高阶摄动波动方程解的Lp-Lp′估计（英文）

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

Lp-Lp′ Estimates for a Higher Order Perturbed Wave Equation

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