Journal of Jishou University(Natural Sciences Edition)

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Gradient Estimation and Analytic Properties of Solutions to Heat Conduction Equations

XING Jiasheng, YANG Yichuan, WU Sang   

  1.  (1. School of Mathematics and Systems Science, Beihang University, Beijing 100191, China; 2. LMIB of the Ministry of Education, Beihang University, Beijing 100191, China)
  • Online:2020-07-25 Published:2020-10-27

Abstract:

This paper provesthat the solution of the initial value problem for homogeneous heat conduction equation is an analytical function by the solution formula of the initial value problem for the heat conduction equation.The paper provides the gradient estimation of solutions for homogeneous heat conduction equation, offers the method of proving that the solution of homogeneous heat conduction equation is an analytical function by estimating the partial derivative of each order and applying Taylor formula.

Key words: heat conduction equation;solution of heat conduction equation, initial value problem, gradient estimation, analytic function

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