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

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• 作者：Yuta Wakasugi ^{y-wakasugi@cr.math.sci.osaka-u.ac.jp}
• 关键词：Damped wave equation ; Space&ndash ; time dependent coefficient ; Sourcing semilinear term ; Critical exponent ; Small data global existence
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2012
• 期刊代码：76_0022247x
• 类别：mt
• 出版时间：1 September, 2012
• 卷：393
• 期：1
• 页码：66-79
• 文件大小：264 K

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.