Volume 13, Issue 3
Inverse Scattering for the Problem with Impedance-type Boundary

Jijun Liu

J. Part. Diff. Eq., 13 (2000), pp. 279-288.

Published online: 2000-08

Preview Purchase PDF 0 2400
Export citation
  • Abstract
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.
  • Keywords

Inverse problem optimal solution convergence

  • AMS Subject Headings

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{JPDE-13-279, author = {}, title = {Inverse Scattering for the Problem with Impedance-type Boundary}, journal = {Journal of Partial Differential Equations}, year = {2000}, volume = {13}, number = {3}, pages = {279--288}, abstract = { 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.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5514.html} }
TY - JOUR T1 - Inverse Scattering for the Problem with Impedance-type Boundary 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.
Jijun Liu . (2019). Inverse Scattering for the Problem with Impedance-type Boundary. Journal of Partial Differential Equations. 13 (3). 279-288. doi:
Copy to clipboard
The citation has been copied to your clipboard