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Singular dynamics of strongly damped beam equation. (English) Zbl 1187.35002
The authors study the dynamics of an integro-differential equation modeling a beam with strong damping. They introduce a simplified equation (which is formally the limit of the full equation as the small parameter tends to 0) and establish several results on singular convergence of solutions.
These results allow them to show that isolated invariant sets of the full equation are continuations of isolated invariant sets of the limit equation with the same Conley index (and the same holds for Morse decompositions). Semicontinuity results for attractors are also obtained.

MSC:
 35-02 Research exposition (monographs, survey articles) pertaining to partial differential equations 35B20 Perturbations in context of PDEs 35B41 Attractors 37N15 Dynamical systems in solid mechanics 37B30 Index theory for dynamical systems, Morse-Conley indices
Keywords:
35B20 35B41 37N15
Full Text:
References:
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