Global existence and asymptotic behavior of solutions to the generalized cubic double dispersion equation
Global existence and asymptotic behavior of solutions to the generalized cubic double dispersion equation
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DOI：
10.1142/s021953051450002x
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发表时间：
2015-03
影响因子：
2.2
通讯作者：
S. Kawashima;Y. Wang
中科院分区：
文献类型：
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作者：
S. Kawashima;Y. Wang
本文研究了n维空间中广义三次双色散方程的初值问题。在初始数据的一个小条件下，证明了所有空间维数n≥1的解的整体存在性和渐近衰减性。此外，当n≥2时，我们证明了当时间趋于无穷时，解可以近似为线性解。
In this paper, we study the initial value problem for the generalized cubic double dispersion equation in n-dimensional space. Under a small condition on the initial data, we prove the global existence and asymptotic decay of solutions for all space dimensions n ≥ 1. Moreover, when n ≥ 2, we show that the solution can be approximated by the linear solution as time tends to infinity.