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Parabolic equations with nonlinear singularities 总被引:2,自引:0,他引:2
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Olena Naboka 《Nonlinear Analysis: Theory, Methods & Applications》2009,71(12):6299-6311
The problem of nonlinear oscillations of two Berger plates occupying bounded domains Ω in different parallel planes and coupled by internal subdomains Ω1⊂Ω is considered. A dynamical system generated by the problem in the space is studied. The long-time behavior of the trajectories of the system and its dependence on the value of the coupling parameter γ is described in terms of the system global attractor. In particular, we prove a synchronization phenomenon at the level of attractor for the system. Namely, we consider a (limiting) dynamical system generated by a suitable second order in time evolution equation in the space consisting of the elements from H with coordinates equal for the values of the spatial variable x from the closed set : , and prove that the attractor of the system describing oscillations of two partially coupled Berger plates approaches the attractor of the limiting system as γ tends to the infinity. 相似文献
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