Differential and Integral Equations
- Differential Integral Equations
- Volume 26, Number 7/8 (2013), 781-814.
Asymptotic profiles to the solutions for a nonlinear damped wave equation
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.
Differential Integral Equations, Volume 26, Number 7/8 (2013), 781-814.
First available in Project Euclid: 20 May 2013
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Kawakami, Tatsuki; Ueda, Yoshihiro. Asymptotic profiles to the solutions for a nonlinear damped wave equation. Differential Integral Equations 26 (2013), no. 7/8, 781--814. https://projecteuclid.org/euclid.die/1369057817