Convergence to nonlinear diffusion waves for solutions of Euler equations with time-depending damping |
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Authors: | Haibo Cui Haiyan Yin Jinshun Zhang Changjiang Zhu |
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Affiliation: | 1. Fujian Province University Key Laboratory of Computation Science, School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, PR China;2. School of Mathematics, South China University of Technology, Guangzhou 510641, PR China |
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Abstract: | In this paper, we are concerned with the asymptotic behavior of solutions to the system of Euler equations with time-depending damping, in particular, include the constant coefficient damping. We rigorously prove that the solutions time-asymptotically converge to the diffusion wave whose profile is self-similar solution to the corresponding parabolic equation, which justifies Darcy's law. Compared with previous results about Euler equations with constant coefficient damping obtained by Hsiao and Liu (1992) [2], and Nishihara (1996) [9], we obtain a general result when the initial perturbation belongs to the same space, i.e. . Our proof is based on the classical energy method. |
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Keywords: | 35L65 76N15 35B45 35B40 Euler equations with time-depending damping Nonlinear diffusion waves Decay estimates |
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