论文标题
傅里叶 - 塔奈方程：随机起源，变分配方和渐近极限
Fourier-Cattaneo equation: stochastic origin, variational formulation, and asymptotic limits
论文作者
论文摘要
我们引入了傅立叶 - 卡塔奈（FC）系统的变异结构，该结构是二阶双曲系统。这种变分结构的灵感来自与FC系统密切相关的KAC过程的大差速器功能。使用这种变分公式，我们为FC方程介绍了适当的解决方案概念，并证明了一个先验估计，该估算将这种变分结构与适当的Lyapunov函数和Fisher信息（所谓的FIR不等式）联系起来。最后，我们使用此公式和估计来研究FC系统的扩散和双曲线限制。
We introduce a variational structure for the Fourier-Cattaneo (FC) system which is a second-order hyperbolic system. This variational structure is inspired by the large-deviation rate functional for the Kac process which is closely linked to the FC system. Using this variational formulation we introduce appropriate solution concepts for the FC equation and prove an a priori estimate which connects this variational structure to an appropriate Lyapunov function and Fisher information, the so-called FIR inequality. Finally, we use this formulation and estimate to study the diffusive and hyperbolic limits for the FC system.
