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

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.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

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

XING Jia-Sheng, WANG Hong-Zhi. Properties of the Solution of the Initial Value Problem for n-Dimensional Heat Conduction Equation[J]. journal6, 2011, 32(6): 15-18.

[1]	XING Jiasheng, YANG Yichuan, WU Sang. Gradient Estimation and Analytic Properties of Solutions to Heat Conduction Equations [J]. Journal of Jishou University（Natural Sciences Edition), 2020, 41(4): 6-11.
[2]	XING Jiasheng, YANG Yichuan, WU Sang. Methods of Proving Solution of the Heat Conduction Equation to be Analytic Function [J]. Journal of Jishou University（Natural Sciences Edition), 2020, 41(3): 1-5.
[3]	PENG Yunmeng,ZHONG Wenyong. Existence of Solutions to the Nonlocal Initial Value Problems of Fractional Differential Equations [J]. Journal of Jishou University（Natural Sciences Edition), 2019, 40(3): 9-13.
[4]	CUI Wen-Hui. Blow-up Criterion of Classical Solution of Quasi-Geostrophic Equation [J]. journal6, 2012, 33(2): 19-23.
[5]	XING Jia-Sheng, ZHU Jian-She. Convergence of Formal Series Solution to a Class of Non-Homogeneous String Vibration Equation [J]. journal6, 2009, 30(5): 13-17.

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

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 5

Recommended Articles

Metrics

Comments