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Annales Mathematicae Silesianae

Editor-in-Chief: Sablik, Maciej

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Mathematical Citation Quotient (MCQ) 2016: 0.10

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An Application Of The Theory Of Scale Of Banach Spaces

Łukasz Dawidowski
Published Online: 2015-09-30 | DOI: https://doi.org/10.1515/amsil-2015-0005

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.

(2010) Mathematics Subject Classification:: Primary 46B70; Secondary 35K10

Key words and phrases:: scale of Banach spaces; parabolic equations

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About the article

Received: 2015-04-13

Revised: 2015-05-09

Published Online: 2015-09-30

Published in Print: 2015-09-01


Citation Information: Annales Mathematicae Silesianae, Volume 29, Issue 1, Pages 51–59, ISSN (Online) 0860-2107, DOI: https://doi.org/10.1515/amsil-2015-0005.

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© Łukasz Dawidowski. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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