On the Rate of Convergence to Equilibrium for a System of Conservation Laws with a Relaxation Term

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Abstract
We analyze a simple system of conservation laws with a strong relaxation term. Well-posedness of the Cauchy problem in the framework of bounded-total-variation (BV) solutions is proved. Furthermore, we prove that the solutions converge towards the solution of an equilibrium model as the relaxation time $delta>0$ tends to zero. Finally, we show that the difference between an equilibrium solution $(delta =0)$ and a nonequilibrium solution $(delta>0)$ measured in $Len$ is bounded by $O(delta^{1/3})$.

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