INVERSE SCATTERING FOR A SMALL NONSELFADJOINT PERTURBATION OF THE WAVE EQUATION

KIYOSHI MOCHIZUKI DEPARTMENT OF MATHEMATICS, TOKYO METROPOLITAN UNIVERSITY HACHIOJI, TOKYO 192-0397, JAPAN

We consider the wave equation of the form

w_{tt} + b(x)w_{t} − Δw = 0, (x, t) ∈ R^{n} × R

where n ≥ 3 and b(x) is a complex valued ”small” function which decays sufficiently fast at infinity. In this talk we discuss the following three problems for this equation:

1) To show the existence of the scattering operator,

2) To obtain the expression of the scattering amplitude,

2) To develop a reconstruction procedure of b(x) from the scattering amplitude.