| 一类变系数非线性波方程的能量估计 |
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| 引用本文： | 赵恒.一类变系数非线性波方程的能量估计[J].太原师范学院学报(自然科学版),2014(2):10-11. |
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| 作者姓名： | 赵恒 |
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| 作者单位： | 山西省医疗器械检测中心,山西太原030006 |
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| 摘 要： | 用Holder不等式,Cauchy不等式和Gronwall不等式,证明变系数非线性波方程{y″-div(c(x)▽y)+a(x,t)y=b(x,t),(x,t)∈Ω×0,T]y(0,t)=y(1,t)=0,t∈0,T]y(0)=y0,y′(0)=y1,x∈Ω}在空间L2(Ω)×L2(Ω)上的能量估计.
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| 关 键 词： | Holder不等式 Cauchy不等式 Gronwall不等式 能量估计 |
The Estimates of a Class of Variable Coefficient Nonlinear Wave Equations |
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| Zhao Heng.The Estimates of a Class of Variable Coefficient Nonlinear Wave Equations[J].Journal of Taiyuan Normal University:Natural Science Edition,2014(2):10-11. |
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| Authors: | Zhao Heng |
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| Institution: | Zhao Heng (The Testing Center of the Medical Equipment of Shanxi,Taiyuan 030006,China) |
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| Abstract: | With Holder＇s inequality,Cauchy＇s inequality and the differential form Gronwall＇s inequality,prove the energy estimates of a class of variable coefficient nonlinear wave equations：{y″-div（c（x）▽y）＋a（x,t）y=b（x,t）,（x,t）∈Ω×0,T]y（0,t）=y（1,t）=0,t∈0,T]y（0）=y0,y′（0）=y1,x∈Ω} |
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| Keywords: | Holder＇s inequality Cauchy＇s inequality Gronwall＇s inequality energy estimates |
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