Title: Traveling waves for unbalanced bistable equation with density dependent diffusion
Authors: Drábek, Pavel
Zahradníková, Michaela
Citation: DRÁBEK, P. ZAHRADNÍKOVÁ, M. Traveling waves for unbalanced bistable equation with density dependent diffusion. Electronic Journal of Differential Equations, 2021, roč. 2021, č. 76, s. 1-21. ISSN: 1072-6691
Issue Date: 2021
Publisher: Department of Mathematics of Texas State University
Document type: článek
URI: 2-s2.0-85115746667
ISSN: 1072-6691
Keywords in different language: density dependent diffusion;unbalanced bistable reaction term;degenerate and singular diffusion;traveling wave;degenerate non-Lipschitz reaction
Abstract in different language: 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 coeffcient. In particular, it allows for singularities and/or degenerations as well as discontinuities of the fi rst kind at a fi nite 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 pro le (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 pro le.
Rights: © Creative Commons Attribution 4.0 International
Appears in Collections:Články / Articles (KMA)

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