez, Juan Luis 25 1991 An a priori interior estimate for the solutions of a non-linear problem representing weak diffusion. Zbl 0446.35018 Vazquez, Juan Luis 25 1981 Extinction for a quasilinear heat equation with absorption. II: A dynamical systems approach. Zbl 0831.35074 Galaktionov, Victor A.; Vazquez, Juan L. 25 1994 Radial equivalence for the two basic nonlinear degenerate diffusion equations. Zbl 1139.35067 Iagar, Razvan Gabriel; Sánchez, Ariel; Vázquez, Juan Luis 25 2008 The Fisher-KPP problem with doubly nonlinear diffusion. Zbl 1386.35197 Audrito, Alessandro; Vázquez, Juan Luis 25 2017 Lack of collision in a simplified 1D model for fluid-solid interaction. Zbl 1387.35634 Vázquez, Juan Luis; Zuazua, Enrique 24 2006 The interfaces of one-dimensional flows in porous media. Zbl 0524.35060 Vazquez, Juan L. 23 1984 Isolated singularities of some semilinear elliptic equations. Zbl 0549.35043 Vázquez, Juan Luis; Véron, Laurent 23 1985 Noncoercive convection-diffusion elliptic problems with Neumann boundary conditions. Zbl 1167.35342 Droniou, Jérôme; Vázquez, Juan-Luis 23 2009 A well posed problem in singular Fickian diffusion. Zbl 0695.76043 Rodríguez, Ana; Vázquez, Juan Luis 23 1990 The balance between strong reaction and slow diffusion. Zbl 0705.35072 de Pablo, Arturo; Vazquez, Juan Luis 23 1990 Blow-up for quasilinear heat equations described by means of nonlinear Hamilton-Jacobi equations. Zbl 0884.35014 Galaktionov, Victor A.; Vazquez, Juan L. 22 1996 Stabilization towards a singular steady state with gradient blow-up for a diffusion-convection problem. Zbl 1116.35070 Souplet, Philippe; Vázquez, Juan Luis 22 2006 Symmetrization and mass comparison for degenerate nonlinear parabolic and related elliptic equations. Zbl 1085.35083 Vázquez, Juan Luis 22 2005 Singular boundary behaviour and large solutions for fractional elliptic equations. Zbl 1521.35181 Abatangelo, Nicola; Gómez-Castro, David; Vázquez, Juan Luis 3 2023 Anisotropic fast diffusion equations. Zbl 1518.35186 Feo, Filomena; Vázquez, Juan Luis; Volzone, Bruno 2 2023 Evolution driven by the infinity fractional Laplacian. Zbl 1520.35161 del Teso, Félix; Endal, Jørgen; Jakobsen, Espen R.; Vázquez, Juan Luis 1 2023 A fast regularisation of a Newtonian vortex equation. Zbl 1510.35180 Carrillo, José A.; Gómez-Castro, David; Vázquez, Juan Luis 4 2022 Growing solutions of the fractional \(p\)-Laplacian equation in the fast diffusion range. Zbl 1476.35320 Vázquez, Juan Luis 3 2022 Vortex formation for a non-local interaction model with Newtonian repulsion and superlinear mobility. Zbl 1484.35283 Carrillo, J. A.; Gómez-Castro, D.; Vázquez, J. L. 3 2022 Infinite-time concentration in aggregation-diffusion equations with a given potential. Zbl 1481.35048 Carrillo, Jose A.; Gómez-Castro, David; Vázquez, Juan Luis 1 2022 Singular solutions for fractional parabolic boundary value problems. Zbl 1498.35567 Chan, Hardy; Gómez-Castro, David; Vázquez, Juan Luis 1 2022 Characterisation of homogeneous fractional Sobolev spaces. Zbl 1471.46030 Brasco, Lorenzo; Gómez-Castro, David; Vázquez, Juan Luis 22 2021 The fractional \(p\)-Laplacian evolution equation in \(\mathbb{R}^N\) in the sublinear case. Zbl 1471.35312 Vázquez, Juan Luis 14 2021 Anisotropic \(p\)-Laplacian evolution of fast diffusion type. Zbl 1472.35234 Feo, Filomena; Vázquez, Juan Luis; Volzone, Bruno 13 2021 The one-phase fractional Stefan problem. Zbl 1473.80010 del Teso, Félix; Endal, Jørgen; Vázquez, Juan Luis 11 2021 Three representations of the fractional \(p\)-Laplacian: semigroup, extension and Balakrishnan formulas. Zbl 1498.35570 del Teso, Félix; Gómez-Castro, David; Vázquez, Juan Luis 9 2021 Blow-up phenomena in nonlocal eigenvalue problems: when theories of \(L^1\) and \(L^2\) meet. Zbl 1458.35070 Chan, Hardy; Gómez-Castro, David; Vázquez, Juan Luis 7 2021 A simple proof of the generalized Leibniz rule on bounded Euclidean domains. Zbl 1486.35442 Nguyen, Quoc-Hung; Sire, Yannick; Vázquez, Juan-Luis 1 2021 The evolution fractional p-Laplacian equation in \(\mathbb{R}^N\). Fundamental solution and asymptotic behaviour. Zbl 1447.35205 Vázquez, J. L. 17 2020 On a fractional thin film equation. Zbl 1437.35429 Segatti, Antonio; Vázquez, Juan Luis 8 2020 Equivalence between radial solutions of different parabolic gradient-diffusion equations and applications. Zbl 1476.35130 Parviainen, Mikko; Vázquez, Juan Luis 8 2020 Estimates on translations and Taylor expansions in fractional Sobolev spaces. Zbl 1462.46038 del Teso, Félix; Gómez-Castro, David; Vázquez, Juan Luis 7 2020 On the two-phase fractional Stefan problem. Zbl 1434.80006 del Teso, Félix; Endal, Jørgen; Vázquez, Juan Luis 7 2020 Travelling wave behaviour arising in nonlinear diffusion problems posed in tubular domains. Zbl 1439.35257 Audrito, Alessandro; Vázquez, Juan Luis 3 2020 Existence of weak solutions for a general porous medium equation with nonlocal pressure. Zbl 1437.35430 Stan, Diana; del Teso, Félix; Vázquez, Juan Luis 15 2019 The fractional Schrödinger equation with singular potential and measure data. Zbl 1425.35212 Gómez-Castro, David; Vázquez, Juan Luis 10 2019 The porous medium equation on Riemannian manifolds with negative curvature: the superquadratic case. Zbl 1411.35261 Grillo, Gabriele; Muratori, Matteo; Vázquez, Juan Luis 9 2019 Sharp global estimates for local and nonlocal porous medium-type equations in bounded domains. Zbl 1443.35067 Bonforte, Matteo; Figalli, Alessio; Vázquez, Juan Luis 31 2018 The fractional Schrödinger equation with general nonnegative potentials. The weighted space approach. Zbl 1402.35093 Díaz, J. I.; Gómez-Castro, D.; Vázquez, J. L. 21 2018 Sharp boundary behaviour of solutions to semilinear nonlocal elliptic equations. Zbl 1392.35144 Bonforte, Matteo; Figalli, Alessio; Vázquez, Juan Luis 20 2018 Flatness implies smoothness for solutions of the porous medium equation. Zbl 1403.35065 Kienzler, Clemens; Koch, Herbert; Vázquez, Juan Luis 12 2018 Asymptotic behaviour for the fractional heat equation in the Euclidean space. Zbl 1388.35216 Vázquez, Juan Luis 10 2018 Porous medium equation with nonlocal pressure in a bounded domain. Zbl 1409.35224 Nguyen, Quoc-Hung; Vázquez, Juan Luis 9 2018 Porous medium equation with nonlocal pressure. Zbl 1406.35302 Stan, Diana; del Teso, Félix; Vázquez, Juan Luis 5 2018 Optimal existence and uniqueness theory for the fractional heat equation. Zbl 1364.35416 Bonforte, Matteo; Sire, Yannick; Vázquez, Juan Luis 58 2017 The mathematical theories of diffusion: nonlinear and fractional diffusion. Zbl 1492.35151 Vázquez, Juan Luis 56 2017 Classical solutions and higher regularity for nonlinear fractional diffusion equations. Zbl 1371.35331 Vázquez, Juan Luis; de Pablo, Arturo; Quirós, Fernando; Rodríguez, Ana 37 2017 The porous medium equation on Riemannian manifolds with negative curvature. the large-time behaviour. Zbl 1437.35428 Grillo, Gabriele; Muratori, Matteo; Vázquez, Juan Luis 26 2017 The Fisher-KPP problem with doubly nonlinear diffusion. Zbl 1386.35197 Audrito, Alessandro; Vázquez, Juan Luis 25 2017 The Fisher-KPP problem with doubly nonlinear “fast” diffusion. Zbl 1365.35065 Audrito, Alessandro; Vázquez, Juan Luis 16 2017 Symmetrization for fractional elliptic and parabolic equations and an isoperimetric application. Zbl 1515.35078 Sire, Yannick; Vázquez, Juan Luis; Volzone, Bruno 12 2017 Weak and smooth solutions for a fractional Yamabe flow: the case of general compact and locally conformally flat manifolds. Zbl 1379.35168 Daskalopoulos, Panagiota; Sire, Yannick; Vázquez, Juan-Luis 6 2017 Nonlocal and nonlinear diffusions and interactions: new methods and directions. Cetraro, Italy, July 4–8, 2016. Lecture notes given at the course. Zbl 1380.35001 3 2017 The Dirichlet problem for the fractional \(p\)-Laplacian evolution equation. Zbl 1348.35042 Vázquez, Juan Luis 43 2016 Fractional nonlinear degenerate diffusion equations on bounded domains. I: Existence, uniqueness and upper bounds. Zbl 1328.35009 Bonforte, Matteo; Vázquez, Juan Luis 27 2016 Finite and infinite speed of propagation for porous medium equations with nonlocal pressure. Zbl 1379.35253 Stan, Diana; del Teso, Félix; Vázquez, Juan Luis 19 2016 Regularity of solutions of the fractional porous medium flow with exponent \(1/2\). Zbl 1335.35273 Caffarelli, L.; Vázquez, J. L. 17 2016 Non-existence and instantaneous extinction of solutions for singular nonlinear fractional diffusion equations. Zbl 1357.35184 Bonforte, Matteo; Segatti, Antonio; Vázquez, Juan Luis 7 2016 Existence of maximal solutions for some very singular nonlinear fractional diffusion equations in 1D. Zbl 1360.35089 Vázquez, Juan Luis 5 2016 Existence, uniqueness and asymptotic behaviour for fractional porous medium equations on bounded domains. Zbl 1347.35129 Bonforte, Matteo; Sire, Yannick; Vázquez, Juan Luis 116 2015 A priori estimates for fractional nonlinear degenerate diffusion equations on bounded domains. Zbl 1334.35382 Bonforte, Matteo; Vázquez, Juan Luis 62 2015 Fundamental solution and long time behavior of the porous medium equation in hyperbolic space. Zbl 1327.35213 Vázquez, Juan Luis 32 2015 Optimal estimates for fractional fast diffusion equations. Zbl 1327.35417 Vázquez, Juan Luis; Volzone, Bruno 20 2015 Exponential convergence towards stationary states for the 1D porous medium equation with fractional pressure. Zbl 1307.35311 Carrillo, J. A.; Huang, Y.; Santos, M. C.; Vázquez, J. L. 17 2015 Transformations of self-similar solutions for porous medium equations of fractional type. Zbl 1383.35248 Stan, Diana; del Teso, Félix; Vázquez, Juan Luis 11 2015 Some free boundary problems involving non-local diffusion and aggregation. Zbl 1353.35320 Carrillo, José Antonio; Vázquez, Juan Luis 9 2015 The mesa problem for the fractional porous medium equation. Zbl 1327.35214 Vázquez, Juan Luis 4 2015 Recent progress in the theory of nonlinear diffusion with fractional Laplacian operators. Zbl 1290.26010 Vázquez, Juan-Luis 119 2014 The Hele-Shaw asymptotics for mechanical models of tumor growth. Zbl 1293.35347 Perthame, Benoît; Quirós, Fernando; Vázquez, Juan Luis 82 2014 Quantitative local and global a priori estimates for fractional nonlinear diffusion equations. Zbl 1288.35127 Bonforte, Matteo; Vázquez, Juan Luis 70 2014 Barenblatt solutions and asymptotic behaviour for a nonlinear fractional heat equation of porous medium type. Zbl 1297.35279 Vázquez, Juan Luis 56 2014 A mean field equation as limit of nonlinear diffusions with fractional Laplacian operators. Zbl 1290.35316 Serfaty, Sylvia; Vázquez, Juan Luis 36 2014 The Fisher-KPP equation with nonlinear fractional diffusion. Zbl 1323.35088 Stan, Diana; Vázquez, Juan Luis 30 2014 Symmetrization for linear and nonlinear fractional parabolic equations of porous medium type. Zbl 1290.35317 Vázquez, Juan Luis; Volzone, Bruno 30 2014 Finite and infinite speed of propagation for porous medium equations with fractional pressure. (Vitesse de propagation finie et infinie pour des équations du milieu poreux avec une pression fractionnaire.) Zbl 1284.35352 Stan, Diana; del Teso, Félix; Vázquez, Juan Luis 19 2014 Classical solutions for a logarithmic fractional diffusion equation. Zbl 1322.35167 de Pablo, Arturo; Quirós, Fernando; Rodríguez, Ana; Vázquez, Juan Luis 17 2014 Progress in the theory of nonlinear diffusion: asymptotics via entropy methods. Zbl 1327.35171 Vázquez, Juan Luis 1 2014 Regularity of solutions of the fractional porous medium flow. Zbl 1292.35312 Caffarelli, Luis A.; Soria, Fernando; Vázquez, Juan Luis 60 2013 Classification of radial solutions to the Emden-Fowler equation on the hyperbolic space. Zbl 1262.35109 Bonforte, Matteo; Gazzola, Filippo; Grillo, Gabriele; Vázquez, Juan Luis 31 2013 Asymptotic behaviour of the doubly nonlinear diffusion equation \(u_t=\Delta_pu^m\) on bounded domains. Zbl 1258.35130 Stan, Diana; Vázquez, Juan Luis 19 2013 Degenerate homogeneous parabolic equations associated with the infinity-Laplacian. Zbl 1262.35137 Portilheiro, Manuel; Vázquez, Juan Luis 12 2013 Hardy type inequalities and hidden energies. Zbl 1277.35017 Vázquez, Juan Luis; Zographopoulos, Nikolaos B. 5 2013 Functional aspects of the Hardy inequality: appearance of a hidden energy. Zbl 1364.35172 Vázquez, J. L.; Zographopoulos, N. B. 3 2013 A general fractional porous medium equation. Zbl 1248.35220 De Pablo, Arturo; Quirós, Fernando; Rodríguez, Ana; Vázquez, Juan Luis 123 2012 Nonlinear diffusion with fractional Laplacian operators. Zbl 1248.35223 Vázquez, Juan Luis 97 2012 Behaviour near extinction for the fast diffusion equation on bounded domains. Zbl 1241.35013 Bonforte, Matteo; Grillo, Gabriele; Vazquez, Juan Luis 33 2012 Rate of convergence to Barenblatt profiles for the fast diffusion equation. Zbl 1315.76032 Fila, Marek; Vázquez, Juan Luis; Winkler, Michael; Yanagida, Eiji 17 2012 Functional aspects of the Hardy inequality: appearance of a hidden energy. Zbl 1258.35008 Vázquez, Juan Luis; Zographopoulos, Nikolaos B. 11 2012 A porous medium equation involving the infinity-Laplacian viscosity solutions and asymptotic behavior. Zbl 1248.35113 Portilheiro, Manuel; Vázquez, Juan Luis 10 2012 Quantitative local bounds for subcritical semilinear elliptic equations. Zbl 1261.35028 Bonforte, Matteo; Grillo, Gabriele; Vazquez, Juan Luis 7 2012 Large-time geometrical properties of solutions of the Barenblatt equation of elasto-plastic filtration. Zbl 1267.35106 Huang, Yong; Vázquez, Juan L. 3 2012 A fractional porous medium equation. Zbl 1208.26016 de Pablo, Arturo; Quirós, Fernando; Rodríguez, Ana; Vázquez, Juan Luis 125 2011 Nonlinear porous medium flow with fractional potential pressure. Zbl 1264.76105 Caffarelli, Luis; Vazquez, Juan Luis 124 2011 Asymptotic behaviour of a porous medium equation with fractional diffusion. Zbl 1211.35043 Caffarelli, Luis; Vázquez, Juan-Luis 52 2011 Heat equation with dynamical boundary conditions of reactive-diffusive type. Zbl 1213.35243 Vázquez, Juan Luis; Vitillaro, Enzo 36 2011 The evolution of singularities in fast diffusion equations: infinite-time blow-down. Zbl 1233.35131 Vázquez, Juan Luis; Winkler, Michael 12 2011 Highly time-oscillating solutions for very fast diffusion equations. Zbl 1252.35168 Vázquez, Juan Luis; Winkler, Michael 12 2011 Multiple blow-up for a porous medium equation with reaction. Zbl 1233.35049 Mizoguchi, Noriko; Quirós, Fernando; Vázquez, Juan Luis 9 2011 A continuum of extinction rates for the fast diffusion equation. Zbl 1229.35124 Fila, Marek; Vázquez, Juan-Luis; Winkler, Michael 9 2011 Asymptotic behaviour of a nonlinear parabolic equation with gradient absorption and critical exponent. Zbl 1227.35064 Iagar, Razvan Gabriel; Laurençot, Philippe; Vázquez, Juan Luis 6 2011 Sharp rates of decay of solutions to the nonlinear fast diffusion equation via functional inequalities. Zbl 1256.35026 Bonforte, Matteo; Dolbeault, Jean; Grillo, Gabriele; Vázquez, Juan Luis 54 2010 Positivity, local smoothing, and Harnack inequalities for very fast diffusion equations. Zbl 1184.35083 Bonforte, Matteo; Vázquez, Juan Luis 52 2010 Local smoothing effects, positivity, and Harnack inequalities for the fast \(p\)-Laplacian equation. Zbl 1198.35136 Bonforte, Matteo; Iagar, Razvan Gabriel; Vázquez, Juan Luis 29 2010 Long time behavior for the inhomogeneous PME in a medium with rapidly decaying density. Zbl 1196.35052 Kamin, Shoshana; Reyes, Guillermo; Vázquez, Juan Luis 28 2010 Special fast diffusion with slow asymptotics: Entropy method and flow on a Riemannian manifold. Zbl 1209.35069 Bonforte, Matteo; Grillo, Gabriele; Vázquez, Juan Luis 26 2010 Anomalous large-time behaviour of the \(p\)-Laplacian flow in an exterior domain in low dimension. Zbl 1185.35021 Iagar, Razvan Gabriel; Vázquez, Juan L. 4 2010 Asymptotics of the fast diffusion equation via entropy estimates. Zbl 1178.35214 Blanchet, Adrien; Bonforte, Matteo; Dolbeault, Jean; Grillo, Gabriele; Vázquez, Juan Luis 79 2009 Local Aronson-Bénilan estimates and entropy formulae for porous medium and fast diffusion equations on manifolds. Zbl 1156.58015 Lu, Peng; Ni, Lei; Vázquez, Juan-Luis; Villani, Cédric 51 2009 Long time behavior for the inhomogeneous PME in a medium with slowly decaying density. Zbl 1169.35313 Reyes, Guillermo; Vázquez, Juan-Luis 27 2009 Noncoercive convection-diffusion elliptic problems with Neumann boundary conditions. Zbl 1167.35342 Droniou, Jérôme; Vázquez, Juan-Luis 23 2009 On the Laplace equation with dynamical boundary conditions of reactive-diffusive type. Zbl 1167.35019 Vázquez, Juan Luis; Vitillaro, Enzo 15 2009 Measure-valued solutions and the phenomenon of blow-down in logarithmic diffusion. Zbl 1197.35153 Vázquez, Juan Luis 8 2009 Asymptotic analysis of the \(p\)-Laplacian flow in an exterior domain. Zbl 1178.35070 Iagar, Razvan Gabriel; Vázquez, Juan Luis 7 2009 ...and 178 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 4,373 Authors 152 Vazquez, Juan Luis 103 Papageorgiou, Nikolaos S. 47 Carrillo de la Plata, José Antonio 46 Boccardo, Lucio 40 Galaktionov, Victor Aleksandrovich 39 Yin, Jingxue 34 Dolbeault, Jean 34 Iagar, Razvan Gabriel 32 Bonforte, Matteo 32 Díaz Díaz, Jesús Ildefonso 31 Grillo, Gabriele 31 Zhan, Huashui 30 Porzio, Maria Michaela 29 Véron, Laurent 28 Orsina, Luigi 28 Rossi, Julio Daniel 27 Quirós Gracián, Fernando 27 Yang, Zuodong 26 Muratori, Matteo 26 Winkler, Michael 25 de Pablo, Arturo 25 Punzo, Fabio 25 Sánchez, Ariel 24 Fila, Marek 24 Mu, Chunlai 23 Redwane, Hicham 22 Gasiński, Leszek 22 King, John Robert 22 Sciunzi, Berardino 21 Ishige, Kazuhiro 21 Kim, Inwon Christina 21 Lam, Nguyen 21 Laurençot, Philippe 21 Perthame, Benoît 21 Zuazua, Enrique 20 Souplet, Philippe 19 Mercaldo, Anna 19 Rădulescu, Vicenţiu D. 19 Vespri, Vincenzo Riccardo 18 del Teso, Félix 18 Drábek, Pavel 18 Motreanu, Dumitru 18 Peral Alonso, Ireneo 17 Chlebicka, Iwona 17 Cianchi, Andrea 17 Hui, Kin Ming 17 Maz’ya, Vladimir Gilelevich 17 Volzone, Bruno 16 Berchio, Elvise 16 Mazón Ruiz, José M. 16 Segura de León, Sergio 16 Staicu, Vasile 16 Takáč, Peter 16 Toscani, Giuseppe 16 Wolanski, Noemi I. 16 Xiang, Mingqi 16 Yanagida, Eiji 16 Zhang, Zhengce 15 Abdellaoui, Boumediene 15 Andreu, Fuensanta 15 Chen, Huyuan 15 Ferreira, Raúl 15 Giacomoni, Jacques 15 Guo, Jong-Shenq 15 Hai, Dang Dinh 15 Sire, Yannick 15 Tedeev, Anatoliĭ Fedorovich 14 Gao, Wenjie 14 Tertikas, Achilles 13 Abdellaoui, Mohammed Amin 13 Azroul, Elhoussine 13 Bennouna, Jaouad 13 Caselles Costa, Vicent 13 Gómez-Castro, David 13 Han, Yuzhu 13 Kang, Dongsheng 13 Kim, Sunghoon 13 Kovalevsky, Alexander Albertovich 13 Petitta, Francesco 13 Tesei, Alberto 13 Wang, Liangwei 13 Zhang, Chao 12 Ding, Juntang 12 Kazakov, Aleksandr Leonidovich 12 Klimsiak, Tomasz 12 Lu, Guozhen 12 Ouaro, Stanislas 12 Porretta, Alessio 12 Pucci, Patrizia 12 Valdinoci, Enrico 11 Aberqi, Ahmed 11 Alonso Rodríguez, Ana 11 Benkirane, Abdelmoujib 11 Caffarelli, Luis Ángel 11 Cazacu, Cristian M. 11 Del Pino, Manuel A. 11 Du, Yihong 11 Fang, Zhongbo 11 Farina, Alberto 11 Ferrero, Alberto ...and 4,273 more Authors all top 5 Cited in 464 Serials 389 Nonlinear Analysis. 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