论文标题
模块化汉堡方程中多个冲击的灭绝
Extinction of multiple shocks in the modular Burgers equation
论文作者
论文摘要
我们考虑具有模块化对流项的汉堡方程中的多个冲击波。以前显示，模块化汉堡的方程式通过单个接口允许旅行的粘性冲击，这在平滑且指数端定位的扰动方面稳定。相比之下，我们建议在能量估计和数值模拟的帮助中，在目前的工作中，具有多个接口的冲击波的演变导致两个连续接口的有限时间合并。我们制定了由界面方程和数值模拟支持的有限时间灭绝的精确缩放定律。
We consider multiple shock waves in the Burgers' equation with a modular advection term. It was previously shown that the modular Burgers' equation admits a traveling viscous shock with a single interface, which is stable against smooth and exponentially localized perturbations. In contrast, we suggest in the present work with the help of energy estimates and numerical simulations that the evolution of shock waves with multiple interfaces leads to finite-time coalescence of two consecutive interfaces. We formulate a precise scaling law of the finite-time extinction supported by the interface equations and by numerical simulations.
