Regularity of solutions of abstract linear evolution equations

被引:4
|
作者
Ta Viet Ton [1 ]
机构
[1] Osaka Univ, Grad Sch Informat Sci & Technol, Dept Informat & Phys Sci, 2-2 Yamadaoka, Suita, Osaka 5650871, Japan
关键词
analytic semigroups; stochastic linear evolution equations; regularity; SPACE; SPDES;
D O I
10.1007/s10986-016-9318-z
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
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 (-alpha) F(alpha > 0) belongs to a weighted Holder 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, A parts per thousand cole d'A parts per thousand t, de Probabilit,s de Saint-Flour, XIV - 1984, Springer, Berlin, 1986, pp. 265-439].
引用
收藏
页码:268 / 290
页数:23
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