Lifespan of classical discontinuous solutions to general quasilinear hyperbolic systems of conservation laws with small BV initial data: Rarefaction waves

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:409

Article

Shao, Zhi-Qiang

关键词: Generalized Riemann problem;    Quasilinear hyperbolic system of conservation laws;    Classical discontinuous solution;    Rarefaction wave;    Lifespan;   

DOI  :  10.1016/j.jmaa.2013.07.060

来源: Elsevier

【 摘 要 】

In the present paper the author investigates the global structure stability of Riemann solutions for general quasilinear hyperbolic systems of conservation laws under small BV perturbations of the initial data, where the Riemann solution contains rarefaction waves, while the perturbations are in BV but they are assumed to be C-1-smooth, with bounded and possibly large C-1-norms. Combining the techniques employed by Li-Kong with the modified Glimm's functional, the author obtains a lower bound of the lifespan of the piecewise C-1 solution to a class of generalized Riemann problems, which can be regarded as a small BV perturbation of the corresponding Riemann problem. This result is also applied to the system of traffic flow on a road network using the Aw-Rascle model. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free