Higher order asymptotic expansions to the solutions for a nonlinear damped wave equation
Higher order asymptotic expansions to the solutions for a nonlinear damped wave equation
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DOI：
10.1007/s00030-016-0408-8
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发表时间：
2016-09
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影响因子：
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通讯作者：
Tatsuki Kawakami;H. Takeda
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文献类型：
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作者：
Tatsuki Kawakami;H. Takeda
研究一类非线性阻尼波动方程的Cauchy问题.在适当的非线性和初始数据的假设下，我们得到了满足加权L1和估计的全局解。此外，我们建立了高阶渐近展开的了解。这意味着我们构造了全局解关于数据权重的非线性近似。我们的证明基于Takeda给出的线性解的近似公式（Asymptot Anal 94：1-31，2015）和Ishige等人开发的非线性抛物方程的非线性近似理论。（J Evol Equ 14：749-777，2014）。
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 weightedL1andestimates. 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).