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 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.

Słowa kluczowe

EN

scale of Banach spaces; parabolic equations

Kategorie tematyczne

• 46B70: Interpolation between normed linear spaces
• 35K10: Second-order parabolic equations

• Wydawca: De Gruyter Open
• Czasopismo: Annales Mathematicae Silesianae
• Rocznik: 2015
• Tom: 29
• Numer: 1
• Strony: 51-59

Daty

wydano

2015-09-01

otrzymano

2015-04-13

poprawiono

2015-05-09

online

2015-09-30

Twórcy

autor

Łukasz Dawidowski

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

Bibliografia

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• [5] Gilbarg D., Trudinger N., Elliptic partial differential equations of second order, Reprint of the 1998 edition, Springer-Verlag, Berlin, 2001.
• [6] Henry D., Geometric theory of semilinear parabolic equations, Lecture Notes in Mathematics 840, Springer-Verlag, Berlin, 1981.
• [7] Komatsu H., Fractional powers of operators, Pacific J. Math. 19 (1966), 285–346.
• [8] Yagi A., Abstract parabolic evolution equations and their applications, Springer Monographs in Mathematics, Springer-Verlag, Berlin, 2010.

Identyfikatory

DOI

10.1515/amsil-2015-0005