GLOBAL EXISTENCE AND \(L^\infty\) ESTIMATES OF SOLUTIONS FOR A QUASILINEAR PARABOLIC SYSTEM

Volume 3, Issue 4, pp 245-255 http://dx.doi.org/10.22436/jnsa.003.04.02

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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 ­ \(\Omega\subset R^N\).

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Keywords

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

MSC

•  35K55
•  35K57

References

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