Reconstruction of a time dependent source term from a single boundary measurement in Maxwell's equations with nonlinear generalized Ohm's law
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.
scientific article; zbMATH DE number 6825418
scientific article