Global analysis of smooth solutions to a hyperbolic-parabolic coupled system |
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Authors: | Yinghui Zhang Haiying Deng Mingbao Sun |
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Institution: | 1. Department of Mathematics, Hunan Institute of Science and Technology, Yueyang, 414006, China 2. School of Mathematics and Statistics, Central China Normal University, Wuhan, 430079, China 3. Department of Mathematics, Hunan First Normal College, Changsha, 410205, China
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Abstract: | We investigate a model arising from biology, which is a hyperbolic-parabolic coupled system. First, we prove the global existence and asymptotic behavior of smooth solutions to the Cauchy problem without any smallness assumption on the initial data. Second, if the H s ∩ L 1-norm of initial data is sufficiently small, we also establish decay rates of the global smooth solutions. In particular, the optimal L 2 decay rate of the solution and the almost optimal L 2 decay rate of the first-order derivatives of the solution are obtained. These results are obtained by constructing a new nonnegative convex entropy and combining spectral analysis with energy methods. |
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Keywords: | Global analysis hyperbolic-parabolic system decay rate convex entropy |
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