A global asymptotic expansion for the solution to the generalized Riemann problem

Article type: Research Article

Authors: Le Floch, Philippe^; | Tatsien, Li

Affiliations: Centre de Mathématiques Appliquées, Ecole Poly technique, Un. Assoc. au CNRS, 91128 Palaiseau Cedex, France | Department of Mathematics, Fudan University, Shanghai, China

Note: [] Part of this research was done while the authors visited the Institute for Mathematics and its Applications at the University of Minnesota, Minneapolis, MN 55455, U.S.A.

Abstract: We study the generalized Riemann problem for quasilinear hyperbolic systems of conservation laws. Assuming that this problem has an entropy weak solution globally defined on t≥0 , we construct an asymptotic expansion of this solution, which is also globally defined in time. For technical reasons, we treat the case where the solution is only composed of shock waves or contact discontinuities. We expect that this expansion gives an approximation to the exact solution, which remains valid uniformly in time. Moreover, some improvements of our general results are obtained for the isentropic gas dynamics system.

DOI: 10.3233/ASY-1991-3404

Journal: Asymptotic Analysis, vol. 3, no. 4, pp. 321-340, 1991