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| 非齐次热传导方程初边值问题的形式级数解的收敛性 | |
| 引用本文： | 邢家省,张愿章,郭秀兰.非齐次热传导方程初边值问题的形式级数解的收敛性[J].河南科学,2010,28(1):1-5. |
| 作者姓名： | 邢家省 张愿章 郭秀兰 |
| 作者单位： | 1. 北京航空航天大学数学与系统科学学院,数学、信息与行为教育部重点实验室,北京,100191 2. 华北水利水电学院,郑州,450011 3. 河南工业大学理学院,郑州,450052 |
| 基金项目： | 国家自然科学基金资助项目，北京市教育委员会共建项目专项资助 |
| 摘 要： | 对线性非齐次热传导方程初边值问题的形式级数解的收敛性问题进行了研究,通过证明形式级数的一致收敛性和可逐项求导性质,得到了线性非齐次热传导方程初边值问题的古典解的存在唯一性和广义解的存在唯一性. |
| 关 键 词： | 热传导方程 初边值问题 形式级数解 一致收敛性 古典解 广义解 |
The Convergence of the Formal Series Solution to the Initial Boundary Value Problem for a Class of Non-Homogeneous Heat Conduction Equation |
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| Xing Jiasheng,Zhang Yuanzhang,Guo Xiulan.The Convergence of the Formal Series Solution to the Initial Boundary Value Problem for a Class of Non-Homogeneous Heat Conduction Equation[J].Henan Science,2010,28(1):1-5. | |
| Authors: | Xing Jiasheng Zhang Yuanzhang Guo Xiulan |
| Institution: | 1. Department of Mathematics, LMIB of the Ministry of Education, Beihang University, Beijing 100191, China;2. North China Institute of Water Conservancy and Hydroelectric Power, Zhengzhou 450011, China;3. College of Science, Henan University of Technology, Zhengzhou 450052, China) |
| Abstract: | This paper studied the convergence of the formal series solution to the initial boundary value problem for the non-homogeneous heat conduction equation. By proving the uniform convergence of the formal series and the property of the termwise derivation,we proved that the existence and uniqueness of classical solution,at the same time we proved the existence of the generalized solution to the initial boundary value problem for the non-homogeneous heat conduction equation. |
| Keywords: | heat conduction equation initial boundary value problem formal series solution uniform convergence classical solution generalized solution |
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