Shouxin Chen, Decheng Huang, and Xiaosen Han Henan University, Xinyang Vocational Technical College, and Henan University
Abstract : In this paper, we consider a generalized Riemann problem of the first order hyperbolic conservation laws. For the case that excludes the centered wave, we prove that the generalized Riemann problem admits a unique piecewise smooth solution $u=u(t,x)$, and this solution has a structure similar to the similarity solution $u=U\left(\frac{x}{t}\right)$ of the corresponding Riemann problem in the neighborhood of the origin provided that the coefficients of the system and the initial conditions are sufficiently smooth.
Keywords : quasilinear hyperbolic systems, generalized Riemann problem, local solution
