We study nonlinear stochastic partial differential equations with Wick-analytic type nonlinearities set in the framework of white noise analysis. These equations include the stochastic Fisher-KPP equations, stochastic Allen-Cahn, stochastic Newell-Whitehead-Segel, and stochastic Fujita-Gelfand equations. By implementing the theory of C 0 −semigroups and evolution systems into the chaos expansion theory in infinite dimensional spaces, we prove existence and uniqueness of solutions for this class of stochastic partial differential equations.
We show that the sheaves of algebras of generalized functions Ω → G(Ω) and Ω → G ∞ (Ω), Ω are open sets in a manifold X, are supple, contrary to the non-suppleness of the sheaf of distributions.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.