摘要
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<m/n.关键词
Lp-Lp′估计/高阶/波动方程/摄动势Key words
Lp-Lp′ estimates/higher order/wave equation/perturbed potential分类
数理科学
