Department of Mathematics2024-11-1020180167-278910.1016/j.physd.2017.12.0012-s2.0-85039740519http://dx.doi.org/10.1016/j.physd.2017.12.001https://hdl.handle.net/20.500.14288/16096The paper is devoted to the study of asymptotic behavior as t -> +infinity of solutions of initial boundary value problem for structurally damped semi-linear wave equation partial derivative(2)(t)u(x, t) - Delta u(x, t)+gamma(-Delta)(theta)partial derivative(t) u(x,t) + f(u) = g(x), theta is an element of(0, 1), x is an element of Omega, t > 0 under homogeneous Dirichlet's boundary condition in a bounded domain Omega subset of R-3. We proved that the asymptotic behavior as t -> infinity of solutions of this problem is completely determined by dynamics of the first N Fourier modes, when N is large enough. We also proved that the semigroup generated by this problem when theta is an element of(1/2, 1) possesses an exponential attractor. (C) 2017 Elsevier B.V. All rights reserved.MathematicsApplied mathematicsPhysicsFluidsPlasmasPhysicsMathematicalJournal Article1872-8022437962900003Q1965