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In this paper, we study the global existence, L 1 estimates and decay estimates of solutions for the quasilinear parabolic system ut = r ¢ (jruj m ru)+f(u;v), vt = r¢(jrvj n rv)+g(u;v) with zero Dirichlet boundary condition in a bounded domain › ‰ R N.

GLOBAL EXISTENCE AND L∞ ESTIMATES OF SOLUTIONS FOR A QUASILINEAR PARABOLIC SYSTEM