| 一类具有非线性异号源项波动方程的初边值问题 |
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| 引用本文： | 卞春雨,白玉成.一类具有非线性异号源项波动方程的初边值问题[J].哈尔滨师范大学自然科学学报,2010,26(2):32-34. |
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| 作者姓名： | 卞春雨 白玉成 |
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| 作者单位： | 哈尔滨师范大学 |
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| 摘 要： | 研究具有两个异号非线性源项波动方程的初边值问题utt+Δ2u+αut+a|u|p-1u-b|u|q-1u=0(α0,a0,b0).该方程用以描述具有两个性质相异的源作用下的物理系统.利用Galerkin方法证明了若1≤n≤4时,1qp∞;n≥5时,1qpnn-+44,u0(x)∈H02(Ω),u1(x)∈L2(Ω),则问题存在一个整体弱解u(x,t)∈L∞(0,T;H20(Ω)).
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| 关 键 词： | 波动方程 整体弱解 初边值问题 |
Initial Boundary Value Problem for Wave Equations with Nonlinear Source Terms of Different Signs |
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| Bian Chunyu,Bai Yucheng.Initial Boundary Value Problem for Wave Equations with Nonlinear Source Terms of Different Signs[J].Natural Science Journal of Harbin Normal University,2010,26(2):32-34. |
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| Authors: | Bian Chunyu Bai Yucheng |
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| Institution: | (Habin Normal University) |
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| Abstract: | The initial boundary value problem for wave equations with two nonlinear source terms of different signs utt＋Δ2u＋αut＋a｜u｜p-1u-b｜u｜q-1u=0（α0,a0,b0） is studied in this paper.This equation describes physical systems are affected by two sources with different properties.It is proved that if 1≤n≤4,1qp∞;n≥5,qqpn＋4n-4,u0（x）∈H20（Ω）,u1（x）∈L2（Ω）,then the problem admits exist the global weak solution u（x,t）∈L∞（0,T;H20（Ω）） by using Galerkin method. |
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| Keywords: | Wave equation Global weak solution Initial boundary value problem |
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