Special Session 146: Nonlinear differential equations: control, delay, and boundary value problems

Shock wavefronts for parabolic equation with sign-changing diffusivity
Diego Berti
Univeristy of Turin
Italy
Co-Author(s):    
Abstract:
This talk focuses on a reaction-diffusion equation in a one-dimensional space, where the diffusion is positive-negative-positive and the reaction term is bistable and changes sign where the diffusivity is negative. In this setting, continuous wavefronts are not allowed. We prove the existence of a family of shock wavefronts with profiles that have a jump discontinuity. We further investigate the properties of these profiles and their propagation speeds. Moreover, we discuss the application of the results to a model describing the movement of a population composed of both isolated and grouped individuals. This is joint work with Andrea Corli (University of Ferrara) and Luisa Malaguti (University Modena and Reggio Emilia).