Open Access
July/August 2013 Asymptotic profiles to the solutions for a nonlinear damped wave equation
Tatsuki Kawakami, Yoshihiro Ueda
Differential Integral Equations 26(7/8): 781-814 (July/August 2013). DOI: 10.57262/die/1369057817


We consider the Cauchy problem for a nonlinear damped wave equation. Under suitable assumptions of the nonlinear term and the initial functions, the Cauchy problem has a global-in-time solution $u$ behaving like the Gauss kernel as time tends to infinity. In this paper we show the asymptotic profiles to the solutions and give precise decay estimates on the difference between the solutions and their asymptotic profiles. Our results are based on the $L^p$--$L^q$-type decomposition of the fundamental solutions of the linearized damped wave equation and asymptotic expansion of the solution of a nonlinear heat equation.


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Tatsuki Kawakami. Yoshihiro Ueda. "Asymptotic profiles to the solutions for a nonlinear damped wave equation." Differential Integral Equations 26 (7/8) 781 - 814, July/August 2013.


Published: July/August 2013
First available in Project Euclid: 20 May 2013

zbMATH: 1299.35209
MathSciNet: MR3098987
Digital Object Identifier: 10.57262/die/1369057817

Primary: 35B40 , 35L15 , 35L71

Rights: Copyright © 2013 Khayyam Publishing, Inc.

Vol.26 • No. 7/8 • July/August 2013
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