Determination of a time-dependent convolution kernel from a boundary measurement in nonlinear Maxwell's equations. (September 2016)

• Record Type: Journal Article
• Authors: Slodička, Marian; Galba, Michal
• Is Part Of: Computers & mathematics with applications. Volume 72:issue 6(2016)
• Page Start: 1484
• Page End: 1500
• Publication Date: 2016-09
• Subjects: Maxwell's equations -- Inverse problem -- Reconstruction -- Time discretization; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2016.06.032
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: A nonlinear hyperbolic Maxwell equation with an unknown solely time dependent convolution kernel is studied. The missing kernel is recovered from an additional normal component measurement over the whole boundary. The existence of a solution to this inverse problem is shown. Moreover a constructive algorithm for approximations is designed and its convergence is established. Uniqueness is proved for a regular solution. Theoretical results are supported by a numerical experiment.