Emeritus Professor
formerly Full Professor of Applied Mathematics
Department of Mathematics
Campus de Cantoblanco, 28049 Madrid
juanluis.vazquez at

Exactas, Físicas y Naturales

Juan Luis Vázquez Suárez  Version in Spanish

List of Mathematical Publications 1980-1999   2000-2016 My books
Mathematical and expository writing Courses, books and notes

Research Interests

Differential equations, especially nonlinear partial differential equations, and their applications to Physics and Engineering.   Diffusion equations, filtration equations in porous media.   Mathematical study of processes with free boundaries and change of phase.   Special solutions, selfsimilarity and asymptotical methods.   Blow-up problems and singularities.  Nonlocal diffusion and fractional Laplacian operators.   PDEs and Riemannian Geometry.   Entropy methods and functional inequalities.

Main news 2017

* 2016-17 Warwick EPSRC Symposium:   "Non-local Equations and Fractional Diffusion".   Organized by José A. Carrillo (Imperial College, London), José L. Rodrigo (Univ. of Warwick), Juan Luis Vázquez (UAM - Madrid); held at Univ. of Warwick, 22 to 26 May 2017.   [Un. of Warwick webpage announcement] .

* International Congress:   "Nonlinear diffusion and free boundary problems. A conference on the occasion of the 70th anniversary of Juan Luis Vázquez".   Organized by Fernando Quirós and Matteo Bonforte, professors at Dpto de Matemáticas of Univ. Autónoma de Madrid, and held in the same university from 17 to 20 May 2017.   [web page of the congress] .   [congress poster].   Main recent research activities

* Scuola Estiva di Fisica Matematica Ravello 2016 XLI Summer School on Mathematical Physics, in Ravello (Italy), Sept, 12-17, 2016. Organizers: GNFM. Speakers: B. Ermentrout, A. C. Liverani, C. Negulescu, L. Preziosi, V. Romano, S. Terracini, G. Toscani, and J. L. Vázquez. * CIME Summer Course 2016 Nonlocal and Nonlinear Diffusions and Interactions: New Methods and Directions in Cetraro (Italy), July, 4-8, 2016. Organizers: M. Bonforte and G. Grillo. Speakers: J. A. Carrillo, A. Figalli, R. Mingione, M. del Pino, and J. L. Vázquez. Course Lectures to appear in Springer Lecture Notes * Summer Course UIMP 2015 Frontiers of Mathematics and Applications IV in Santander (Spain), July 20-24, 2015. Main speakers: P. Daskalopoulos, S. Terracini, J. L. Vázquez, and L. Vega. * Semester Programme at the Newton Institute Free Boundary Problems in Cambridge, UK, 6 January to 4 July, 2014. Co-organizer with Henrik Shahgholian (Stockholm) and Gui-Qiang Chen (Oxford). * Summer Course UIMP 2012 Frontiers of Mathematics and Applications in Santander (Spain), August 13-17, 2012. Organizers: M. Bonforte and J. L. Vázquez. Main speakers: X. Cabré (Barcelona), L. A. Caffarelli (Texas, USA), L. C. Evans (Berkeley, USA). * Corso Estivo di Matematica Cortona 2012 Trends in Nonlinear Elliptic and Parabolic Equations Scuola Matematica Interuniversitaria held in Cortona (Italy), July 16-28, 2012. Professors: S. Terracini and J. L. Vázquez. * Workshop Centro Ennio De Giorgi Recent Trends in Nonlinear Diffusion in Pisa (Italy), 2-6 July 2012. Main organizer. * Summer School Centro Ennio De Giorgi Topics in Nonlinear Parabolic Equations in Pisa (Italy), 24-29 June 2012. Main organizer. * MSRI Semester Programme Free Boundary Problems, Theory and Applications in Berkeley, California, January to May 2011. Invited fellow. * Summer Course UIMP 2011 Frontiers of Mathematics and Applications in Santander (Spain), August 15-19, 2011. Organizers: M. Bonforte and J. L. Vázquez. * Workshop Spain-Italy Nonlinear PDEs and Functional Inequalities in Madrid (Spain) September 19-20, 2011. Organizers: M. Bonforte and J. L. Vázquez.


Institutional and personal news


Double Special Volume of the Journal Nonlinear Analysis Theory Methods & Applications, "Nonlinear Partial Differential Equations", in honor of Juan Luis Vázquez for his 70th birthday

Volume 1          Volume 2


*  Fellow of the American Mathematical Society, since 2012 AMS

*   Member of the Spanish Royal Academy of Science/ Real Academia de Ciencias Exactas, Físicas y Naturales RAC , 2013.     Discurso de Ingreso   (Acceptance address),   26 March 2014.

*  Nominated Doctor Honoris Causa by Universidad de Oviedo.   Acceptance address, 16 October 2015.

*   Nominated Fellow of the European Academy of Sciences EURASC, November 2016.

  See more professional information in Spanish in "Árbol de las Matemáticas"

imagen de ICM2006 10 years ago
ICM 2006 International Congress of Mathematicians
Held in Madrid August 22-30, 2006
The great event of the international mathematical community
organized by the International Mathematical Union (IMU)
It occurs every 4 years. First ICM: Zurich, 1897.
A famous ICM: Paris 1900. See ICM Proceedings list

My article appeared in Proceedings of ICM 2006
"Perspectives in Nonlinear Diffusion. Between Analysis, Physics and Geometry"

The slides of my Plenary Talk at ICM 2006

The curious observer

* On the scientific spirit

Galileo Galilei, one of the founding fathers of the common house of science, who was a mathematician and an experimenter at the same time, wrote in favor of clarity in science in his dialogues, like “Dialogo sopra i due massimi sistemi del mondo”. This is to be remembered in the present times where mathematics is still flooded with abstruse theories expressed in impossible language.   According to Galileo, the wise scholar must be occupied above all with being understood,  d’altro più non si cura fuorché d’essere inteso.

Aristotle, one of the great minds of Antiquity and founder of the Lyceum, recommended: before teaching something, you should know it yourself.    Blog "La República de las Matemáticas" (in Spanish)  My Ph D students  Social occasions  Prize