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

Author： Shao Zhi-Qiang  

Publisher： Oxford University Press

ISSN： 1464-3634

Source： IMA Journal of Applied Mathematics, Vol.78, Iss.1, 2013-02, pp. : 1-31

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Abstract

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)t0, x0. 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 BornInfeld system arising in the string theory and high energy physics.

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