Electronic Journal of Differential Equations, Vol. 2021 (2021), No. 76, pp. 1-21.

Title: Traveling waves for unbalanced bistable equations with density dependent diffusion
       
Authors: Pavel Drabek (Univ. of West Bohemia, Plzen, Czech Republic)
         Michaela Zahradnikova (Univ. of West Bohemia, Plzen, Czech Republic)

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.