Well-posedness of quasilinear parabolic equations in time-weighted spaces

DOI to cite this document:: 10.5283/epub.75037

Matioc, Bogdan-Vasile

; Walker, Christoph

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Date of publication of this fulltext: 19 Feb 2025 06:40

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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 dom(f)⊊dom(A) of the domains of the nonlinearities u↦f(u) and u↦A(u). Based on regularizing effects of parabolic equations it is shown that a semiflow is generated in intermediate spaces. In applications this ...