Regularity of solutions of abstract linear evolution equations *

Research output: Contribution to journalArticle

4 Citations (Scopus)

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 −α F(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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Regularity of Solutions
Evolution Equation
Linear equation
Sectorial Operator
Separable Hilbert Space
Stochastic Partial Differential Equations
Wiener Process
Additive Noise
Function Space
Continuous Function
Banach space
Form
Model

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Regularity of solutions of abstract linear evolution equations * . / Ta, Ton Viet.

In: Lithuanian Mathematical Journal, Vol. 56, No. 2, 01.04.2016, p. 268-290.

Research output: Contribution to journalArticle

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