journal6 ›› 2011, Vol. 32 ›› Issue (6): 15-18.

• Mathematics • Previous Articles     Next Articles

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


  1. (1.Department of  Mathematics and System Science,Beihang University,Beijing 100191;2.Key Laboratory of Mathematics,Information and Behavior,Ministry of Education,Beihang University,Beijing 100191,China)
  • Online:2011-11-25 Published:2012-03-22

Abstract: 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.

Key words: n-dimensional heat conduction equation, initial value problem, formula of solution, classical solution

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