Year-end Sale % OFF 
Abstract
In this paper, we investigate the long‐time behavior for the nonautonomous semilinear second‐order evolution equation (∂2u/∂t2) − Δu − Δ(∂u/∂t) − Δ(∂2u/∂t2) = f(t, u(x, t − ρ(t))) + g(t, x), in(τ, ∞) × Ω with some hereditary characteristics, where Ω is an open‐bounded domain of ℝN(N ≥ 3) with smooth boundary ∂Ω. Firstly, we establish the existence of solutions for the second‐order nonautonomous evolution equation by the standard Faedo–Galerkin method, but without the uniqueness of solutions. Then by proving the pullback asymptotic compactness for the multivalued process {U(t, τ)} on , we obtain the existence of pullback attractors in the Banach spaces for the multivalued process generated by a class of second‐order nonautonomous evolution equations with hereditary characteristics and ill‐posedness.
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
