n维热传导方程初值问题解的一些性质

Properties of the Solution of the Initial Value Problem for n-Dimensional Heat Conduction Equation

考虑热传导方程解的性质的问题,应用n维热传导方程初值问题的求解公式,证明了齐次方程解的光滑性,给出应用于对Weierstrass逼近定理的证明,并对非齐次方程给出了古典解存在的一个充分条件.

This paper investigates the properties of the solution of the initial value problem for heat conduction equation.Using the formula of the solution of the initial value problem for n-dimensional heat conduction equation,the smoothness of the solution of homogeneous equation is proved.In addition,a proof of the Weierstrass Approximation Theorem is given.Finally,a sufficient condition of the existence of the classical solution of the non-homogeneous equation is obtained.