Strauss exponent for semilinear wave equations with scattering space dependent damping

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:489

Article

Lai, Ning-An^1,2,3  Tu, Ziheng⁴ 

[1] Lishui Univ, Inst Nonlinear Anal, Lishui 323000, Peoples R China

[2] Lishui Univ, Dept Math, Lishui 323000, Peoples R China

[3] Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China

[4] Zhejiang Univ Finance & Econ, Sch Data Sci, Hangzhou 310018, Peoples R China

关键词: Semilinear wave equation;    Space dependent damping;    Blow-up;    Lifespan;   

DOI  :  10.1016/j.jmaa.2020.124189

来源: Elsevier

【 摘 要 】

It has been asserted that the semilinear wave equation with scattering damping admits the same Strauss critical exponent as the classical semilinear wave equation. In this paper, we devote to showing that this assertion holds for the space dependent damping wave equation when the decay rate of the space dependent variable coefficients of the damping is greater than 2. In particular, we derive the lifespan upperbound estimates for both sub-critical and critical exponents. Moreover, when the nonlinear term is of derivative type, we also obtain the same Glassey exponent and the same upper bound lifespan as that of the corresponding problem for wave equation without damping. Both results show the hyperbolicity of the equation from the blow-up aspect. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free