Asymptotic behavior of global classical solutions to Goursat problem for quasilinear hyperbolic systems with small BV data

作者：Shao, Zhi-Qiang^*

来源：Zeitschrift fur Angewandte Mathematik und Physik, 2014, 65(2): 241-278.

DOI：10.1007/s00033-013-0327-z

• Quasilinear hyperbolic system
• Goursat problem
• Global classical solution
• Linear degeneracy
• Traveling wave
• Asymptotic behavior

This paper is concerned with the asymptotic behavior of global C-1 solutions of the Goursat problem for quasilinear hyperbolic systems. Based on the existence result on the global classical solution, we prove that when t tends to the infinity, the solution approaches a combination of Lipschitz continuous and piecewise C-1 traveling wave solutions, provided that the C-1 norm of the boundary data is bounded but possibly large, and the BV norm of the boundary data is sufficiently small. Applications include the 1D compressible Euler equations for Chaplygin gases.

• 出版日期2014-4
• 单位福州大学