Convergence to systems of waves for viscous scalar conservation laws

Article type: Research Article

Authors: Mejai, Maher | Volpert, Vitaly^;

Affiliations: Laboratoire d’Analyse Numérique, UMR 5585 CNRS, Bâtiment 101, Université Claude Bernard Lyon I, 43 Boulevard du 11 Novembre 1918, F‐69622 Villeurbanne Cédex, France

Note: [] Corresponding author. Fax: (+33) 4 72 44 80 53; E‐mail: volpert@lan.univ‐lyon1.fr.

Abstract: We study the large time asymptotic behavior of solutions of the Cauchy problem for the viscous scalar conservation laws. If there exists a travelling wave solution, then it is well known that solutions of the Cauchy problem converge to it. In the case where a wave does not exist we introduce a notion of system of waves, which is a set of waves propagating with different velocities. We show that solutions of the Cauchy problem converge to the system of waves.

Journal: Asymptotic Analysis, vol. 20, no. 3‐4, pp. 351-366, 1999