Inverse Problems in Nonlinear Phenomena

点击翻译按钮获取中文摘要

This research was intended to make a scheme for determination of the nonlinearities and/or governed equations in nonlinear problems from a viewpoint of inverse problems. Main results are as follows :1.An inverse problem to determine an unknown velocity in two-dimensional, time-independent advection-diffusion equation from data observed at a depth-level was discussed. A procedure by which the velocity is reconstructed from the observed data is established and, as a consequence, the uniqueness of the velocity realizing the prescribed data was proved.2.Related with the problem in (1), an inverse scattering problem to recover the potentials of an energy dependent Schrodinger equation from the scattering data was discussed. A new inversion formula was developed, by which the potentials are recovered directly through the solution of a Marchenko equation. By means of this inverse formula, a necessary and sufficient condition for a given function to be the scattering data was obtained.