Geodesic
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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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 $W_2^1(\Omega)$. 
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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/

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