Global existence and regularity of solutions to a system of nonlinear Maxwell equations.
A model for the propagation of electromagnetic fields in ferroelectric media is considered. The corresponding material relations linking the magnetic induction \(B\) with the magnetic field \(H\) and the displacement current density \(D\) with the electric field \(E\) are \(B=\mu H\), \(\mu \in \mathbb{R}_{>0}\) and \(D=\varepsilon (E+P(E))\), \(\varepsilon \in \mathbb{R}_{>0}\). The current density induced by the electric field is assumed to be proportional to it. The non-linear polarization term \(P(E)\) is itself given as the solution of a Maxwell type system with a Lipschitz continuous lower order non-linearity and a source term proportional to \(E\). The paper establishes global existence, uniqueness and regularity of solutions.
scientific article; zbMATH DE number 2003887
scientific article