Propagation in Reaction-Diffusion Equations with Obstacles: The Effect of Geometry

Abstract

This talk is about travelling fronts going through an array of obstacles for reaction-diffusion equations. The speaker will consider the setting of bistable type equations and periodic obstacles. He will show in general that the wave is either blocked or it completely invades the domain. This hinges on results related to a celebrated conjecture of DE GIORGI regarding stable solutions of elliptic equations in unbounded domains, a conjecture, which, in turn, is related to the theory of minimal surfaces. The speaker will then describe geometric conditions on the obstacles under which there is either blocking or propagation. The speaker will report on the joint work with F. HAMEL and H. MATANO and will also recall the earlier joint work with L. CAFFARELLI and L. NIRENBERG.

About the speaker

Prof. Henri Berestycki received his PhD from Université Pierre et Marie Curie in 1975, and was a CNRS researcher at the University of Paris VI before joining the University of Paris XIII as a Professor in 1983. He then returned to Université Pierre et Marie Curie as a Professor of Mathematics in 1988. In 2001, he moved to École des Hautes Études en Sciences Sociales (which became a constituent college of the federal PSL Research University later), where he is currently a Professor. He was appointed the Dean of Research in PSL Research University in 2015-2017.

Prof. Berestycki’s current research interests include the mathematical modelling of financial markets, mathematical models in biology and especially in ecology, and modelling in social sciences.

Prof. Berestycki received numerous awards including the Sophie Germain Prize of the French Academy of Sciences (2004); the Gay-Lussac Humboldt Prize of the Humboldt Foundation (2004); the French Legion of Honor (2010). He was selected as a Fellow of the American Mathematical Society and an International Honorary Member of the American Academy of Arts and Sciences in 2013.