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Long-time behavior and stability of entropy solutions for linearly degenerate hyperbolic systems of rich type

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  • We study linearly degenerate hyperbolic systems of rich type in one space dimension. It is showed that such a system admits exact traveling wave solutions after a finite time, provided that the initial data are Riemann type outside a space interval. We prove the convergence of entropy solutions toward traveling waves in the $L^1$ norm as the time goes to infinity. The traveling waves are determined explicitly in terms of the initial data and the system. We also obtain the stability of entropy solutions in $L^1$. Applications concern physical models such as the generalized extremal surface equations, the Born-Infeld system and augmented Born-Infeld system.
    Mathematics Subject Classification: Primary: 35L45, 35L65; Secondary: 35B40, 35B35.

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