一类三维抛物方程解的稳定性

Stability of Solutions for a Class of Three Dimensional Parabolic Equations

摘要: 本文主要通过辅助积分法对具有时空依赖的外波源的热传导方程$\frac{\partial u}{\partial t}=a^2\Delta u+f\left(x,y,z,t,u\right)$ 的解的稳定性进行了讨论。分别讨论了方程关于$g\left(x,y,z,t\right)$ 的稳定性，关于不同初值情况下的稳定性和关于不同初值和边值情况下的稳定性。

Abstract: In this paper, the stability of the solution of the heat conduction equation $\frac{\partial u}{\partial t}=a^2\Delta u+f\left(x,y,z,t,u\right)$ for a time-space dependent external wave source is discussed by means of the auxiliary integral method. The stability of the equation with respect to $g\left(x,y,z,t\right)$ , with respect to different initial values and with respect to different initial and boundary values are discussed respectively.