| 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). |
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