拟线性双曲型方程组解的整体存在性  

The global existence of quasilinear hyperbolic equations

作　　者：宋娈娈 

机构地区：[1]中北大学理学院,山西太原030051

出　　处：《高师理科学刊》2014年第6期1-6,共6页Journal of Science of Teachers＇College and University

基　　金：国家自然科学基金资助项目(61171179;61227003;61301259);山西省自然科学基金资助项目(2012021011-2);高等学校博士学科点专项科研基金资助项目(20121420110006);山西省回国留学人员科研资助项目(2013-083);山西省高等学校优秀创新团队支持计划资助项目

摘　　要：考虑一阶拟线性双曲型方程组的柯西问题.假设特征弱线性退化,非齐次项满足相应与此特征的匹配条件,初值满足慢衰减小,得到拟线性严格双曲型方程组柯西问题的整体经典解的存在性.在整体经典解存在的基础上,采用正规化坐标和波的分解公式得到拟线性双曲型方程组解的一些模的先验估计,证明了解的逐点衰减估计.The Cauchy problem of first order quasilinear hyperbolic equations was considerded.Under the assum-ptions that the eigenvalues are weakly linearly degenerste,the non-homogeneous items meet the corresponding with the characteristics of the matching conditions,and Initial value satisfies slow attenuation is small,the global existence of quasilinear hyperbolic differential equations of Cauchy problem was obtained.On the basis of global classical solution exists,using normalized coordinates and wave decomposition theorem,some prior estimates of the molds of quasilinear hyperbolic equations was obtained,point by point decay estimate was proved.

关 键 词：柯西问题 拟线性双曲型方程组 整体经典解 

分 类 号：O175.27[理学—数学]