Published: 2015-09-30

An application of the theory of scale of Banach spaces

Łukasz Dawidowski

Abstract

The abstract Cauchy problem on scales of Banach space was considered by many authors. The goal of this paper is to show that the choice of the space on scale is significant. We prove a theorem that the selection of the spaces in which the Cauchy problem ut - Δu = u|u|s with initial–boundary conditions is considered has an influence on the selection of index s. For the Cauchy problem connected with the heat equation we will study how the change of the base space influents the regularity of the solutions.

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Dawidowski, Łukasz. (2015). An application of the theory of scale of Banach spaces. Annales Mathematicae Silesianae, 29, 51–59. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/13977

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Domyślna okładka

Vol. 29 (2015)
Published: 2015-09-30


ISSN: 0860-2107
eISSN: 2391-4238
Ikona DOI 10.1515/amsil

Publisher
University of Silesia Press

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