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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
Full-text PDF (341 kB) Citations (1)
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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
Document Type: Article
UDC: 517.9
Language: Russian
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
Citation in format AMSBIB
\Bibitem{Mam08}
\by H.~A.~Mamikonyan
\paper Attractors of semigroups generated by an equation of Sobolev type
\jour Proceedings of the YSU, Physical and Mathematical Sciences
\yr 2008
\issue 1
\pages 18--23
\mathnet{http://mi.mathnet.ru/uzeru283}
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  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Proceedings of the Yerevan State University, series Physical and Mathematical Sciences
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