Pavel Drabek, Michaela Zahradnikova
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.
Submitted August 22, 2021. Published September 14, 2021.
Math Subject Classifications: 35Q92, 35C07, 34A12, 35K92.
Key Words: Density dependent diffusion; unbalanced bistable reaction term;
degenerate and singular diffusion; traveling wave;
degenerate non-Lipschitz reaction.
DOI: https://doi.org/10.58997/ejde.2021.76
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Pavel Drábek Department of Mathematics, Faculty of Applied Sciences University of West Bohemia Univerzitní 8, 30100 Plzen, Czech Republic email: pdrabek@kma.zcu.cz |
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Michaela Zahradníková Department of Mathematics, Faculty of Applied Sciences University of West Bohemia Univerzitní 8, 30100 Plzen, Czech Republic email: mzahrad@kma.zcu.cz |
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