Asymptotic Behavior of the Nonlinear Parabolic Equations

Asymptotic Behavior of the Nonlinear Parabolic Equations

Year:    2004

Journal of Partial Differential Equations, Vol. 17 (2004), Iss. 3 : pp. 255–263

Abstract

This paper is concerned with the large time behavior for solutions of the nonlinear parabolic equations in whole spaces R^n. The spectral decomposition methods of Laplace operator are applied and it is proved that if the initial data u_0 ∈ L² ∩ L^r for 1 ≤ r ≤ 2, then the solutions decay in L² norm at t^{-\frac{n}{2}(\frac{1}{r}-\frac{1}{2})}. The decay rates are optimal in the sense that they coincide with the decay rates of the solutions to the heat equations with the same initial data.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/2004-JPDE-5391

Journal of Partial Differential Equations, Vol. 17 (2004), Iss. 3 : pp. 255–263

Published online:    2004-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    9

Keywords:    L² decay