Global and exponential attractors for a Ginzburg-Landau model of superfluidity
Global and exponential attractors for a Ginzburg-Landau model of superfluidity
复制标题
DOI：
10.3934/dcdss.2011.4.247
复制
发表时间：
2010-11
期刊：
影响因子：
--
通讯作者：
A. Berti;V. Berti;I. Bochicchio
中科院分区：
文献类型：
--
作者：
A. Berti;V. Berti;I. Bochicchio
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 4 He 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.
