Traveling waves for unbalanced bistable equations with density dependent diffusion

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dc.contributor.authorDrabek, Pavel
dc.contributor.authorZahradnikova, Michaela
dc.date.accessioned2022-10-25T17:37:42Z
dc.date.available2022-10-25T17:37:42Z
dc.date.issued2021-09-14
dc.description.abstractWe 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.
dc.description.departmentMathematics
dc.formatText
dc.format.extent21 pages
dc.format.medium1 file (.pdf)
dc.identifier.citationDrábek, 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.
dc.identifier.issn1072-6691
dc.identifier.urihttps://hdl.handle.net/10877/16234
dc.language.isoen
dc.publisherTexas State University, Department of Mathematics
dc.rightsAttribution 4.0 International
dc.rights.holderThis work is licensed under a Creative Commons Attribution 4.0 International License.
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.sourceElectronic Journal of Differential Equations, 2021, San Marcos, Texas: Texas State University and University of North Texas.
dc.subjectDensity dependent diffusion
dc.subjectUnbalanced bistable reaction term
dc.subjectDegenerate and singular diffusion
dc.subjectTraveling wave
dc.subjectDegenerate non-Lipschitz reaction
dc.titleTraveling waves for unbalanced bistable equations with density dependent diffusion
dc.typeArticle

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