Long-time asymptotic behaviors of solutions of $N$-dimensional dissipative partial differential equations

Linghai Zhang

doi:10.3934/dcds.2002.8.1025

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2002, Volume 8, Issue 4: 1025-1042. Doi: 10.3934/dcds.2002.8.1025

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Long-time asymptotic behaviors of solutions of $N$-dimensional dissipative partial differential equations

Linghai Zhang^1,

1.
School of Mathematics, University of Minnesota, 206 Church Street S.E., Minneapolis, MN 55455

Received: January 2001

Revised: April 2002

Published: October 2002

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Abstract

We establish the optimal rate of decay for the global solutions of some nonlinear partial differential equations with dissipation. We apply the well known Fourier splitting technique invented by Maria Schonbek in [1] -- [5] to achieve our goal.

Keywords:

Decay estimates,
dissipative partial differential equations,
Fourier splitting method,
iteration technique.

Mathematics Subject Classification: 35Q20.

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