Traveling waves for unbalanced bistable equations with density dependent diffusion




Drabek, Pavel
Zahradnikova, Michaela

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Texas State University, Department of Mathematics


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.



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


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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