Stabilization of the critical nonlinear Klein-Gordon equation with variable coefficients on R^3

We prove the exponential stability of the defocusing critical semilinear wave equation with variable coefficients and locally distributed damping on \(\mathbb{R}^3\). The construction of the variable coefficients is almost equivalent to the geometric control condition. We develop the traditional Mor...

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Bibliographic Details
Published in:Electronic journal of differential equations 2022-08, Vol.2022 (1-87), p.59
Main Authors: Fu, Song-Ren, Ning, Zhen-Hu
Format: Article
Language:English
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Summary:We prove the exponential stability of the defocusing critical semilinear wave equation with variable coefficients and locally distributed damping on \(\mathbb{R}^3\). The construction of the variable coefficients is almost equivalent to the geometric control condition. We develop the traditional Morawetz estimates and the compactness-uniqueness arguments for the semilinear wave equation to prove the unique continuation result. The observability inequality and the exponential stability are obtained subsequently.
ISSN:1072-6691
1072-6691
DOI:10.58997/ejde.2022.59