TY - JOUR
T1 - Inverse Scattering for the Problem with Impedance-type Boundary
AU - Jijun Liu 
JO - Journal of Partial Differential Equations
VL - 3
SP - 279
EP - 288
PY - 2000
DA - 2000/08
SN - 13
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5514.html
KW - Inverse problem
KW - optimal solution
KW - convergence
AB -  This paper deals with the inverse scattering problems for the Helmholtz equation with impedance boundary condition. It aims at reconstructing the unknown impedance coefficient from the knowledge of scattered wave fields. We generalize the concept of classic solution (CS) to optimal solution (OS) by a nonlinear optimization problem. Then, based on potential theory, we establish an inversion procedure to get the approximation of OS which is defined as the regularized solution (RS) in this paper. The convergence result for RS is proven from which one can get OS and CS stably and efficiently.