Cahiers du CEREMADE 

Unité
Mixte de Recherche du C.N.R.S. N°7534 

Abstract : In this paper, using entropy techniques, we study the rate of convergence of nonnegative solutions of a simple scalar conservation law to their asymptotic states in a weighted L^{1} norm. After an appropriate rescaling and for a well chosen weight, we obtain an exponential rate of convergence to a stationary solution. Written in the original coordinates,this provides intermediate asymptotics estimates in L^{1}, with an algebraic rate. We also prove a uniform convergence result on the support of the solutions, provided the initial data is compactly supported and has an appropriate behaviour on a neighborhood of the lower end of its support. 





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07012003 

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