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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.
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참고문헌 (19)
참고문헌 신청
A. Ichikawa / 1982 / Stability of semilinear stochastic evolution equations / J. Math. Anal. Appl 90 (1) : 12 ~ 44
A. Yagi / 1988 / Fractional powers of operators and evolution equations of parabolic type / Proc. Japan Acad. Ser. A Math. Sci 64 (7) : 227 ~ 230
A. Yagi / 2010 / Abstract Parabolic Evolution Equations and their Applications / Springer
E. Hille / 1948 / Functional analysis and semi-groups / American Mathematical Society
G. Da Prato / 1992 / Stochastic Equations in Infinite Dimensions
A. Yagi / 1988 / Fractional powers of operators and evolution equations of parabolic type / Proc. Japan Acad. Ser. A Math. Sci 64 (7) : 227 ~ 230
A. Yagi / 2010 / Abstract Parabolic Evolution Equations and their Applications / Springer
E. Hille / 1948 / Functional analysis and semi-groups / American Mathematical Society
G. Da Prato / 1992 / Stochastic Equations in Infinite Dimensions
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