一类双曲守恒律方程组退化Goursat问题整体光滑解的存在性

Existence of Global Smooth Solutions for Degenerate Goursat Problem of a Class of Hyperbolic Conservation Law Systems

针对一类双曲守恒律方程组退化Goursat问题,研究其整体光滑解的存在性.首先,引入特征角α,β,建立α,β和压力P的特征分解;其次,利用α,β的特征分解得到不变区域,进而得到特征角的最大模估计;最后,通过压力P的特征分解以及连续性方法建立解的梯度估计,从而证明退化Goursat问题解的存在性.

We studied the existence of the global smooth solutions for degenerate Gourset problem of a class of hyperbolic conversation law systems.Firstly,we introduced characteristic anglesα,β,and established characteristic decompositions forα,βand pressure P.Secondly,the characteristic decompositions ofα,βwere used to obtain the invariant region,and then the maximum norm estimate of the characteristic angles were obtained.Finally,the gradient estimates of the solution were established by the characteristic decomposition of pressure P and continuity method,which proved the existence of the solutions to the degenerate Gourset problem.