| 半线性伪抛物型方程组的初边值问题 |
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| 引用本文： | 郑露璐.半线性伪抛物型方程组的初边值问题[J].福建师大福清分校学报,2013(2):9-12. |
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| 作者姓名： | 郑露璐 |
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| 作者单位： | 福州大学数学与计算机科学学院,福建福州 350108 |
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| 摘 要： | 主要讨论半线性伪抛物型方程组在Dirichlet边界条件下解的性质.利用严格压缩映射和不动点理论建立了解的局部存在唯一性,再通过建立比较原理和构造上下解的方法,验证了若初值充分小时,解是全局存在的,若初值充分大时,解在有限时刻爆破.
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| 关 键 词： | 伪抛物型 比较原理 全局存在 爆破 |
The Dirichlet boundary problems for semi-linear pseudo-parabolic equation |
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| ZHENG Lulu.The Dirichlet boundary problems for semi-linear pseudo-parabolic equation[J].Journal of Fuqing Branch of Fujian Normal University,2013(2):9-12. |
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| Authors: | ZHENG Lulu |
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| Institution: | ZHENG Lulu(College of Mathamatic and Computer science,Fuzhou University,Fuzhou Fujian,350108) |
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| Abstract: | This paper investigates the properties of nonnegative solutions of a semi-linear pseudoparabolic equations with zero Dirichlet boundary conditions in a smooth bounded domain.We first construct contraction mapping,by using the fixed point,then we can prove that the system admits a unique nonnegative solution.By constructing comparison lemma and upper solution,lower solution,we then can prove that if the initial values are under different conditions,then the properties of the solutions are also different. |
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| Keywords: | pseudo-parabolic equations comparison lemma global existence blow-up |
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