用变量代换法求解一类非齐次热传导方程Cauchy问题

A Solution to the Nonhomogeneous Cauchy Problem of Heat Equation Through Variable Replacement Method

在一维热传导方程的Cauchy问题中,非齐次项具有形式f(x,t)=(kx+b)g(t),通过变量代换法将原方程齐次化,从而可用泊松公式求解,这样避免了传统方法中由二重积分带来的繁琐计算.

In the one-dimensional Cauchy problem of heat equation,the nonhomogeneous item has the form f（x,t）=（kx＋b）g（t）,to homogenize the original equation through variable replacement method.The Poisson formula can be used to solve the problem,which can avoid the tedious calculation of the application of double integral in the traditional method.