Quasi-variational solutions for scalar conservation laws with gradient constraint
Speaker:Prof. Jose Francisco Rodrigues
Professor
Centro de Matematica e Aplicacoes Fundamentais
Universidade de Lisboa
Date & Time:11 Mar 2011 (Friday) 16:00 - 17:00
Venue:J215
Organized by:Department of Mathematics

Abstract

We prove the existence of variational solutions for an evolution quasi-variational inequality with a first order quasilinear operator and a variable convex set which is characterized by a constraint on the absolute value of the gradient that depends on the solution itself. The only required assumption on the nonlinearity of this constraint is its continuity and positivity. The method relies on an appropriate parabolic regularization and suitable "a priori" estimates and allows us to obtain also the existence of stationary solutions, by studying the asymptotic behavior in time. This is joint work with Lisa Santos.

Biography

Professor of Mathematics at the University of Lisbon, Faculty of Sciences, he is director of the Centro Internacional de Matematica (CIM) since 2008 and member of the Lisbon Academy of Sciences (ACL). He works in Nonlinear Partial Differential Equations and their applications in Science and is the coordinator-Editor of the EMS journal "Interfaces and Free Boundaries", a journal he co-founded in 1999 in the sequence of directing the European Science Foundation Scientific Programme Mathematical Treatment of Free Boundary Problems. He was the recipient of the 1986 ACL prize in Mathematical Sciences and of the Gulbenkian Foundation prize for basic sciences in 2004. In 1990, being vice-president of the Portuguese Mathematical Society, he participated at the EMS foundational meeting. He was the president of the Portuguese National Committee of mathematicians from 2002-2010 and of their delegation to the International Mathematical Union.