Small data global existence for the semilinear wave equation with space-time dependent damping

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:393

Article

Wakasugi, Yuta

关键词: Damped wave equation;    Space-time dependent coefficient;    Sourcing semilinear term;    Critical exponent;    Small data global existence;   

DOI  :  10.1016/j.jmaa.2012.03.035

来源: Elsevier

【 摘 要 】

In this paper we consider the critical exponent problem for the semilinear wave equation with space-time dependent damping. When the damping is effective, it is expected that the critical exponent agrees with that of only the space dependent coefficient case. We shall prove that there exists a unique global solution for small data if the power of nonlinearity is larger than the expected exponent. Moreover, we do not assume that the data are compactly supported. However, it is still open whether there exists a blow-up solution if the power of nonlinearity is smaller than the expected exponent. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free