Asymptotic profiles of solutions to convection-diffusion 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 zero mass solutions to the Cauchy problem for a convection-diffusion equation. We provide conditions on the size and shape of the initial datum such that the large time asymptotics of solutions is given either by the derivative of the Guass-Weierstrass kernel or by a self-similar solution or by a hyperbolic N-wave

Mots clés: Convection-diffusion equations Viscous Hamilton-Jacobi equations Asymptotic profiles

Domaines: Equations aux dérivées partielles [math.AP]

Said Benachour, Grzegorz Karch, Philippe Laurençot. Asymptotic profiles of solutions to convection-diffusion equations. Comptes rendus de l'Académie des sciences. Série I, Mathématique, 2004, 338, pp.369-374. ⟨hal-00140801⟩