| 带有阻尼项的偏泛函微分方程解的振动性 |
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| 引用本文： | 俞元洪,胡庆席.带有阻尼项的偏泛函微分方程解的振动性[J].数学的实践与认识,2000,30(3):331-338. |
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| 作者姓名： | 俞元洪 胡庆席 |
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| 作者单位： | 1. 北京文登学校，北京 100081
2. 中科院应用教学所，北京 100080 |
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| 摘 要： | 本文研究带有阻尼项的双曲型时滞偏微分方程 2 t2 u(x,t) +m(t) u t=a(t)△ u(x,t) +b(t)△ u(x,ρ(t) ) -q(t) f (u(x,σ(t) ) ,(x,t)∈ G≡Ω× R+ (1 )其中 ,R+=0 ,+∞ ) ,Ω是一个具有逐段光滑边界的有界区域 .利用平均法和微分不等式方法得到方程 (1 )的若干新的振动准则 .
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| 关 键 词： | 双曲型 偏微分方程 微分不等式 时滞 振动 |
| 修稿时间： | 1999年12月24 |
Oscillation of Solutions of Partial FunctionalDifferential Equationis with Damped Terms |
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| YU Yuan-hong,HU Qing-xi.Oscillation of Solutions of Partial FunctionalDifferential Equationis with Damped Terms[J].Mathematics in Practice and Theory,2000,30(3):331-338. |
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| Authors: | YU Yuan-hong HU Qing-xi |
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| Abstract: | In this paper we study partial diffevential equations with deviating arguments and damped terms of neutral type of the form
u(x,t) + m(t) = a(t)△u(x,t) + b(t)Δu(x,ρ(t) ) － q(t)f(u(x,σ(t) ),
(x,t) ∈ G≡ Ω × R+ (1)
where Ω is a bounded domain with piecewise smooth boundary, and R+ = 0, +∞). With average method and differential inequality method used, some new criteria for oscillation of equation(1) are obtained. |
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| Keywords: | hyperbolic type partial differential equation differential inequality deviating arguments oscillation |
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