The generalized Riemann problem for first order quasilinear hyperbolic systems of conservation laws I
Bull. Korean Math. Soc. 2009 Vol. 46, No. 3, 409-434
https://doi.org/10.4134/BKMS.2009.46.3.409
Printed May 1, 2009
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
MSC numbers : 35L45, 35A07
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