Let £1 c: R^ be an unbounded domain with smooth boundary 9O. We consider the mixed initial-boundary value problem For solution w (t} of(l.l), we simply write and call it the energy of w (t) at time t.

No abstract

No abstract

We consider the inverse scattering problem for the Schrödinger operator with optical potential introduced in nuclear physics to study the scattering of nucleons by nuclei. We show that the corresponding spin-orbit interaction and the complex matrix potential can be uniquely reconstructed from the scattering amplitude at fixed energy.

Exponential decaying states for the wave equations are considered and some examples are given. Moreover, the spectral structure of the operator with coulomb type dissipation is investigated.