Asymptotic behavior of solutions to the generalized cubic double dispersion equation in one space dimension
Asymptotic behavior of solutions to the generalized cubic double dispersion equation in one space dimension
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DOI：
10.3934/krm.2013.6.969
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发表时间：
2013-12
影响因子：
1
通讯作者：
Masakazu Kato;Y. Wang;S. Kawashima
中科院分区：
文献类型：
--
作者：
Masakazu Kato;Y. Wang;S. Kawashima
研究了一维空间中广义三次双色散方程的初值问题。我们建立了我们在[6]中得到的整体解的一个非线性逼近结果。此外，我们还证明了当时间趋于无穷大时，解趋于非线性扩散波的叠加，这些非线性扩散波是根据粘性Burgers型方程的自相似解显式给出的。证明是基于半群论证并结合波分解的分析。
We study the initial value problem for the generalized cubic double dispersion equation in one space dimension. We establish a nonlinear approximation result to our global solutions that was obtained in [6]. Moreover, we show that as time tends to infinity, the solution approaches the superposition of nonlinear diffusion waves which are given explicitly in terms of the self-similar solution of the viscous Burgers equation. The proof is based on the semigroup argument combined with the analysis of wave decomposition.