Abstract
AbstractIn this paper, the main purpose is to study existence of the global attractor for the weakly damped wave equation with gradient type nonlinearity. To this end, we first verify the existence and uniqueness of global weak solution by the Galerkin method and compulsively variational method. Furthermore, we obtained the global strong solution under some mild assumptions on f. Secondly, we utilize the $$\omega$$
ω
-limit compactness to show the semigroup generated by the equation has a compact, connected and invariant attractor.
Publisher
Springer Science and Business Media LLC
Subject
Mathematical Physics,Statistical and Nonlinear Physics
Reference28 articles.
1. Babin, A.V., Vishik, M.I.: Attractors of Evolution Equations (English transl North-Holland 1992). Nauka, Moscow (1989)
2. Babin, A.V., Vishik, M.I.: Attractors of Evolution Equations (English translation North-Holland 1989). Nauka, Moscow (1992)
3. Ball, J.M.: Global attractors for damped semilinear wave equations. Disc. Control Dyn. Syst. 10, 31–52 (2004)
4. Cárdenas, A.S., Niche, C.J.: Decay character and estimates for the damped wave equation. J. Math. Anal. Appl. 506, 125548 (2022)
5. Chepyzhov, V.V., Vishik, M.I.: Attractors for equations of mathematical physics, mathematical physics, volume 49 of American Mathematical Society Colloquium Publications. American Mathematical Society, Providence (2002)