Inverse problems for singular differential equations.

摘要

In this dissertation we consider two inverse problems which arise in singular differential equations posed on unbounded domains. The first is the recovery of a Schroedinger potential ;It is proved that the potential ;Next we consider the recovery of the dispersion coefficient ;The convection-diffusion equation can be written in its variational form, and it can be shown that the forward problem has a unique solution. The inverse problem was studied for the steady-state case, and a new Sinc-Galerkin method was developed to solve the steady-state forward problem. This problem was also formulated as a nonlinear least-squares problem, and the Tikhonov functional was minimized using the Levenberg-Marquardt method.