L^1 Nonlinear Stability of Travelling Waves for a Hyperbolic System with Relaxation

Abstract: We investigate the existence and the asymptotic stability of travelling wave solutions for a hyperbolic $2\times2$ system with a relaxation source term. Using the subcharacteristic stability condition, which implies special monotonicity properties of the solutions, we are able to establish the $L^1$ asymptotic attractivity of these solutions.

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Title:
L^1 Nonlinear Stability of Travelling Waves for a Hyperbolic System with Relaxation
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