Ontology type: schema:ScholarlyArticle
2019-03
AUTHORSGuy Vallet, Aleksandra Zimmermann
ABSTRACTOur 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... »
PAGES153-202
http://scigraph.springernature.com/pub.10.1007/s00028-018-0472-0
DOIhttp://dx.doi.org/10.1007/s00028-018-0472-0
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