Uniform stability of semilinear wave equations with arbitrary local memory effects versus frictional dampings |
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Authors: | Kun-Peng Jin Jin Liang Ti-Jun Xiao |
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Institution: | 1. School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, China;2. Shanghai Key Laboratory for Contemporary Applied Mathematics, School of Mathematical Sciences, Fudan University, Shanghai 200433, China |
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Abstract: | This paper is concerned with the mixed initial–boundary value problem for semilinear wave equations with complementary frictional dampings and memory effects. We successfully establish uniform exponential and polynomial decay rates for the solutions to this initial–boundary value problem under much weak conditions concerning memory effects. More specifically, we obtain the exponential and polynomial decay rates after removing the fundamental condition that the memory-effect region includes a part of the system boundary, while the condition is a necessity in the previous literature; moreover, for the polynomial decay rates we only assume minimal conditions on the memory kernel function g, without the usual assumption of controlled by g. |
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Keywords: | 35Q74 74H55 74H40 35B35 93D15 Wave equation Local memory effect and frictional damping Polynomial and exponential stability Uniform decay rates Memory kernel |
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