热传导方程解在边界附近的渐近行为

ASYMPTOTIC BEHAVIOR OF THE SOLUTION NEAR THE BOUNDARY FOR THE HEAT EQUATION

考虑热传导方程的初边值问题的解 ,当初值与边值“不相容”时 ,由于热传导方程的特性这个解可以在很短时间内变得光滑 ,并形成一个边界层 ,本文将通过上。

In this paper, the solution of the initial-boundary value problem for the heat equation is considered. When the initial value of the solution is not smooth near the boundary, because of the peculiarity of the equation the solution can become smooth in a short time and forming boundary layers. Here, we will show the asymptotic behavior of the Heat Equation’s solution near boundary through the upper and lower solutions methods.