An Application of the Theory of Scale of Banach Spaces

• Autorzy: Łukasz Dawidowski
• Języki publikacji: EN

Abstrakty

EN

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 `u_{t}-\triangle u=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(original abstract)

Słowa kluczowe

EN

Mathematics; Differential equations

PL

Matematyka; Równania różniczkowe

• Czasopismo: Annales Mathematicae Silesianae
• Rocznik: 2015
• Tom: 29
• Strony: 51--59

Twórcy

autor

Łukasz Dawidowski

• An Application of the Theory of Scale of Banach Spaces

Bibliografia

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• Gilbarg D., Trudinger N., Elliptic partial differential equations of second order, Reprint of the 1998 edition, Springer-Verlag, Berlin, 2001.
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• Komatsu H., Fractional powers of operators, Pacific J. Math. 19 (1966), 285-346.
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Identyfikatory

DOI

10.1515/amsil-2015-0005