<abstract xmlns="http://www.w3.org/1999/xhtml">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 <italic>ut</italic> − Δ<italic>u</italic> = <italic>u|u|s</italic> with initial–boundary conditions is considered has an influence on the selection of index <italic>s</italic>. 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.</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.

An Application Of The Theory Of Scale Of Banach Spaces

Institute of Mathematics, University of Silesia, Bankowa 14 40-007 Katowice, Poland

Annales Mathematicae Silesianae

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"An Application Of The Theory Of Scale Of Banach Spaces"}

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...

An Application Of The Theory Of Scale Of Banach Spaces

Published Online: Sep 30, 2015

Page range: 51 - 59

Received: Apr 13, 2015

DOI: https://doi.org/10.1515/amsil-2015-0005

© Łukasz Dawidowski

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.