Front Propagation in Reaction-Diffusion Equations and the Domain Geometry

This BIMSA Colloquium lecture by Distinguished Professor Emeritus Hiroshi Matano explores the complex behavior of solution fronts in reaction-diffusion equations when obstacles are present. Discover how boundary geometry influences front propagation speed in infinite strips with bumpy boundaries, including homogenization limits when boundary bumps become increasingly fine. Learn about the fascinating mathematical questions that arise when examining whether solution fronts can pass through walls with multiple holes or become blocked. The presentation draws from Matano's collaborative research with Bendong Lou, Ken-ichi Nakamura, Ryunosuke Mori, Henri Berestycki, and Francois Hamel. Professor Matano, a recipient of the prestigious Spring Prize from the Mathematical Society of Japan and former ICM invited speaker, brings his extensive expertise in nonlinear parabolic equations, order-preserving dynamical systems, and the relationship between solution stability and domain geometry to this in-depth mathematical exploration.