Stability of the Riemann solutions for a nonstrictly hyperbolic system of conservation laws |
| |
Authors: | Chun Shen |
| |
Institution: | School of Mathematics and Information, Ludong University, Yantai 264025, PR China Laboratory of Mathematics Physics, Wuhan Institute of Physics and Mathematics, The Chinese Academy of Sciences, Wuhan 430071, PR China |
| |
Abstract: | We prove that the Riemann solutions are stable for a nonstrictly hyperbolic system of conservation laws under local small perturbations of the Riemann initial data. The proof is based on the detailed analysis of the interactions of delta shock waves with shock waves and rarefaction waves. During the interaction process of the delta shock wave with the rarefaction wave, a new kind of nonclassical wave, namely a delta contact discontinuity, is discovered here, which is a Dirac delta function supported on a contact discontinuity and has already appeared in the interaction process for the magnetohydrodynamics equations M. Nedeljkov and M. Oberguggenberger, Interactions of delta shock waves in a strictly hyperbolic system of conservation laws, J. Math. Anal. Appl. 344 (2008) 1143-1157]. Moreover, the global structures and large time asymptotic behaviors of the solutions are constructed and analyzed case by case. |
| |
Keywords: | 35L65 35L67 35B30 |
本文献已被 ScienceDirect 等数据库收录! |
|