The Cauchy problem for the Moore-Gibson-Thompson equation in the dissipative case

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:292

Article

Chen, Wenhui¹  Ikehata, Ryo² 

[1] Shanghai Jiao Tong Univ, Sch Math Sci, Shanghai 200240, Peoples R China

[2] Hiroshima Univ, Grad Sch Humanities & Social Sci, Dept Math, Div Educ Sci, Higashihiroshima 7398524, Japan

关键词: Moore-Gibson-Thompson equation;    Third-order hyperbolic equation;    Fourier analysis;    Asymptotic profiles;    Singular limit;    Global existence;   

DOI  :  10.1016/j.jde.2021.05.011

来源: Elsevier

【 摘 要 】

In this paper, we study the Cauchy problem for the linear and semilinear Moore-Gibson-Thompson (MGT) equation in the dissipative case. Concerning the linear MGT model, by utilizing WKB analysis associated with Fourier analysis, we derive some L-2 estimates of solutions, which improve those in the previous research [51]. Furthermore, asymptotic profiles of the solution and an approximate relation in a framework of the weighted L-1 space are derived. Next, with the aid of the classical energy method and Hardy's inequality, we get singular limit results for an energy and the solution itself. Concerning the semilinear MGT model, basing on the obtained sharp L-2 estimates and constructing time-weighted Sobolev spaces, we investigate global (in time) existence of Sobolev solutions with different regularities. Finally, under a sign assumption on initial data, nonexistence of global (in time) weak solutions is proved by applying a test function method. (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free