Regularity of solutions of abstract linear evolution equations*

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Abstract

In this paper, we study regularity of solutions to linear evolution equations of the form dX/dt +AX = F(t) in a Banach space H, where A is a sectorial operator in H, and A−αF(α > 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 is a cylindrical Wiener process. Our results are applied to a model arising in neurophysiology, which has been proposed byWalsh [J.B. Walsh, An introduction to stochastic partial differential equations, École d’Été de Probabilités de Saint-Flour, XIV – 1984, Springer, Berlin, 1986, pp. 265–439].

Original languageEnglish
Pages (from-to)268-290
Number of pages23
JournalLithuanian Mathematical Journal
Volume56
Issue number2
DOIs
Publication statusPublished - Apr 1 2016
Externally publishedYes

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All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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