Well-posedness for a pseudomonotone evolution problem with multiplicative noise View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2019-03

AUTHORS

Guy Vallet, Aleksandra Zimmermann

ABSTRACT

Our aim is the study of well-posedness for the stochastic evolution equation du-div(|∇u|p-2∇u+F(u))dt=H(u)dW,for T>0, on a bounded Lipschitz domain D⊂Rd with homogeneous Dirichlet boundary conditions, initial values u0∈L2(D), p>2 and F:R→Rd Lipschitz continuous. W(t) is a cylindrical Wiener process in L2(D) with respect to a filtration (Ft) satisfying the usual assumptions on a complete, countably generated probability space (Ω,F,P). We consider the case of multiplicative noise satisfying appropriate regularity conditions. By a semi-implicit time discretization, we obtain approximate solutions. Using the theorems of Skorokhod and Prokhorov, we are able to pass to the limit and show existence of martingale solutions. We establish pathwise L1-contraction and uniqueness and obtain existence and uniqueness of strong solutions. More... »

PAGES

153-202

References to SciGraph publications

Journal

TITLE

Journal of Evolution Equations

ISSUE

1

VOLUME

19

Author Affiliations

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00028-018-0472-0

DOI

http://dx.doi.org/10.1007/s00028-018-0472-0

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1106837145


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