Large time decay estimates of solutions of nonlinear parabolic equations

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January 2002, 8(1): 69-114. doi: 10.3934/dcds.2002.8.69

Large time decay estimates of solutions of nonlinear parabolic equations

1.	Laboratory of Mathematical Physics, Wuhan Institute of Physics and Mathematics, The Chinese Academy of Sciences, P. O. Box 71010, Wuhan 430071

Received February 2001 Published October 2001

Abstract
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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.

Keywords: asymptotic behaviors, large time decay estimates, Nonlinear parabolic equations, global existence, optimal growth conditions..

Mathematics Subject Classification: 35K15, 35K57, 35B4.

Citation: Huijiang Zhao. Large time decay estimates of solutions of nonlinear parabolic equations. Discrete & Continuous Dynamical Systems - A, 2002, 8 (1) : 69-114. doi: 10.3934/dcds.2002.8.69

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