论文标题
模块化汉堡方程中粘性冲击的渐近稳定性
Asymptotic stability of viscous shocks in the modular Burgers equation
论文作者
论文摘要
在模块化汉堡方程式中考虑了粘性冲击的动力学，由于模块化非线性产生的奇异性，时间演化变得复杂。我们证明，在奇数和一般扰动下，粘性冲击是渐近稳定的。对于奇数扰动，证明依赖于模块化汉堡方程的减少到半线上的线性扩散方程。对于一般的扰动，通过将时间进化问题转换为接口位置的非线性方程的线性方程系统来开发证明。空间中的指数重量是对一般扰动的初始数据施加的，以便在时间上获得扰动的渐近衰减。我们给出一般扰动下粘性冲击的渐近稳定性的数值插图。
Dynamics of viscous shocks is considered in the modular Burgers equation, where the time evolution becomes complicated due to singularities produced by the modular nonlinearity. We prove that the viscous shocks are asymptotically stable under odd and general perturbations. For the odd perturbations, the proof relies on the reduction of the modular Burgers equation to a linear diffusion equation on a half-line. For the general perturbations, the proof is developed by converting the time-evolution problem to a system of linear equations coupled with a nonlinear equation for the interface position. Exponential weights in space are imposed on the initial data of general perturbations in order to gain the asymptotic decay of perturbations in time. We give numerical illustrations of asymptotic stability of the viscous shocks under general perturbations.
