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Global Existence of Solutions for Dirichlet Problem to Nonlinear Diagonal Parabolic System with Maximal Growth Conditions
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W. M. Zaja̧czkowski
Published/Copyright:
June 3, 2010
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∞ – estimate in terms of data for a priori bounded weak solutions is found. Next following the methods of Ladyzhenskaya and Uraltseva the Hölder continuity with some exponent is proved. Next applying the results of Amann global existence of solutions is shown.
Key words and phrases.: Nonlinear diagonal parabolic system; regularity of solutions; global existence
Published Online: 2010-06-03
Published in Print: 1995-December
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- Global Existence of Solutions for Dirichlet Problem to Nonlinear Diagonal Parabolic System with Maximal Growth Conditions
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Keywords for this article
Nonlinear diagonal parabolic system;
regularity of solutions;
global existence
Articles in the same Issue
- An Alternative Model of the General Relativity Theory
- Nonlinear Contractions on Semimetric Spaces
- On Weakly Darboux Functions and Some Problem Connected with the Morrey Monotonicity
- On Translations of Sets and Functions
- Global Existence of Solutions for Dirichlet Problem to Nonlinear Diagonal Parabolic System with Maximal Growth Conditions
- On Affine Selections of Set–Valued Functions
- Coinitial Families of Perfect Sets
- Fixed Point and Approximate Fixed Point Theorems for Non–Affine Maps
- Domains of Attraction with Inner Norming on Sturm–Liouville Hypergroups
