A degenerate migration-consumption model in domains of arbitrary dimension

In a smoothly bounded convex domain with ≥ 1, a no-flux initial-boundary value problem for is considered under the assumption that near the origin, the function suitably generalizes the prototype given by By means of separate approaches, it is shown that in both cases ∈ (0, 1) and ∈ [1, 2] some glob...

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Bibliographic Details
Published inAdvanced nonlinear studies Vol. 24; no. 3; pp. 592 - 615
Main Author Winkler, Michael
Format Journal Article
LanguageEnglish
Published De Gruyter 01.07.2024
Subjects
35K51
35K57 (secondary)
35K65 (primary)
35Q92
92C17
a priori estimate
chemotaxis
degenerate diffusion
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ISSN2169-0375
2169-0375
DOI10.1515/ans-2023-0131

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Summary:In a smoothly bounded convex domain with ≥ 1, a no-flux initial-boundary value problem for is considered under the assumption that near the origin, the function suitably generalizes the prototype given by By means of separate approaches, it is shown that in both cases ∈ (0, 1) and ∈ [1, 2] some global weak solutions exist which, inter alia, satisfy with sup ) < ∞ if ∈ [1, 2].
ISSN:2169-0375
2169-0375
DOI:10.1515/ans-2023-0131