热传导网络：热浴配置与不变测度
Heat Conduction Networks: Disposition of Heat Baths and Invariant Measure
摘要：
我们考虑一个模型的热传导网络组成的振荡器在不同温度下的热浴接触。我们的目的是推广已经得到的结果时，网络减少到一个链的粒子的stationnary状态的存在性和唯一性。利用Lasalle原理，我们建立了一个条件，在网络之间的热浴的配置，确保不变测度的唯一性。我们将证明当振子是线性的时，这个条件是尖锐的。此外，当粒子间的相互作用强于钉扎时，我们证明了这个条件蕴含着不变测度的存在。
英文摘要：
We consider a model of heat conduction networks consisting of oscillators in contact with heat baths at different temperatures. Our aim is to generalize the results concerning the existence and uniqueness of the stationnary state already obtained when the network is reduced to a chain of particles. Using Lasalle's principle, we establish a condition on the disposition of the heat baths among the network that ensures the uniqueness of the invariant measure. We will show that this condition is sharp when the oscillators are linear. Moreover, when the interaction between the particles is stronger than the pinning, we prove that this condition implies the existence of the invariant measure.
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