The Influence of Domain Shape in Reaction-diffusion Equations

Abstract

The broad theme of this talk will be the interplay between diffusion and geometry of domains in the framework of reaction-diffusion equations of bistable type. These equations arise in a variety of contexts, in biology, ecology, phase transitions, etc. Bistable equations describe situations when two stable states compete with each other. Here, we are interested in understanding how the geometry of the domain interacts with the dynamical properties. I will first present classical results related to convexity. I will then discuss general properties for propagation of invasion waves. These questions involve new qualitative results for some non-linear elliptic and parabolic partial differential equations. I will also discuss recent results about uniqueness/non uniqueness of stationary solutions in unbounded domains in which the geometry of the domain plays a surprisingly strong role.

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 (EHESS, 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.

For Attendees' Attention

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