摘要
研究具非线性耗散项的p-方程组的初值问题.在非线性耗散项较弱的假设条件下,解除了对初值的C1-模的小性限制.即对初值的C0-模不加小性限制,而需其一阶导数的C0-模足够小.运用经典的特征线法和极值原理,分别得到解的C0-模估计和偏导数的C0-模估计.根据光滑解的局部存在性定理和先验估计的结果,利用逐步延拓法,证明初值问题的整体光滑解的唯一存在性.
We consider the initial value problem for the nonlinear damped p-system. We prove thatit doesn＇t require that the C^0-norm of the initial data is small, while it just needs the C^0-norm of the first order derivative to be sufficiently small. Utilizing some priori estimate, we prove he existences of the global smooth solution for the initial value problem. In order to get a priori estimate of the solutions, by the classical characteristic method, which is used to get the priori C^0- norm estimate on the solutions, and by applying the maximum principle, we get uniformly estimates on the derivatives of the solutions with respect to x.
出处
《华侨大学学报（自然科学版）》
CAS
北大核心
2008年第2期305-307,共3页
Journal of Huaqiao University(Natural Science)
基金
福建省自然科学基金资助项目(A97020)
厦门市2006年度第三批科技计划项目(3502Z2006020)
