Note on abstract stochastic semilinear evolution equations

T$\hat{\rm \text{o}}$n Vi$\hat{\d{e}}$t T\d{a}

doi:10.4134/JKMS.j160311

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J. Korean Math. Soc. 2017; 54(3): 909-943

Online first article January 12, 2017 Printed May 1, 2017

https://doi.org/10.4134/JKMS.j160311

Note on abstract stochastic semilinear evolution equations

T$\hat{\rm \text{o}}$n Vi$\hat{\d{e}}$t T\d{a}

Kyushu University

Abstract

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Abstract

This paper is devoted to studying abstract stochastic semilinear evolution equations with additive noise in Hilbert spaces. First, we prove the existence of unique local mild solutions and show their regularity. Second, we show the regular dependence of the solutions on initial data. Finally, some applications to stochastic partial differential equations are presented.

Keywords: stochastic evolution equations, analytic semigroups, regularity

MSC numbers: Primary 60H15, 35R60; Secondary 58D25