论文标题
粘性汉堡类型方程中的非线性增强耗散
Nonlinear enhanced dissipation in viscous Burgers type equations
论文作者
论文摘要
我们构建了一类无限质量函数，该功能的粘液汉堡方程衰变的溶液比热方程的溶液更高，以便在此类中进行初始数据。换句话说，我们显示了来自非线性运输术语的增强耗散。我们在两个方程式中计算此类中的渐近概况。对于粘性汉堡方程式，主要新颖性是用边界层的时间依赖轮廓的构造和描述，从而增强了耗散。根据扰动，此配置文件将保持稳定至可计算的非线性校正。我们还将结果扩展到其他对流扩散方程。
We construct a class of infinite mass functions for which solutions of the viscous Burgers equation decay at a better rate than solution of the heat equation for initial data in this class. In other words, we show an enhanced dissipation coming from a nonlinear transport term. We compute the asymptotic profile in this class for both equations. For the viscous Burgers equation, the main novelty is the construction and description of a time dependent profile with a boundary layer, which enhanced the dissipation. This profile will be stable up to a computable nonlinear correction depending on the perturbation. We also extend our results to other convection-diffusion equations.
