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Abstrakty
The purpose of this paper is to describe the smoothness of solutions of semilinear parabolic equations with 2m-th order elliptic operator. Similar result for second order equations was given e.g. by F. Rothe [RO] under the name of "bootstrap" and "feedback".
Słowa kluczowe
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Czasopismo
Rocznik
Tom
Strony
355--368
Opis fizyczny
Bibliogr. 10 poz.
Twórcy
autor
- Institute of Mathematics and Computer Science, Opole University, ul. Oleska 48, 45-052 Opole, Poland
- Institute of Mathematics, Silesian University, Bankowa 14, 40-007 Katowice, Poland
Bibliografia
- [CH-D] J. W. Cholewa, T. Dłotko, Asymptotic Behaviour of Abstract Parabolic Problems, London Mathematical Society Lecture Notes Series, Cambridge Univ. Press, Cambridge, 2000.
- [DL1] T. Dłotko, Local solvability of semilinear parabolic equations, Hokkaido Math. J. 20 (1991), 481-496.
- [DL2] T. Dłotko, Fourth order semilinear parabolic equations, Tsukuba J. Math., 16 (1992), 389-405.
- [FR] A. Friedman, Partial Differential Equations, Holt, Rinehart and Winston, New York, 1969.
- [G-T] G. Gilbarg, N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer-Verlag, Berlin, 1983.
- [GU] D. Guidetti, On elliptic systems in L1, Osaka J. Math. 30 (1993), 397-429.
- [HE] D. Henry, Geometric Theory of Semilinear Parabolic Equations, Springer-Verlag, Berlin, 1981.
- [L-S-U] O. A. Ladyzhenskaya, V. A. Solonnikov, N. N. Uralceva, Linear and Quasilinear Equations of Parabolic Type, Translations of Math. Monographs, 23, Amer. Math. Soc., Providence R.I., 1977.
- [PA] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New York, 1983.
- [RO] F. Rothe, Global Solutions of Reaction-Diffusion Systems, Springer Lecture Notes in Mathematics, 1072, Springer-Verlag, Berlin, 1984.
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Bibliografia
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bwmeta1.element.baztech-article-PWA5-0009-0006