| 研究実績の概要 |
In this academic year, I studied the following two problems.
1. Stochastic parabolic evolution equations of the form: dX+AXdt=[F_1(t)+F_2(X)]dt+G(t)dW(t) in Hilbert spaces and Banach spaces of M-type 2.
First, I studied the linear case, i.e. F_2=0, in Hilbert spaces. Strong regularity of mild solutions to the equations has been shown. This result is published in Lithuanian Mathematical Journal(Volume 56 April 2016).
Second, I handled the general case in Banach spaces of M-type 2. Strict solutions to that equations as well as their maximal regularity has been investigated. I submitted this study to an academic journal for possible publication.
2. Non-autonomous stochastic linear evolution equations of the form: dX+A(t)Xdt=F(t)dt+G(t)dW(t) in Banach spaces of M-type 2. On the basis of the theory of deterministic linear evolution equations, I constructed strict solutions to the equations. This result is also submitted to an academic journal.
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