| n维热传导方程初值问题解的一些性质 |
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| 引用本文： | 邢家省,王洪志.n维热传导方程初值问题解的一些性质[J].吉首大学学报(自然科学版),2011,32(6):15-18. |
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| 作者姓名： | 邢家省 王洪志 |
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| 作者单位： | （1.北京航空航天大学数学与系统科学学院,北京 100191；2.北京航空航天大学数学、信息与行为教育部重点实验室,北京 100191） |
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| 基金项目： | 国家自然科学基金资助项目(10771011) |
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| 摘 要： | 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.
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| 关 键 词： | n维热传导方程 初值问题 求解公式 古典解 |
Properties of the Solution of the Initial Value Problem for n-Dimensional Heat Conduction Equation |
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| XING Jia-sheng,WANG Hong-zhi.Properties of the Solution of the Initial Value Problem for n-Dimensional Heat Conduction Equation[J].Journal of Jishou University(Natural Science Edition),2011,32(6):15-18. |
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| Authors: | XING Jia-sheng WANG Hong-zhi |
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| Institution: | (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） |
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| 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. |
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| Keywords: | n-dimensional heat conduction equation initial value problem formula of solution classical solution |
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