On Solvability of Boundary Value Problems for Kinetic Operator-Differential Equations
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- 作者：Sergey Pyatkov (1)
Sergey Popov (2)
Vasilii Antipin (2) - 关键词：Primary 34G10 ; Secondary 47A50 ; 74A25 ; 82C40 ; Kinetic equation ; Operator ; differential equation ; Krein space ; Forward–backward parabolic equation
- 刊名：Integral Equations and Operator Theory
- 出版年：2014
- 出版时间：December 2014
- 年：2014
- 卷：80
- 期：4
- 页码：557-580
- 全文大小：386 KB
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23. Lions, J.L., Magenes, E.: Problemes aux li - 作者单位：Sergey Pyatkov (1)
Sergey Popov (2)
Vasilii Antipin (2)
1. Ugra State University, Chekhov st. 16, 628012, Khanty-Mansiysk, Russia
2. North-Eastern Federal University, Belinskii st. 58, 677000, Yakutsk, Russia - ISSN：1420-8989
文摘
We study solvability of boundary value problems for the so-called kinetic operator-differential equations of the form B(t)u t sub>?em class="a-plus-plus">L(t)u?=?f, where L(t) and B(t) are families of linear operators defined in a complex Hilbert space E. We do not assume that the operator B is invertible and that the spectrum of the pencil L ?em class="a-plus-plus">λ B is included into one of the half-planes Re λ a or Re λ >?a \({(a\in {\mathbb{R}})}\) . Under certain conditions on the above operators, we prove several existence and uniqueness theorems and study smoothness questions in weighted Sobolev spaces for solutions.