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Article Dans Une Revue Journal of Mathematical Analysis and Applications Année : 2016

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

Résumé

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.
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Dates et versions

hal-01581274 , version 1 (08-01-2019)

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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⟩
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