The stochastic $p(ω,t,x)$-Laplace equation with cylindrical Wiener process

Guy Vallet (1) , Aleksandra Zimmermann (2)

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]
2 University of Duisbourg-Essen

We propose the analysis of a non-linear parabolic problem of $p(ω,t,x)$-Laplace type in the framework of Orlicz Lebesgue and Sobolev spaces with variable random exponents and a stochastic forcing by a cylindrical Wiener process. We give a result of well-posedness: existence, uniqueness and stability of the solution, for additive and multiplicative problems.

Mots clés: Random variable exponent; p-Laplace; Stochastic forcing

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]; Topologie géométrique [math.GT]; Probabilités [math.PR]

Guy Vallet, Aleksandra Zimmermann. The stochastic $p(ω,t,x)$-Laplace equation with cylindrical Wiener process. Journal of Mathematical Analysis and Applications, 2016, 444 (2), pp.1359-1371. ⟨10.1016/j.jmaa.2016.07.018⟩. ⟨hal-01581274⟩