ON THE EQUATION OF BARENBLATT–SOBOLEV - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Communications in Contemporary Mathematics Année : 2011

ON THE EQUATION OF BARENBLATT–SOBOLEV

Résumé

In this paper, we are interested in the following pseudoparabolic problem, known as the Barenblatt–Sobolev problem: f(∂u t ) - Δu - ϵΔ∂u t = g with u(0, ⋅) = u 0 where f is a non-monotone Lipschitz-continuous function, ϵ > 0 and [Formula: see text]. We show the existence of a critical value ϵ 0 >0 such that: if ϵ > ϵ 0 , then the problem admits a unique solution; if ϵ = ϵ 0 , the solution is unique and it exists under an additional assumption on f; if ϵ < ϵ 0 , then the solution is not unique in general. Passing to the limit with ϵ to 0 + , we prove the existence (and uniqueness) of the solution of the Barenblatt differential inclusion Δu + g ∈ f(∂u t ) for a class of maximal monotone operators f. Next, we give an extension of the main result for a stochastic perturbation of the problem and we give some numerical illustrations of the Barenblatt and the Barenblatt–Sobolev equation.
Fichier non déposé

Dates et versions

hal-04312910 , version 1 (28-11-2023)

Identifiants

Citer

Adi Adimurthi, Ngonn Seam, Guy Vallet. ON THE EQUATION OF BARENBLATT–SOBOLEV. Communications in Contemporary Mathematics, 2011, 13 (05), pp.843-862. ⟨10.1142/S0219199711004476⟩. ⟨hal-04312910⟩
0 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More