Well-posedness and stability for a thermoelectromagnetic system

Francesca Bucci; Matthias Eller; Nella Rotundo

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arXiv · 2606.11124

Well-posedness and stability for a thermoelectromagnetic system

Francesca Bucci·Matthias Eller·Nella Rotundo

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Abstract

In this article we consider a system of coupled partial differential equations that mirrors the interconnection between the evolution of an electromagnetic field -- described by the Maxwell's system -- and that of the temperature distribution in a bounded region in three-dimension. A discussion of the mathematical model is provided. We establish the well-posedness of the initial-boundary value problems associated with the thermoelectromagnetic system, in an appropriate functional-analytic framework. Then, our investigation and main results pertain to the long-time behaviour of the solutions. It is shown that either exponential stability or convergence to stationary solutions hold true, according as the conductivity is positive definite or semidefinite, respectively; in the latter case, strong stability is attained in specific topological or analytical settings. This complements and expands earlier results obtained for the uncoupled Maxwell's system.

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Francesca Bucci, Matthias Eller, Nella Rotundo. 2026-06-09. Well-posedness and stability for a thermoelectromagnetic system. https://arxiv.org/abs/2606.11124

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