Explicit solution for a class of coupled hyperbolic systems of conservation laws

ABSTRACT

Under suitably generalized Rankine–Hugoniot relation and entropy condition, by introducing a convex hull of potential function, the global explicit solution for the Cauchy problem to a class of coupled hyperbolic systems of conservation laws, which involves the piecewise initial value problem as a special case, is constructively obtained in the measure space.

COMMUNICATED BY:

• A. Constantin

Keywords:

• Cauchy problem
• delta shock waves
• generalized Rankine–Hugoniot relation
• convex hull
• Riemann problem

MSC:

• 35L60
• 35L65
• 76N10

Acknowledgments

The authors would like to express their sincere gratitude to professor Wancheng Sheng and Hanchun Yang for their stimulating discussions. The authors express special thanks to professor Yuxi Zheng for the help discussions during the authors' visiting to Penn State University.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This project was supported by the National Natural Science Foundation of China [grant numbers 11026048, 11326156].