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Large time decay estimates of solutions of nonlinear parabolic equations
We are concerned with the large time decay estimates of solutions to the
Cauchy problem of nonlinear parabolic equations. Under the optimal growth conditions
on the smooth nonlinear function
$F(u,D_x u)$ as $(u,D_x u) \to (0,0)$, a global
existence result is obtained and the influence of the nonlinear function $F(u,D_x u)$
on the large time behavior of the corresponding global smooth solution is also established.