| 一类非线性波方程初边值问题解的爆破 |
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| 引用本文： | 王艳萍. 一类非线性波方程初边值问题解的爆破[J]. 数学物理学报(A辑), 2009, 29(4): 1093-1103 |
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| 作者姓名： | 王艳萍 |
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| 作者单位： | 郑州航空工业管理学院数理系,郑州,450015 |
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| 基金项目： | 国家自然科学基金，河南省高等学校青年骨干教师资助计划项目 |
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| 摘 要： | 该文研究如下具有非线性阻尼项和非线性源项的波方程的初边值问题utt -uxxt -uxx -(σ(u2x)ux)x+δ|ut|p-1ut=μ|u|q-1u, 0 < x <1, 0≤ t ≤T, (0.1)u(0, t)=u(1, t)=0, 0≤t≤ T, (0.2)u(x, 0)=u0(x), ut(x, 0)=u1(x),0≤x≤1.(0.3)文章将给出问题(0.1)--(0.3)的解在有限时刻爆破的充分条件, 同时将证明问题的局部广义解和局部古典解的存在性和唯一性.
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| 关 键 词： | 非线性波方程 初边值问题 局部解 解的爆破 |
| 收稿时间： | 2007-03-22 |
| 修稿时间： | 2008-09-12 |
Blow-up of Solutions of an Initial Boundary Value Problem for a Class of Nonlinear Wave Equation |
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| Affiliation: | (Department of Mathematics and Physics, Zhengzhou Institute of Aeronautical Industry Management, Zhengzhou 450015) |
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| Abstract: | In this paper, the following initial boundary value problem of the nonlinear wave equation involving the nonlinear damping term and thenonlinear source term utt -uxxt -uxx -(σ(u2x)ux)x+δ|ut|p-1ut=μ|u|q-1u, 0 < x <1, 0 ≤ t ≤ T, u(0, t)=u(1, t)=0, 0 ≤ t ≤ T, u(x, 0)=u0(x), ut(x, 0)=u1(x), 0 ≤ x ≤1 is discussed. This paper gives sufficient conditions of blow-up of the solutions for the problem in finite time and proves the existence and uniqueness of the local generalized solution and classical solution of this problem. |
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| Keywords: | Nonlinear wave equationzz Initial boundary value problemzz Local solutionzz Blow-up of solutionzz |
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