Juan Luis Vázquez

Juan Luis Vázquez Suárez (cited as Juan Luis Vázquez ; born July 26, 1946 in Oviedo ) is a Spanish applied mathematician.

life and work

Vázquez studied from 1964 to 1969 at the Escuela Técnica Superior de Ingenieros de Telecomunicación (ETSIT) in Madrid and graduated as a telecommunications engineer . He then studied mathematics at the Universidad Complutense de Madrid , where he received his doctorate from Haïm Brezis in 1979 ( Existencia, unicidad y propiedades de las soluciones de algunas ecuaciones en derivadas parciales semilineales , existence, uniqueness and properties of some semilinear partial differential equations). He has been Professor of Applied Mathematics at the Universidad Autónoma de Madrid since 1986 .

Vázquez deals with the solution of partial differential equations (PDE), especially non-linear heat conduction equations (PDE of the parabolic type) and flows in porous media ( porous media equation , with applications in the petroleum industry).

In 2006 he gave a plenary lecture at the ICM in Madrid ( Perspectives in Nonlinear Diffusion: Between Analysis, Physics, and Geometry ). In 2003 he received the Premio Nacional de Investigación Julio Rey Pastor. He is a fellow of the American Mathematical Society .

From 1996 to 1998 he was President of the Spanish Society for Applied Mathematics (Sociedad Española de Matemática Aplicada, SEMA).

Fonts (selection)

Books

• The porous medium equation. Mathematical Theory . Clarendon, Oxford 2007, ISBN 978-0-19-856903-9 .
• Smoothing and Decay Estimates for Nonlinear Diffusion Equations. Equations of Porous Medium Type (Oxford lecture series in mathematics and its applications; Vol. 33). Oxford University Press, Oxford 2006, ISBN 0-19-920297-4 .
• A Stability Technique for Evolution Partial Differential Equations. A Dynamical Systems Approach (Progress in nonlinear differential equations and their applications; Vol. 56). Birkhäuser, Basel 2003, ISBN 3-7643-4146-7 (together with Viktor A. Galaktionov).
• Recent trends in partial differential equations (Contemporary Mathematics; Vol. 409). American Mathematical Society, Providence RI 2006, ISBN 0-8218-3891-1 (together with Xavier Cabré and José A. Carrillo).

Essays

• Thermal avalanche for blowup solutions of semilinear heat equations . In: Communications on Pure and Applied Mathematics , Vol. 57 (2004), Issue 1, pp. 59-98, ISSN  0010-3640 (together with Fernando Quirós and Julio D. Rossi).
• Geometrical properties of solutions of the porous medium equation for large times . In. Indiana University Mathematics Journal , Vol. 52 (2003), No. 4, pp. 991-1016, ISSN  0022-2518 (together with Ki-Ahm Lee).
• The Hardy inequality and the asymptotic behavior of the heat equation with an inverse-square potential . In: Journal of Functional Analysis , Vol. 173 (2000), Issue 1, pp. 103-153, ISSN  0022-1236 (together with Enrique Zuazua).
• Continuation of blowup solutions of nonlinear heat equations in several space dimensions . In: Communications on Pure and Applied Mathematics , Vol. 50 (1997), Issue 1, pp. 1-67, ISSN  0010-3640 (together with Viktor A. Galaktionov).
• Blow-up solutions of some non-linear elliptic problems . In: Rev. Mat. Univ. Complut. Madrid , Vol. 10 (1997), No. 2, pp. 443-469, (together with Haïm Brezis).
• An L1-theory of existence and uniqueness of solutions of nonlinear elliptic equations . In: Annali della Scuola Normale Superiore di Pisa, Classe di Scienze / Serie 4 , Vol. 22 (1995), Issue 2, pp. 241-273, ISSN  0391-173X (together with Philippe Benilan, Lucio Boccardo, Thierry Gallouët, Ron Gariepy and Michel Pierre).
• A free-boundary problem for the heat equation arising in flame propagation . In: Transactions of the American Mathematical Society , Vol. 347 (1995), Issue 2, pp. 411-441, ISSN  0002-9947 (together with Luis Caffarelli ).
• On the stability or instability of the singular solution of the semilinear heat equation with exponential reaction term . In: Archive for Rational Mechanics and Analysis , Vol. 129 (1995), Issue 3, pp. 201-224, ISSN  0003-9527 (together with Ireneo Peral).
• Nonexistence of solutions for nonlinear heat equations of fast diffusion type . In: Journal de Mathématiques Pures et Appliquées / Série 9 , Vol. 71 (1992), Issue 6, pp. 503-526, ISSN  0021-7824 .
• Asymptotic behavior of nonlinear parabolic equations with critical exponents. A dynamical systems approach . In: Journal of Functional Analysis , Vol. 100 (1991), Issue 2, pp. 435-462, ISSN  0022-1236 (together with Viktor A. Galaktionov).
• Eventual regularity and concavity for flows in one-dimensional porous media ${\displaystyle C^{\infty }}$ . In: Archive for Rational Mechanics and Analysis , Vol. 99 (1987), No. 4, pp. 329-348, ISSN  0003-9527 (together with Donald G. Aronson).
• A strong maximum principle for some quasilinear elliptic equations . In: Applied Mathematics & Optimization , Vol. 12 (1984), Issue 3, pp. 191-202, ISSN  0095-4616 .
• Asymptotic behavior and propagation properties of the one-dimensional flow of gas in a porous medium . In: Transactions of the American Mathematical Society , Vol. 277 (1983), No. 2, pp. 507-527, ISSN  0002-9947 .

Web links

• Homepage
• Juan Luis Vázquez in the Mathematics Genealogy Project (English)