DCDS-S
Global and exponential attractors for a Ginzburg-Landau model of superfluidity
Alessia Berti Valeria Berti Ivana Bochicchio
Discrete & Continuous Dynamical Systems - S 2011, 4(2): 247-271 doi: 10.3934/dcdss.2011.4.247
The long-time behavior of the solutions for a non-isothermal model in superfluidity is investigated. The model describes the transition between the normal and the superfluid phase in liquid 4He by means of a non-linear differential system, where the concentration of the superfluid phase satisfies a non-isothermal Ginzburg-Landau equation. This system, which turns out to be consistent with thermodynamical principles and whose well-posedness has been recently proved, has been shown to admit a Lyapunov functional. This allows to prove existence of the global attractor which consists of the unstable manifold of the stationary solutions. Finally, by exploiting recent techinques of semigroups theory, we prove the existence of an exponential attractor of finite fractal dimension which contains the global attractor.
keywords: Superfluids Lyapunov functional Ginzburg-Landau equations exponential attractors.
EECT
On the viscoelastic coupled suspension bridge
Ivana Bochicchio Claudio Giorgi Elena Vuk
Evolution Equations & Control Theory 2014, 3(3): 373-397 doi: 10.3934/eect.2014.3.373
In this paper we discuss the asymptotic behavior of a doubly nonlinear problem describing the vibrations of a coupled suspension bridge. The single-span road-bed is modeled as an extensible viscoelastic beam which is simply supported at the ends. The main cable is modeled by a viscoelastic string and is connected to the road-bed by a distributed system of one-sided elastic springs. A constant axial force $p$ is applied at one end of the deck, and time-independent vertical loads are allowed to act both on the road-bed and on the suspension cable. For this general model we obtain original results, including the existence of a regular global attractor for all $p\in\mathbb{R}$.
keywords: viscoelastic beam Suspension bridge system viscoelastic string nonlinear oscillations global attractor.

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