摘要
Cauchy问题是偏微分方程研究中的重要问题之一,而初值的性质在很大程度上决定了偏微分方程解的性质.本文研究了DGH方程的Cauchy问题在初值解析的情形下解的性质:我们在一个合适度量的Banach空间中利用压缩的思想证明,DGH方程Cauchy问题初值解析时,其解关于空间变量全局解析,而关于时间变量局部解析.
Cauchy problem is a kind of important problems in the study of partial differential equations. To a great degree, the properties of solutions depend on properties of initial values. Considered herein is the property of solutions of Cauchy problem for the Dullin-Gottwald-Holm equation when the initial values are analytic. Based on a contraction type argument in a suitable scale of Banach spaces, we show that the solutions of this problem are analytic in both variables, globally in space and locally in time.
出处
《工程数学学报》
CSCD
北大核心
2014年第6期943-948,共6页
Chinese Journal of Engineering Mathematics
基金
The National Natural Science Foundation of China(11001219)
the Natural Science Foundation of Shaanxi Province(2014JQ1002)
