|
Proceedings of the Yerevan State University, series Physical and Mathematical Sciences, 2008, Issue 1, Pages 18–23
(Mi uzeru283)
|
|
|
|
This article is cited in 1 scientific paper (total in 1 paper)
Mathematics
Attractors of semigroups generated by an equation of Sobolev type
H. A. Mamikonyan Chair of the theory of optimal control and approximate methods YSU, Armenia
Abstract:
In this paper the behavior of solutions of the following initial boundary value problem for a class of sobolev type equations is considered. $$A\left(\frac{\partial u}{\partial t}\right)+Bu=0,~u\Big|_{t=0}=u_0,~u\Big|_{\Sigma}=0 $$ where $A$ and $B$ are nonlinear operators of the following form: $$Au=-\sum_{i,j=1}^n\frac{\partial}{\partial x_i}a_j(x, u, \nabla u),~~Bu=-\sum_{i,j=1}^n\frac{\partial}{\partial x_i}b_j(x, u, \nabla u)$$ It’s proved that when functions $a_j(x, u, \nabla u)$ and $b_j(x, u, \nabla u)$ specify some conditions, the semigroup generated by this equation has attractor $\{S_t,~t \geq0\}$,, which is bounded in $W_2^1(\Omega)$.
Received: 19.04.2007 Accepted: 30.08.2007
Citation:
H. A. Mamikonyan, “Attractors of semigroups generated by an equation of Sobolev type”, Proceedings of the YSU, Physical and Mathematical Sciences, 2008, no. 1, 18–23
Linking options:
https://www.mathnet.ru/eng/uzeru283 https://www.mathnet.ru/eng/uzeru/y2008/i1/p18
|
Statistics & downloads: |
Abstract page: | 103 | Full-text PDF : | 21 | References: | 35 |
|