Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8256173 | Physica D: Nonlinear Phenomena | 2018 | 8 Pages |
Abstract
The paper is devoted to the study of asymptotic behavior as tâ+â of solutions of initial boundary value problem for structurally damped semi-linear wave equation ât2u(x,t)âÎu(x,t)+γ(âÎ)θâtu(x,t)+f(u)=g(x),θâ(0,1),xâΩ,t>0 under homogeneous Dirichlet's boundary condition in a bounded domain ΩâR3. We proved that the asymptotic behavior as tââ 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 θâ(12,1) possesses an exponential attractor.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
B.A. Bilgin, V.K. Kalantarov,