Song-Ren Fu, Zhen-Hu Ning
Abstract:
We prove the exponential stability of the defocusing critical semilinear wave equation
with variable coefficients and locally distributed damping on R3.
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.
Submitted May 11, 2022. Published August 5, 2022.
Math Subject Classifications: 93B05, 93C20, 35G16, 35L72, 35L15.
Key Words: Critical semilinear wave equation; variable coefficients; stability;
Morawetz estimates; Riemannian geometry; unique continuation.
DOI: https://doi.org/10.58997/ejde.2022.59
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Song-Ren Fu Key Laboratory of Systems and Control Institute of Systems Science Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing, 100190, China email: songrenfu@amss.ac.cn |
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Zhen-Hu Ning Faculty of Information Technology Beijing University of Technology Beijing, 100124, China email: nzh41034@163.com |
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