On Well-Posedness for a Piezo-Electromagnetic Coupling Model with Boundary Dynamics

Abstract: We consider a coupled system of Maxwell's equations and the equations of elasticity, which is commonly used to model piezo-electric material behavior. The boundary influence is encoded as a separate dynamics on the boundary data spaces coupled to the partial differential equations. Evolutionary well-posedness, i.e. Hadamard well-posedness and causal dependence on the data, is shown for the resulting model system.