Reconstruction of a time dependent source term from a single boundary measurement in Maxwell's equations with nonlinear generalized Ohm's law
type: Item
instance of: scholarly article
title: Reconstruction of a time dependent source term from a single boundary measurement in Maxwell's equations with nonlinear generalized Ohm's law
zbMATH Open document ID: 1387.78014
author: Jaroslav Chovan
author: M. Slodička
published in: Journal of Computational and Applied Mathematics
publication date: 2018-01-12T00:00:00Z
review text: The authors explore the hyperbolic Maxwell system with an unknown time dependent source. Additionally, a nonlinear Ohm's law is imposed, such that the nonlinearity is globally Lipschitz and fulfills a certain homogeneous boundary condition. No noise is assumed to occur in the measurements in this model. A weak formulation of this problem is derived, and then a time discretization is employed via an implicit Euler method. A numerical scheme for providing the solution is obtained, along with stability results. Rothe's functions are used to discretize the system and to obtain a weak solution. Finally, a numerical experiment is done using Lagrange finite elements to support the theory.
reviewed by: Eric Stachura
Mathematics Subject Classification ID: 78M30
Mathematics Subject Classification ID: 78A25
Mathematics Subject Classification ID: 78M10
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 78M25
Mathematics Subject Classification ID: 93B30
Mathematics Subject Classification ID: 35Q60
Mathematics Subject Classification ID: 35R30
Mathematics Subject Classification ID: 65M32
Mathematics Subject Classification ID: 65M20
zbMATH DE Number: 6825418
zbMATH Keywords: Maxwell's equations
zbMATH Keywords: inverse source problem
zbMATH Keywords: Rothe's method
zbMATH Keywords: boundary measurement
Wikidata QID: Q115100155
MaRDI profile type: Publication
full work available at URL: j.cam.2017.11.014
OpenAlex ID: W2771606706
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DOI: 10.1016/J.CAM.2017.11.014
description: scientific article; zbMATH DE number 6825418