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Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
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
Kategorie tematyczne
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
51-59
Opis fizyczny
Daty
wydano
2015-09-01
otrzymano
2015-04-13
poprawiono
2015-05-09
online
2015-09-30
Twórcy
autor
- Institute of Mathematics, University of Silesia, Bankowa 14 40-007 Katowice, Poland, lukasz.dawidowski@us.edu.pl
Bibliografia
- [1] Adams R.A., Sobolev spaces, Academic Press, New York–San Francisco–London, 1975.
- [2] Cholewa J.W., Dłotko T., Global attractors in abstract parabolic problems, Cambridge University Press, Cambridge, 2000.
- [3] Dawidowski Ł., Scales of Banach spaces, theory of interpolation and their applications, Wydawnictwo Uniwersytetu Śląskiego, Katowice, 2012.
- [4] Evans L.C., Partial differential equations, Graduate Studies in Mathematics 19, American Mathematical Society, Providence, Rhode Island, 1998.
- [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.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_amsil-2015-0005