Bistable equation with discontinuous density dependent diffusion with degenerations and singularities

In this article we introduce rather general notion of the stationary solution of the bistable equation which allows to treat discontinuous density dependent diffusion term with singularities and degenerations, as well as degenerate or non-Lipschitz balanced bistable reaction term. We prove the exist...

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Bibliographic Details
Main Authors: Drábek Pavel
Zahradníková Michaela
Format: Serial
Published: 2021
Series:Electronic journal of qualitative theory of differential equations
Kulcsszavak:Differenciálegyenlet
doi:10.14232/ejqtde.2021.1.61

Online Access:http://acta.bibl.u-szeged.hu/73713
Description
Summary:In this article we introduce rather general notion of the stationary solution of the bistable equation which allows to treat discontinuous density dependent diffusion term with singularities and degenerations, as well as degenerate or non-Lipschitz balanced bistable reaction term. We prove the existence of new-type solutions which do not occur in case of the “classical” setting of the bistable equation. In the case of the power-type behavior of the diffusion and bistable reaction terms near the equilibria we provide detailed asymptotic analysis of the corresponding solutions and illustrate the lack of smoothness due to the discontinuous diffusion.
Physical Description:16
ISSN:1417-3875