Scaling variables and asymptotic profiles for the semilinear damped wave equation with variable coefficients

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:447

Article

Wakasugi, Yuta¹ 

[1] Nagoya Univ, Grad Sch Math, Chikusa Ku, Furocho, Nagoya, Aichi 4648602, Japan

关键词: Semilinear damped wave equation;    Diffusion phenomena;    Scaling variables;   

DOI  :  10.1016/j.jmaa.2016.10.018

来源: Elsevier

【 摘 要 】

We study the asymptotic behavior of solutions for the semilinear damped wave equation with variable coefficients. We prove that if the damping is effective, and the nonlinearity and other lower order terms can be regarded as perturbations, then the solution is approximated by the scaled Gaussian of the corresponding linear parabolic problem. The proof is based on the scaling variables and energy estimates. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free