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Title: An application of the theory of scale of Banach spaces
Authors: Dawidowski, Łukasz
Keywords: Scale of Banach spaces; Parabolic equations
Issue Date: 2015
Citation: Annales Mathematicae Silesianae, Nr 29 (2015), s. 51-59
Abstract: he author considers, in an abstract setting, a semilinear evolutionary equation of the form ut+Au=F(u), where A:D(A)⊂X→X is a positive sectorial operator on a Banach space X and F satisfies a suitable local Lipschitz condition. He studies the regularity of solutions when the equation is settled in the scale of Banach spaces Xα=D(Aα). In particular, he focuses on the case when F is a power function. The general results are illustrated by a number of specific applications.
DOI: 10.1515/amsil-2015-0005
ISSN: 0860-2107
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