Asymptotic behaviour of global classical solutions to the mixed initial-boundary value problem for diagonalizable quasilinear hyperbolic systems

作者：Shao, Zhi-Qiang^*

来源：IMA Journal of Applied Mathematics, 2013, 78(1): 1-31.

DOI：10.1093/imamat/hxr032

• asymptotic behaviour
• quasilinear hyperbolic system
• linear degeneracy
• mixed initial-boundary value problem
• global classical solution
• travelling wave

In this paper, we investigate the asymptotic behavior of global classical solutions to the mixed initial-boundary value problem with large bounded total variation (BV) data for linearly degenerate quasilinear hyperbolic systems of diagonal form with general non-linear boundary conditions in the half space {(t, x)vertical bar t >= 0, x >= 0}. 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 C-1 travelling wave solutions, provided that the C-1 norm and the BV norm of the initial and boundary data are bounded but possibly large. Applications include the 1D Born-Infeld system arising in the string theory and high energy physics.

• 出版日期2013-2
• 单位福州大学