Asymptotic behavior of dispersive electromagnetic waves in bounded domains

TL;DR

This paper investigates the stability and energy decay of Maxwell's equations with electric and magnetization effects in bounded domains, providing conditions for exponential or polynomial decay and illustrating the results with examples.

Contribution

It establishes well-posedness and decay properties of Maxwell's equations considering electric and magnetization effects, under passitivity assumptions.

Findings

Semigroup theory confirms well-posedness of the model.

Passitivity ensures boundedness of the semigroup.

Exponential or polynomial energy decay is achieved under certain conditions.

Abstract

We analyze the stability of Maxwell equations in bounded domains taking into account electric and magnetization effects. Well-posedness of the model is obtained by means of semigroup theory. A passitivity assumption guarantees the boundedness of the associated semigroup. Further the exponential or polynomial decay of the energy is proved under suitable sufficient conditions. Finally, several illustrative examples are presented.