Well-Posedness of Quasilinear Parabolic Equations in Time-Weighted Spaces

Research output: Working paper/Preprint › Preprint

Authors

  • Bogdan Matioc
  • Christoph Walker

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Original languageEnglish
Publication statusE-pub ahead of print - 13 Dec 2023

Abstract

Well-posedness in time-weighted spaces of certain quasilinear (and semilinear) parabolic evolution equations \(u'=A(u)u+f(u)\) is established. The focus lies on the case of strict inclusions \(\mathrm{dom}(f)\subsetneq \mathrm{dom}(A)\) of the domains of the nonlinearities \(u\mapsto f(u)\) and \(u\mapsto A(u)\). Based on regularizing effects of parabolic equations it is shown that a semiflow is generated in intermediate spaces. In applications this allows one to derive global existence from weaker a priori estimates. The result is illustrated by examples of chemotaxis systems.

Keywords

    math.AP

Cite this

Well-Posedness of Quasilinear Parabolic Equations in Time-Weighted Spaces. / Matioc, Bogdan; Walker, Christoph.
2023.

Research output: Working paper/Preprint › Preprint

Matioc B, Walker C. Well-Posedness of Quasilinear Parabolic Equations in Time-Weighted Spaces. 2023 Dec 13. Epub 2023 Dec 13. doi: 10.48550/arXiv.2312.07974
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