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

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\).