Asymptotic profiles of solutions to viscous Hamilton-Jacobi equations

Said Benachour (1) , Grzegorz Karch (2) , Philippe Laurençot (3)

1 IECN - Institut Élie Cartan de Nancy
2 Instytut Matematyczny
3 MIP - Mathématiques pour l'Industrie et la Physique

The large time behavior of solutions to Cauchy problem for viscous Hamilton-Jacobi equation is classified. The large time asymptotics are given by very singular self-similar solutions on one hand and by self-similar viscosity solutions on the other hand

Mots clés: Viscous Hamilton-Jacobi equations Self similar large time behavior Laplacian unilateral estimates

Domaines: Equations aux dérivées partielles [math.AP]

Said Benachour, Grzegorz Karch, Philippe Laurençot. Asymptotic profiles of solutions to viscous Hamilton-Jacobi equations. Journal de Mathématiques Pures et Appliquées, 2004, 83, pp.1275-1308. ⟨hal-00140768⟩