Entropy Dissipation and Wasserstein Metric Methods for the Viscous Burgers’ Equation: Convergence to Diffusive Waves
نویسندگان
چکیده
In this paper we study the large time behavior for the viscous Burgers’ equation with initial data in L(R). In particular, after a time dependent scaling, we provide the optimal rate of convergence in relative entropy and Wasserstein metric, towards an equilibrium state corresponding to a positive diffusive wave. The main tool in our analysis is the reduction of the rescaled Burgers’ equation to the linear Fokker–Planck equation by means of the Hopf–Cole transformation. We then employ well known results concerning the decay in relative entropy and in Wassertstein metric towards stationary solutions for the Fokker– Planck equation.
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