Initial value problem of quasi-linear hyperbolic systems and global geometric optics approximation

研究目的：(1)拟线性对称强双曲型偏微分方程系统初始数据包含参数λ的形式解的构造(2)作为全局有效弱形式解的验证(3)阐明了这种弱全局形式解与原系统真解的关系函数(2)引入形式解的最小类组成函数(3)使用简化相位参数的派生调制方程的可处理表示(4)在守恒律系统下，派生调制方程的弱解与原始系统的弱形式解之间的自然关系的验证(5)作为派生调制方程的全局弱解的原始系统的弱形式解的有效性细节将在准备中的论文中加以阐述，这些论文将在其他地方发表。

The aim of research :(1) Construction of formal solutions with the initial data involving a parametery lambda for quasi-linear symmetric strongly hyperbolic systems of partial differential equations(2) Verification of such formal solutions as globally valid weak formal solutions(3) Clarification of the relation of such weak global formal solutions and the genuine solution of the original systemsResults obtained through the present research :(1) 2-dimensionality of the range of the linear phase functions(2) Introduction of a minimal class of constituent functions for formal solutions(3) Tractable representaions of derived modultion equations using simplified phase parameters(4) Verification of a natural relation between weak solutions of derived modulation equations and weak formal solutions of the original systems in case of systems of conservation laws(5) Validity as weak formal solutions to the original systems of such global weak solutions of derived modulation equationsThe details will be expounded in papers in preparation which will be published elsewhere.