动边界上Burgers方程的非线性边值一初值问题

A Nonlinear Boundary-Initial Value Problem to Burgers Equation on a Moving Boundary

借助应用齐次平衡原则导出的B¨acklund变换和Cole-Hopf变换将动边界上给定流量型条件的Burgers方程的非线性边值—初值问题化为线性方程的边值—初值问题。当动边界是时间t的线性函数时,得出了问题的精确解析解。

A nonlinear boundary-initial value problem to Burgers equation, in which a flux-type condition is given along the moving boundary, is transformed into a linear one by using two changes of variables. When the moving boundary depends linearly on the time, the exact solution of the problem is obtained.