Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 1 (2008), pp. 18-23
Citer cet article
H. A. Mamikonyan. Attractors of semigroups generated by an equation of Sobolev type. Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 1 (2008), pp. 18-23. http://geodesic.mathdoc.fr/item/UZERU_2008_1_a2/
@article{UZERU_2008_1_a2,
author = {H. A. Mamikonyan},
title = {Attractors of semigroups generated by an equation of {Sobolev} type},
journal = {Proceedings of the Yerevan State University. Physical and mathematical sciences},
pages = {18--23},
year = {2008},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/UZERU_2008_1_a2/}
}
TY - JOUR
AU - H. A. Mamikonyan
TI - Attractors of semigroups generated by an equation of Sobolev type
JO - Proceedings of the Yerevan State University. Physical and mathematical sciences
PY - 2008
SP - 18
EP - 23
IS - 1
UR - http://geodesic.mathdoc.fr/item/UZERU_2008_1_a2/
LA - ru
ID - UZERU_2008_1_a2
ER -
%0 Journal Article
%A H. A. Mamikonyan
%T Attractors of semigroups generated by an equation of Sobolev type
%J Proceedings of the Yerevan State University. Physical and mathematical sciences
%D 2008
%P 18-23
%N 1
%U http://geodesic.mathdoc.fr/item/UZERU_2008_1_a2/
%G ru
%F UZERU_2008_1_a2
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 $W_2^1(\Omega)$.
