Global attractor for suspension bridge equations with memory. (English) Zbl 1338.35060
Summary: This paper is concerned with a suspension bridge equation with memory effects \(u_{tt} + \alpha \Delta^2u - \int_0^\infty \mu(s)\Delta^2u(t-s)ds + ku^+ + f(u) = h(x)\), defined in a bounded domain of \(\mathbb R^N\). For the suspension bridge equation without memory, there are many classical results. Existing results mainly devoted to existence and uniqueness of a weak solution, energy decay of solution and existence of global attractors. However the existence of global attractors for the suspension bridge equation with memory was no yet considered. The object of the present paper is to provide some results on the well-posedness and long-time behavior to the suspension bridge equation in a more with past history.
MSC:
| 35B41 | Attractors |
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 35L76 | Higher-order semilinear hyperbolic equations |
| 35L35 | Initial-boundary value problems for higher-order hyperbolic equations |
| 35R09 | Integro-partial differential equations |
Keywords:
existence of solution; attractors; suspension bridge equation; memory; damping by the memory termReferences:
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