# GLOBAL EXISTENCE AND $L^\infty$ ESTIMATES OF SOLUTIONS FOR A QUASILINEAR PARABOLIC SYSTEM

Volume 3, Issue 4, pp 245-255 Publication Date: November 14, 2010
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### Authors

JUN ZHOU - School of mathematics and statistics, Southwest University, Chongqing, 400715, P. R. China.

### Abstract

In this paper, we study the global existence, $L^\infty$ estimates and decay estimates of solutions for the quasilinear parabolic system $u_t = \nabla .(\mid\nabla u\mid^m\nabla u)+f(u, v), v_t = \nabla . (\mid \nabla v\mid^n\nabla v)+g(u, v)$ with zero Dirichlet boundary condition in a bounded domain ­ $\Omega\subset R^N$.

### Keywords

• Global existence
• quasilinear parabolic system
• $L^\infty$ estimates and decay estimates.

•  35K55
•  35K57

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