ATTRACTORS OF SEMIGROUPS GENERATED BY AN EQUATION OF SOBOLEV TYPE - Mamikonyan, H. A. (Proceedings of the YSU A: Physical and Mathematical Sciences, 2023)
In this paper the behavior of solutions of the following initial boundary value problem for a class of Sobolev type equations is considered. cases A(ut)+Bu=0, u|_t=0=u_0, u|_Σ=0, cases where A and B are nonlinear operators of the following form: Au=-^n_i,j=1x_ia_j(x,u, riangledown u), Bu= -^n_i,j=1x_ib_j (x,u, riangledown u). It’s proved that when functions a_j (x, u, riangledown u) and b_j (x, u, riangledown u) specify some conditions, the semigroup generated by this equation has attractor, which is bounded in ^0 W^1_ 2 (Ω).