Title: Bistable equation with discontinuous density dependent diffusion with degenerations and singularities
Authors: Drábek, Pavel
Zahradníková, Michaela
Citation: DRÁBEK, P. ZAHRADNÍKOVÁ, M. Bistable equation with discontinuous density dependent diffusion with degenerations and singularities. Electronic Journal of Qualitative Theory of Differential Equations, 2021, roč. 2021, č. 61, s. 1-16. ISSN: 1417-3875
Issue Date: 2021
Publisher: Bolyai Institute
University of Szeged
Document type: článek
URI: 2-s2.0-85115764882
ISSN: 1417-3875
Keywords in different language: density dependent diffusion;bistable balanced nonlinearity;asymptotic behavior;discontinuous diffusion;degenerate and singular diffusion;degenerate non-Lipschitz reaction
Abstract in different language: 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.
Rights: © autoři
Appears in Collections:Články / Articles (KMA)

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