Very singular solutions to a nonlinear parabolic equation with absorptionII- Uniqueness

Said Benachour (1) , Herbert Koch (2) , Philippe Laurençot (3)

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

We prove the uniqueness of the very singular solution to a Hamilton-Jacobi equation with absorption. We mention thatthe very singular solutions play an important role in the description of the large time behavior of the solutions.

Mots clés: Very singular solutions; Hamilton-Jacobi equations; Uniqueness

Domaines: Equations aux dérivées partielles [math.AP]

Said Benachour, Herbert Koch, Philippe Laurençot. Very singular solutions to a nonlinear parabolic equation with absorptionII- Uniqueness. Proceedings of the Royal Society of Edinburgh: Section A, Mathematics, 2004, 134 (1), pp.39-54. ⟨hal-00140898⟩