EMIS ELibM Electronic Journals Journal of Applied Analysis
Vol. 1, No. 2, pp. 159-172 (1995)

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Global existence of solutions for Dirichlet problem to nonlinear diagonal parabolic system with maximal growth conditions

W.M. Zajaczkowski

Institute of Mathematics
Polish Academy of Sciences
ul. Sniadeckich 8
00-950 Warsaw, Poland
e-mail: wmzajacz@impan.gov.pl

Abstract: The Dirichlet problem to nonlinear diagonal parabolic system with some special right--hand sides but still satisfying the maximum growth conditions is considered. First applying the idea of Stampacchia a $L_\infty$ -- estimate in terms of data for a priori bounded weak solutions is found. Next following the methods of Ladyzhenskaya and Uraltseva the H{ö}lder continuity with some exponent is proved. Next applying the results of Amann global existence of solutions is shown.

Keywords: Nonlinear diagonal parabolic system, regularity of solutions, global existence

Classification (MSC2000): 35B50, 35D10, 35K50, 35K65

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Electronic fulltext finalized on: 29 May 2002. This page was last modified: 21 Dec 2002.

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