Uniqueness of the inverse scattering problem for the wave equation with a potential depending on time

Published under licence by IOP Publishing Ltd
, , Citation P D Stefanov 1988 Inverse Problems 4 913 DOI 10.1088/0266-5611/4/3/023

0266-5611/4/3/913

Abstract

The author studies the inverse scattering problem for the equation utt- Delta u+q(t,x)u=0, t in R, x in R3. Let KHash ( sigma , theta ; s, omega ) be the 'echo kernel' which describes the scattering of the sharp plane waves delta (t+s-x. omega ). The author proves that if q1>or=q2 and K1Hash =K2Hash for mod sigma -s mod < delta , mod theta - omega 0 mod < delta with some delta >0, omega 0 in S2, then q1=q2.

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10.1088/0266-5611/4/3/023