Regularity of solutions of abstract linear evolution equations

Abstract

In this paper, we study regularity of solutions to linear evolution equations of the form $dX+AXdt=F(t)dt$ in a Banach space $H$, where $A$ is a sectorial operator in $H$ and $A^{-\alpha }F(\alpha >0)$ belongs to a weighted Hölder continuous function space. Similar results are obtained for linear evolution equations with additive noise of the form $dX+AXdt=F(t)dt+G(t)dW(t)$ in a separable Hilbert space $H$, where $W(t)$ is a cylindrical Wiener process. Our results are applied to a model arising in neurophysiology, which has been proposed by Walsh \cite{Walsh}.

25 pages

References in corpus (3)

• An Introduction to Stochastic PDEs
• Strict solutions to stochastic parabolic evolution equations in M-type 2 Banach spaces
• Abstract stochastic evolution equations in M-type 2 Banach spaces