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)|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 C1 travelling wave solutions, provided that the C1 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. [ABSTRACT FROM AUTHOR]