Dynamics of a critical semilinear Lamé system with memory. (English) Zbl 1526.35082
Summary: This paper is devoted to studying the asymptotic behavior of a semilinear Lamé system with past history and a source term with Sobolev-critical growth. Based on the quasi-stability approach, we show that the dynamical system generated by the weak solutions of the model has a smooth global attractor with finite fractal dimension in an extended energy space.
MSC:
| 35B41 | Attractors |
| 35L53 | Initial-boundary value problems for second-order hyperbolic systems |
| 35L71 | Second-order semilinear hyperbolic equations |
| 74H40 | Long-time behavior of solutions for dynamical problems in solid mechanics |
| 34K24 | Synchronization of functional-differential equations |
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