【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 <m/n更多还原

【Abstract】 The authors consider L p-L p′ 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∈R n,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.更多还原