Abstract
We study the Cauchy problem for a nonlinear damped wave equation. Under suitable assumptions for the nonlinearity and the initial data, we obtain the global solution which satisfies weighted L 1 and \({L^\infty}\) estimates. Furthermore, we establish the higher order asymptotic expansion of the solution. This means that we construct the nonlinear approximation of the global solution with respect to the weight of the data. Our proof is based on the approximation formula of the linear solution, which is given by Takeda (Asymptot Anal 94:1–31, 2015), and the nonlinear approximation theory for a nonlinear parabolic equation developed by Ishige et al. (J Evol Equ 14:749–777, 2014).
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Kawakami, T., Takeda, H. Higher order asymptotic expansions to the solutions for a nonlinear damped wave equation. Nonlinear Differ. Equ. Appl. 23, 54 (2016). https://doi.org/10.1007/s00030-016-0408-8
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DOI: https://doi.org/10.1007/s00030-016-0408-8