关于一个非线性几何光学中的非严格双曲守恒律系统的研究

摘要

研究了一个产生于非线性几何光学中的非严格双曲守恒律系统.该系统具有强非线性流函数项,且狄拉克激波可能同时出现在解的两个状态变量中.通过未知函数的一个变换,该系统的非线性流函数项得到弱化,从而其黎曼问题被完全解决.%This paper studies a non-strictly hyperbolic system of conservation laws with strong nonlinearity on the flux-functions arising in nonlinear geometric optics,whose solutions may contain delta shock waves in two state variables. By performing a transformation of unknown variables,the system is reduced to another one with weak nonlinearity on the flux-functions. Then the Riemann problem for the later is solved completely.