Asymptotic behaviour of solutions of quasilinear parabolic equation with Robin boundary condition

Michèle Grillot (1) , Philippe Grillot (1)

1 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans

In this paper we study solutions of the quasi-linear parabolic equations @u=@t pu = a(x)jujq1u in (0; T) with Robin boundary condition @u=@ jrujp2 = b(x)jujr1u in (0; T) @ where is a regular bounded domain in IRN, N 3, q > 1, r > 1 and p 2. Some su cient conditions on a and b are obtained for those solutions to be bounded or blowing up at a nite time. Next we give the asymptotic behavior of the solution in special cases.

Mots clés: partial di fferential equations; quasilinear parabolic equations; blow-up; asymptotic behavior; Robin boundary condition

Domaines: Equations aux dérivées partielles [math.AP]

Michèle Grillot, Philippe Grillot. Asymptotic behaviour of solutions of quasilinear parabolic equation with Robin boundary condition. 2011. ⟨hal-00638562⟩