On some Impedance Boundary Conditions for a Thermo-Piezo-Electromagnetic System

Based on a combination of insights afforded by Rainer Picard in Picard (Comput Methods Appl Math 17(3):499–513, 2017) and Serge Nicaise in Ammari and Nicaise (Asymptot Anal 73(3):125–146, 2011), we extend a set of abstract piezo-electromagnetic impedance boundary conditions. We achieve this by accommodating for the influence of heat with the inclusion of a new equation and additional boundary terms. We prove the evolutionary well-posedness of a known thermo-piezo-electromagnetic system under these boundary conditions. Evolutionary well-posedness here means unique solvability as well as continuous and causal dependence on the given data.