2023 - Research.com Mathematics in Spain Leader Award
2022 - Research.com Mathematics in Spain Leader Award
2016 - Member of the European Academy of Sciences
2013 - Fellow of the American Mathematical Society
His main research concerns Mathematical analysis, Nonlinear system, Heat equation, Porous medium and Uniqueness. He combines subjects such as Inverse and Diffusion equation with his study of Mathematical analysis. His research in Nonlinear system intersects with topics in Semigroup, Elliptic curve, Algebra, Thermal diffusivity and Space.
His studies in Heat equation integrate themes in fields like Initial value problem, Simultaneous equations, Sign, Statistical physics and Independent equation. His Uniqueness research is multidisciplinary, incorporating elements of Mathematical proof, Combinatorics, Type, Symmetry in biology and Weak solution. His Bounded function research is multidisciplinary, incorporating perspectives in Nonlinear heat equation, Function space, Pure mathematics and Domain.
The scientist’s investigation covers issues in Mathematical analysis, Bounded function, Nonlinear system, Porous medium and Heat equation. His Diffusion equation research extends to Mathematical analysis, which is thematically connected. His study in Bounded function is interdisciplinary in nature, drawing from both Pure mathematics, Mathematical physics, Dirichlet problem, Boundary value problem and Domain.
Juan Luis Vázquez has included themes like p-Laplacian and Laplace operator in his Pure mathematics study. The Domain study combines topics in areas such as Zero and Dirichlet boundary condition. His study on Nonlinear system also encompasses disciplines like
Mathematical analysis, Bounded function, Pure mathematics, Nonlinear system and Space are his primary areas of study. In his works, Juan Luis Vázquez performs multidisciplinary study on Mathematical analysis and Porous medium. His work carried out in the field of Bounded function brings together such families of science as Boundary value problem, Dirichlet conditions, Uniqueness, Domain and Laplace operator.
His Pure mathematics study combines topics in areas such as p-Laplacian and Scalar curvature. His studies deal with areas such as Order, Logarithm, Statistical physics, Exponential function and Degenerate energy levels as well as Nonlinear system. His Space study also includes
Juan Luis Vázquez mainly investigates Bounded function, Mathematical analysis, Pure mathematics, Domain and Nonlinear system. The concepts of his Bounded function study are interwoven with issues in Omega, Measure, Dirichlet conditions, Uniqueness and Degenerate energy levels. Juan Luis Vázquez merges Mathematical analysis with Porous medium in his study.
His work deals with themes such as Smoothness and Laplace operator, which intersect with Pure mathematics. His Domain research is multidisciplinary, incorporating perspectives in Zero and Fractional Laplacian. He has researched Nonlinear system in several fields, including Dimension, Mathematical physics, Logarithmic scale, Fractional diffusion and Sigma.
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The Porous Medium Equation: Mathematical Theory
Juan Luis Vázquez.
A Strong Maximum Principle for some quasilinear elliptic equations
J. L. Vázquez.
Applied Mathematics and Optimization (1984)
An $L^1$ -theory of existence and uniqueness of solutions of nonlinear elliptic equations
Philippe Bénilan;Lucio Boccardo;Thierry Gallouët;Ron Gariepy.
Annali Della Scuola Normale Superiore Di Pisa-classe Di Scienze (1995)
The Porous Medium Equation
Juan Luis Vazquez.
Blow-up solutions of some nonlinear elliptic problems
Haim Brezis;Juan Luis Vázquez.
Revista Matematica Complutense (1997)
Smoothing and decay estimates for nonlinear diffusion equations : equations of porous medium type
Juan Luis Vázquez.
The problem of blow-up in nonlinear parabolic equations
Victor A. Galaktionov;Juan-Luis Vázquez.
Discrete and Continuous Dynamical Systems (2002)
The Hardy Inequality and the Asymptotic Behaviour of the Heat Equation with an Inverse-Square Potential
Juan Luis Vazquez;Enrike Zuazua.
Journal of Functional Analysis (2000)
Smoothing and Decay Estimates for Nonlinear Diffusion Equations
Juan Luis Vázquez.
Continuation of blowup solutions of nonlinear heat equations in several space dimensions
Victor A. Galaktionov;Juan L. Vazquez.
Communications on Pure and Applied Mathematics (1997)
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