高阶摄动波动方程解的Lp-Lp′估计(英文) |
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引用本文: | 王菊,崔泽建. 高阶摄动波动方程解的Lp-Lp′估计(英文)[J]. 四川大学学报(自然科学版), 2002, 39(2) |
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作者姓名: | 王菊 崔泽建 |
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作者单位: | 1. 成都纺织高等专科学校,成都610063 2. 四川师范学院,四川南充637002 |
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摘 要: | 研究了高阶摄动波动方程ttu+(-Δ)mu+V(x)u=0,u(x,0)=0,tu(x,0)=f(x),x∈Rn,n>3m,解的Lp-Lp′估计.在摄动和始值f(x)为紧支且V(x)充分小的假定下,得到了该问题解的Lp-Lp′估计:‖u(*,t)‖p′≤Ct-d‖f‖p,t>0,其中 m>1,d=n/m(1/p-1/p′)-1,1/p+1/p′=1,m/(2n)<1/p-1/2
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关 键 词: | Lp-Lp′估计 高阶 波动方程 摄动势 Lp-Lp′ estimates |
Lp-Lp′ Estimates for a Higher Order Perturbed Wave Equation |
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Abstract: | The authors consider Lp-Lp′ estimates for the solution u(x,t) to the following higher order perturbed equation ttu+(-Δ)mu+V(x)u=0,u(x,0)=0,tu(x,0)=f(x),x∈Rn,n>3m,and assume that the potential V(x) and the initial data f(x) are compactly supported, and V(x) is sufficiently small, then the solution u(x,t) of the this problem satisfies ‖u(*,t)‖p′≤Ct-d‖f‖p,for t>0,where m>1,d=n/m(1/p-1/p′)-1,1/p+1/p′=1 and m/(2n)<1/p-1/2
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Keywords: | higher order wave equation perturbed potential |
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