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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 −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].

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Authors and Affiliations

  1. Department of Information and Physical Sciences, Graduate School of Information Science and Technology, Osaka University, Suita, Osaka, 565-0871, Japan

    Tạ Việt Tôn

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  1. Tạ Việt Tôn
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Correspondence to Tạ Việt Tôn.

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* This work is supported by JSPS KAKENHI grant No. 20140047.

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Tôn, T.V. Regularity of solutions of abstract linear evolution equations* . Lith Math J 56, 268–290 (2016). https://doi.org/10.1007/s10986-016-9318-z

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  • DOI: https://doi.org/10.1007/s10986-016-9318-z

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