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

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.