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

作　　者：赵佳敏 肖伟 ZHAO Jiamin;XIAO Wei(School of Sciences,Chang’an University,Xi’an 710064,China)

机构地区：[1]长安大学理学院,西安710064

出　　处：《吉林大学学报（理学版）》2024年第2期197-204,共8页Journal of Jilin University:Science Edition

基　　金：陕西省自然科学基础研究计划项目(批准号:2018JQ1084);陕西省重点研发计划项目(批准号:2019GY202);长安大学中央高校基本科研业务费专项基金(批准号:300102121101)。

摘　　要：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.

关 键 词：双曲守恒律方程组 特征分解 退化Goursat问题 平面稀疏波 

分 类 号：O175.2[理学—数学]