Focusing of Spherical Nonlinear Pulses for Nonlinear Wave Equations Ⅲ. Subcritical Case |
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引用本文: | 袁明生.Focusing of Spherical Nonlinear Pulses for Nonlinear Wave Equations Ⅲ. Subcritical Case[J].上海交通大学学报(英文版),2005,10(3):322-326. |
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作者姓名: | 袁明生 |
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作者单位: | Dept. of Mathematics, Shanghai Jiaotong Univ. , Shanghai 200240, China |
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基金项目: | National Natural Science Foundation of China(No. 10131050) ; Educational Ministry of China and Shanghai Science and Tehchnology Committee Foundation(No. 03QMH1407) |
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摘 要: | IntroductionConsider the following initial value problem inR1++3={t>0, x∈R3}: ( t2-Δx)ε+ F1( tε p1-1 t+ε), tθε q1-1 tθε) = 0( t2- 4Δx)θε+ F2( tε p2-1 tε, tθε q2-1 tθε) = 0ε t=0=εJ+1U0r,r -ε r0 tε t=0=εJU1r,r -ε r0θε t=0=εJ+1V0r,r -ε 2r0 tθε t=0=εJV1r,r -ε 2r0(1)where r= x with x=(x1,x2,x3)∈R3, r0>0,and 1
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关 键 词: | 非线性波方程 球形脉冲 数学引理 几何光学 |
文章编号: | 1007-1172(2005)03-0322-06 |
收稿时间: | 2004-07-05 |
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