Development of New Methods for Solving the Target Identification or Inverse Scattering Problem for Time-Harmonic Acoustic and Electromagnetic Waves

摘要

During this period, the single investigator investigated two topics. On the inverse scattering problem he wrote 1 book, 8 research papers and 7 survey papers. On the inverse Stefan problem he wrote 3 research papers and 1 survey paper. The papers on inverse scattering derive and numerically implement new, stable methods for solution, obtain a variety of uniqueness theorems and investigate the class of far field patterns associated with the scattering of planes waves by a bounded obstacle. (The set of far field patterns is in general not dense in the space of square integrable functions defined on the unit sphere when the wave number is an eigenvalue of the interior problem. This suggests new methods of solution currently being investigated.) The papers on the inverse Stefan problem derive and numerically implement new methods for solution in two space variables, prove in a new way the strong maximum principle for the heat equation and obtain expansion theorems for analytic solutions for the heat equation.