On the asymptotic behaviour of solution for the generalized double dispersion equation |
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Authors: | Shubin Wang Fang Da |
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Institution: | 1. Department of Mathematics , Zhengzhou University , Zhengzhou , 450001 , China wangshubin@zzu.edu.cn;3. Department of Mathematics , Zhengzhou University , Zhengzhou , 450001 , China |
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Abstract: | In this article, we investigate the Cauchy problem for the generalized double dispersion equation in n-dimensional space. We establish the decay estimates of solution to the corresponding linear equation. Under smallness condition on the initial data, we prove the global existence and asymptotic behaviour of the small amplitude solution in the time-weighted Sobolev space by the contraction mapping principle. |
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Keywords: | double dispersion equation decay estimates global existence asymptotic behaviour |
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