On a class of quasilinear Barenblatt equations

Caroline Bauzet (1) , Jacques Giacomoni (1) , Guy Vallet (1)

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]

In this paper, we first investigate a quasilinear parabolic equation of Barenblatt type. We prove the existence of a weak solution and give some related regularity results. Next, we are concerned by the study of a Barenblatt problem involving a stochastic perturbation and we prove the existence and the uniqueness of the stochastic weak solution.

Mots clés: Quasilinear parabolic equation; Barenblatt equation; time-semi-discretization; stochastic perturbation; pseudo-parabolic equation; p-Laplace operator

Domaines: Equations aux dérivées partielles [math.AP]

Caroline Bauzet, Jacques Giacomoni, Guy Vallet. On a class of quasilinear Barenblatt equations. Monografias de la Real Academia de Ciencias de Zaragoza, 2012, A special tribute to Professor Monique Madaune-Tort 38, pp.35-51. ⟨hal-01309558⟩