论文标题
对局部阻尼的传输扩散方程的影响对局部阻尼的影响
Ergodicity effects on transport-diffusion equations with localized damping
论文作者
论文摘要
本文的主要目的是研究多维圆环中不均匀的局部阻尼的运输扩散方程的时间衰减。漂移受自动lipschitz矢量场的控制，以及带有小粘度参数$ν$的标准热方程的扩散。在第一部分中，我们处理了无关的情况，并以至关重要的方式显示了能量的时间衰减的一些结果，而漂移产生的流量的唯一性和独特的流动性。在第二部分中，我们通过小粘度分析了相同的问题，并在\ mbox {0，c_0 \ ln（1/n（1/ν）的某些对数时间缩放中，就粘度均匀地提供了相似的结果衰减结果。
The main objective of this paper is to study the time decay of transport-diffusion equation with inhomogeneous localized damping in the multi-dimensional torus. The drift is governed by an autonomous Lipschitz vector field and the diffusion by the standard heat equation with small viscosity parameter $ν$. In the first part we deal with the inviscid case and show some results on the time decay of the energy using in a crucial way the ergodicity and the unique ergodicity of the flow generated by the drift. In the second part we analyze the same problem with small viscosity and provide quite similar results on the exponential decay uniformly with respect to the viscosity in some logarithmic time scaling of the \mbox{type $t\in [0,C_0\ln(1/ν)]$}.
