Traveling waves for unbalanced bistable equations with density dependent diffusion

Date

2021-09-14

Authors

Drabek, Pavel
Zahradnikova, Michaela

Journal Title

Journal ISSN

Volume Title

Publisher

Texas State University, Department of Mathematics

Abstract

We study the existence and qualitative properties of traveling wave solutions for the unbalanced bistable reaction-diffusion equation with a rather general density dependent diffusion coefficient. In particular, it allows for singularities and/or degenerations as well as discontinuities of the first kind at a finite number of points. The reaction term vanishes at equilibria and it is a continuous, possibly non-Lipschitz function. We prove the existence of a unique speed of propagation and a unique traveling wave profile (up to translation) which is a non-smooth function in general. In the case of the power-type behavior of the diffusion and reaction near equilibria we provide detailed asymptotic analysis of the profile.

Description

Keywords

Density dependent diffusion, Unbalanced bistable reaction term, Degenerate and singular diffusion, Traveling wave, Degenerate non-Lipschitz reaction

Citation

Drábek, P., & Zahradníková, M. (2021). Traveling waves for unbalanced bistable equations with density dependent diffusion. <i>Electronic Journal of Differential Equations, 2021</i>(76), pp. 1-21.

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Attribution 4.0 International

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This work is licensed under a Creative Commons Attribution 4.0 International License.

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