Global well-posedness and exponential stability for heterogeneous anisotropic Maxwell's equations under a nonlinear boundary feedback with delay

@article{Anikushyn2019GlobalWA,
  title={Global well-posedness and exponential stability for heterogeneous anisotropic Maxwell's equations under a nonlinear boundary feedback with delay},
  author={Andrii Anikushyn and Michael Pokojovy},
  journal={Journal of Mathematical Analysis and Applications},
  year={2019}
}
Abstract We consider an initial–boundary value problem for the Maxwell's system in a bounded domain with a linear nonhomogeneous anisotropic instantaneous material law subject to a nonlinear Silver–Muller-type boundary feedback mechanism incorporating both an instantaneous damping and a time-localized delay effect. By proving the maximal monotonicity property of the underlying nonlinear generator, we establish the global well-posedness in an appropriate Hilbert space. Further, under suitable… Expand
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References

SHOWING 1-10 OF 41 REFERENCES
Boundary stabilization of quasilinear Maxwell equations
We investigate an initial-boundary value problem for a quasilinear nonhomogeneous, anisotropic Maxwell system subject to an absorbing boundary condition of Silver & M\"uller type in a smooth,Expand
Strong and Mild Extrapolated L2-Solutions to the Heat Equation with Constant Delay
TLDR
An exponential decay rate for the energy in the dissipative case is proved and an explicit representation of solutions is given and it is shown that lower order regularizations lead to ill-posedness, also for higher order equations. Expand
EXACT BOUNDARY CONTROLLABILITY OF MAXWELL'S EQUATIONS WITH WEAK CONDUCTIVITY IN THE HETEROGENEOUS MEDIUM INSIDE A GENERAL DOMAIN
This paper considers the question of control of Maxwell’s Equations (ME) in a non-homogeneous medium with positive conductivity by means of boundary surface currents applied over the entire boundary.Expand
Exact Boundary Controllability of Maxwell's Equations in Heterogeneous Media and an Application to an Inverse Source Problem
  • S. Nicaise
  • Mathematics, Computer Science
  • SIAM J. Control. Optim.
  • 2000
TLDR
The question of control of Maxwell's equations in a heterogeneous medium with a nonsmooth boundary by means of control currents on the boundary of that medium is examined, and some energy estimates are established which allow for the control results owing to the Hilbert uniqueness method. Expand
Continuous Observability for the Anisotropic Maxwell System
A boundary observability inequality for the homogeneous Maxwell system with variable, anisotropic coefficients is proved. The result implies uniqueness for an ill-posed Cauchy problem for Maxwell'sExpand
Stability and Instability Results of the Wave Equation with a Delay Term in the Boundary or Internal Feedbacks
TLDR
This paper considers the wave equation with a delayed velocity term and mixed Dirichlet-Neumann boundary condition and proves exponential stability of the solution under suitable assumptions. Expand
Boundary stabilization of Maxwell's equations with space-time variable coefficients
We consider the stabilization of Maxwell's equations with space-time variable coefficients in a bounded region with a smooth boundary by means of linear or nonlinear Silver–Muller boundary condition.Expand
On a Kelvin-Voigt Viscoelastic Wave Equation with Strong Delay
TLDR
An initial-boundary value problem for a viscoelastic wave equation subject to a strong time-localized delay in a Kelvin & Voigt-type material law is considered and a global well-posedness theory is established using the operator semigroup theory both in Sobolev-valued $C^{0}$- and BV-spaces. Expand
Internal stabilization of Maxwell's equations in heterogeneous media
We consider the internal stabilization of Maxwell's equations with Ohm's law with space variable coefficients in a bounded region with a smooth boundary. Our result is mainly based on an Expand
Boundary regularity for Maxwell's equations with applications to shape optimization
Abstract The dynamic Maxwell equations with a strictly dissipative boundary condition is considered. Sharp trace regularity for the electric and the magnetic field are established for both: weak andExpand
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