The Cauchy problem for a generalized Dullin–Gottwald–Holm equation in Besov spaces
The Cauchy problem for a generalized Dullin–Gottwald–Holm equation in Besov spaces
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DOI：
10.1080/00036811.2013.854331
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发表时间：
2014-07
影响因子：
1.1
通讯作者：
Rong Chen;Shouming Zhou
中科院分区：
文献类型：
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作者：
Rong Chen;Shouming Zhou
本文研究了一类广义Dullin-Gottwald-霍尔姆（DGH）方程的Cauchy问题.利用输运方程理论和经典的Friedrichs正则化方法，在Besov空间中得到了广义DGH方程的局部适定性。此外，还考虑了临界情形下的局部适定性。最后给出了解的最大存在时间的一个下界。最后给出了解的解析表达式。
This paper deals with the Cauchy problem for a generalized Dullin–Gottwald–Holm (DGH) equation. The local well-posedness of the generalized DGH equation is obtained in Besov space with and by the transport equations theory and the classical Friedrichs regularization method. Moreover, the local well-posedness in critical case is also considered. Then a lower bound for the maximal existence time of the solution is derived. Finally, the analytic of the solution is given.