Long-time behaviour of the solution of Maxwell’s equations in dissipative generalized Lorentz materials. I: A frequency-dependent Lyapunov function approach. (English) Zbl 1525.35213
The authors aim to quantify the loss in dissipative media through a generalized Drude-Lorentz model. They consider the long-time decay rate of the electromagnetic energy and show, using Lyapunov estimates, that this decay is polynomial in time. Frequency dependent Lyapunov functions are introduced which can distinguish between low and high frequencies. The authors also discuss how to apply their method to bounded domains. Semigroup methods in particular are employed throughout.
Reviewer: Eric Stachura (Marietta)
MSC:
| 35Q61 | Maxwell equations |
| 35Q60 | PDEs in connection with optics and electromagnetic theory |
| 78A60 | Lasers, masers, optical bistability, nonlinear optics |
| 78A35 | Motion of charged particles |
| 35L45 | Initial value problems for first-order hyperbolic systems |
| 37C75 | Stability theory for smooth dynamical systems |
| 34D20 | Stability of solutions to ordinary differential equations |
| 35B05 | Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs |
Keywords:
Maxwell’s equations; passive electromagnetic media; dissipative generalized Lorentz models; long-time electromagnetic energy decay rate; frequency-dependent Lyapunov estimatesReferences:
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