The Generalized Riemann Problem for First Order Quasilinear Hyperbolic Systems of Conservation Laws II |
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Authors: | Shouxin Chen Xiaosen Han Hao Zhang |
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Institution: | (1) Department of Mathematics, Fuzhou University, Fuzhou, 350002, China |
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Abstract: | In this paper, we are concerned with the existence and uniqueness of the local solution to the generalized Riemann problem
for first order quasi-linear hyperbolic systems of conservation laws in the presence of the shock wave with large amplitude
and the centered wave. Apart from some exceptions, we prove the problem admits a unique piecewise smooth solution u=u(t,x), and this solution has a structure similar to the similarity solution u=u(x/t) 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. The application of our results in rich system is also given. |
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