Asymptotics of solutions of nonlinear parabolic equations

This paper is concerned with the large time behaviour of solutions to the Cauchy problem of the following nonlinear parabolic equations: Under the optimal growth conditions on the smooth nonlinear function F(u,Dxu,Dx2u), we obtain the global existence results to the above Cauchy problem. The influence of the nonlinear function F(u,Dxu,Dx2u) on the large time behaviour of the global smooth solution u(t,x) is also studied.