Traveling waves for unbalanced bistable equations with density dependent diffusion
DOI:
https://doi.org/10.58997/ejde.2021.76Keywords:
Density dependent diffusion; unbalanced bistable reaction term; degenerate and singular diffusion; traveling wave; degenerate non-Lipschitz reactionAbstract
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.
For more information see https://ejde.math.txstate.edu/Volumes/2021/76/abstr.html
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Copyright (c) 2021 Pavel Drabek, Michaela Zahradnikova
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