Affiliations: Ceremade (UMR CNRS no. 7534), Université Paris IX‐Dauphine, Place de Lattre de Tassigny, 75775 Paris cedex 16, France E‐mail: [email protected] URL: http://www.ceremade.dauphine.fr/∼dolbeaul/ | Universidad del País Vasco, Departamento de Matemáticas Facultad de Ciencias, Apartado 644, 48080 Bilbao, Spain E‐mail: [email protected] URL: http://www.ehu.es/mat/
Note: [] Corresponding author.
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 L1 norm. After an appropriate rescaling and for a well chosen weight, we obtain an exponential rate of convergence. Written in the original coordinates, this provides intermediate asymptotics estimates in L1, 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.
