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

## TL;DR

This paper establishes the well-posedness of a coupled piezo-electromagnetic model involving Maxwell's equations and elasticity, with boundary dynamics influencing the system, ensuring mathematical stability and causality.

## Contribution

It introduces a boundary dynamic framework into the piezo-electromagnetic model and proves evolutionary well-posedness for the coupled PDE system.

## Key findings

- Proves Hadamard well-posedness of the model
- Demonstrates causal dependence on initial and boundary data
- Establishes stability of the coupled system

## 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.