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| 一类半线性Cauchy问题整体解的存在唯一性 | |
| 引用本文： | 赵新俊,邹杰涛. 一类半线性Cauchy问题整体解的存在唯一性[J]. 石河子大学学报(自然科学版), 2010, 28(1): 118-120 |
| 作者姓名： | 赵新俊 邹杰涛 |
| 作者单位： | 石河子大学师范学院数学系;北方工业大学理学院; |
| 基金项目： | 北京市教委科技基金项目(KM200710009012) |
| 摘 要： | 对一类半线性热传导方程Cauchy问题整体解的存在唯一性进行了讨论,运用衰减估计和能量估计相结合的方法,结合Banach不动点定理得到了整体解存在且唯一的条件,该条件不对其非齐次项系数加任何限制,其适用范围更加广泛。 |
| 关 键 词： | 半线性Cauchy问题 衰减估计 能量估计 不动点定理 |
Unique Existence of Global Solution of Cauchy Problem of a Class of Partial Differential Equation |
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| ZHAO Xinjun,ZOU Jietao. Unique Existence of Global Solution of Cauchy Problem of a Class of Partial Differential Equation[J]. Journal of Shihezi University(Natural Science), 2010, 28(1): 118-120 | |
| Authors: | ZHAO Xinjun ZOU Jietao |
| Affiliation: | 1 Teachers' College;Shihezi University;Shihezi 832003;China;2 College of Sciences;North China University of Technology;Beijing 100041;China |
| Abstract: | The unique existence of the global solution of Cauchy problem for a class of semi-linear heat equation is discussed in this paper.The condition that the unique existence of the global solution is satisfied is derived by using the energy decay estimates and the Banach fixed point theorem.Moreover,if any resriction is not put on the coefficient of non-homogenous term,its applicable region will be more broad. |
| Keywords: | semi-linear Cauchy problem estimation of degeneration estimation of energy fixed point theorem ] |
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