Smoothing effect in semilinear parabolic equations

• Autorzy: Napiórkowska J.
• Języki publikacji: EN

Abstrakty

EN

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

EN

semigroups; semilinear parabolic equations

PL

równania paraboliczne

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2003
• Tom: Vol. 36, nr 2
• Strony: 355--368
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Napiórkowska J.

• 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

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• [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.