Large time decay estimates of solutions of nonlinear parabolic equations

Huijiang  Zhao

doi:10.3934/dcds.2002.8.69

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2002, Volume 8, Issue 1: 69-114. Doi: 10.3934/dcds.2002.8.69

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Large time decay estimates of solutions of nonlinear parabolic equations

Huijiang Zhao^1,

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

Received: January 31, 2001

Published: December 2001

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Abstract

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.

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Mathematics Subject Classification: 35K15, 35K57, 35B40.

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