Research Article
Global existence, asymptotic behavior, and uniform attractor for a nonautonomous equation
Yuming Qin,
Jia Ren,
Corresponding Author
Yuming Qin
Department of Applied Mathematics, Donghua University, Shanghai 201620, China
Correspondence to: Yuming Qin, Department of Applied Mathematics, Donghua University, Shanghai 201620, China.
E-mail: [email protected]
Search for more papers by this authorJia Ren
Department of Applied Mathematics, Donghua University, Shanghai 201620, China
Search for more papers by this authorYuming Qin,
Jia Ren,
Corresponding Author
Yuming Qin
Department of Applied Mathematics, Donghua University, Shanghai 201620, China
Correspondence to: Yuming Qin, Department of Applied Mathematics, Donghua University, Shanghai 201620, China.
E-mail: [email protected]
Search for more papers by this authorJia Ren
Department of Applied Mathematics, Donghua University, Shanghai 201620, China
Search for more papers by this authorAbstract
In this paper, we establish the global existence, asymptotic behavior, and uniform attractor for a nonautonomous viscoelastic equation with a delay term. Under some suitable assumptions, we firstly prove the global well-posedness of the problem by using the Faedo–Galerkin approximations together with some energy estimates and then obtain the general decay results of the energy via suitable Lyapunov functionals. Finally, we prove the existence of uniform attractors. Copyright © 2013 John Wiley & Sons, Ltd.
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