On the resonances and the inverse scattering problem for perturbed wave equations - Menzala, Gustavo Perla (Partial Differential Equations, 2006)
We consider finite energy solutions of the perturbed wave equation □u+q(x,t)u=0 where x ε ℝ3, t ε ℝ. We analyse two type of problems: First, we give suitable conditions on q and we prove that there exist infinite many "resonances" λj associated with q. Secondly, we study the problem of determining q from the scattering operator associated with the above equation. We describe a uniqueness result on the inverse scattering problem and state some open problems on the subject.