| 一类具粘性阻尼项的拟线性波动方程解的局部存在性和整体不存在性（英文） |
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| 引用本文： | 宋瑞丽,王书彬.一类具粘性阻尼项的拟线性波动方程解的局部存在性和整体不存在性（英文）[J].应用数学,2020,33(1):91-99. |
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| 作者姓名： | 宋瑞丽 王书彬 |
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| 作者单位： | 1. 中原工学院信息商务学院, 河南 郑州 450007; 2. 郑州大学数学与统计学院, 河南 郑州 450001 |
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| 基金项目： | Supported by the National Natural Science Foundation of China(11171311) |
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| 摘 要： | 本文针对三维空间中一类具有粘性阻尼项的拟线性波动方程的初边值问题.利用Galerkin方法和紧性原理,证明了该问题局部解的存在唯一性;借助能量积分不等式证明了该问题的解在有限时间内发生爆破.
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| 关 键 词： | 粘性阻尼 拟线性波动方程 初边值问题 局部解 解的爆破 |
Local Existence and Global Nonexistence Theorems for a Viscous Damped Quasi-Linear Wave Equations |
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| SONG Ruili,WANG Shubin.Local Existence and Global Nonexistence Theorems for a Viscous Damped Quasi-Linear Wave Equations[J].Mathematica Applicata,2020,33(1):91-99. |
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| Authors: | SONG Ruili WANG Shubin |
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| Institution: | (College of Information and Business,Zhongyuan University of Technology,Zhengzhou 450007,China;School of Mathematics and Statistics,Zhengzhou University,Zhengzhou 450001,China) |
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| Abstract: | In this paper,the existence and uniqueness of the local solution for the initial boundary value problem for a class of three-dimensional space of quasi-linear viscous damping wave equation are proved by the Galerkin method and compactness principle.The blow-up of the solution in limited time for this question is proved by means of the energy integral inequality. |
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| Keywords: | Viscous damped Quasi-linear wave equation Initial boundary problem Local solution Blow-up of solution |
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