On a p(t,x)-Laplace evolution equation with a stochastic force

Caroline Bauzet (1) , Guy Vallet (1) , Petra Wittbold (2) , Aleksandra Zimmermann (2)

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]
2 Fakultät für Mathematik der Universität Duisburg-Essen

In this paper, we are interested in the stochastic forcing of a nonlinear singular/degenerated parabolic problem of p(t,x)-Laplace type. Since the Lebesgue and Sobolev spaces with variable exponents of variables t and x are Orlicz type spaces and do not fit into the classical framework of Bochner spaces, we have to adapt to this framework classical methods based on monotonicity arguments.

Mots clés: p(t; x) Laplace; Variable exponent; Stochastic forcing; Monotonicity

Domaines: Equations aux dérivées partielles [math.AP]

Caroline Bauzet, Guy Vallet, Petra Wittbold, Aleksandra Zimmermann. On a p(t,x)-Laplace evolution equation with a stochastic force. Stochastics and Partial Differential Equations: Analysis and Computations, 2013, 1 (3), pp.552-570. ⟨10.1007/s40072-013-0017-z⟩. ⟨hal-01309575⟩