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

DOI10.1016/j.jmaa.2019.02.042zbMath1416.35258arXiv1807.00098OpenAlexW2810192184WikidataQ115570284 ScholiaQ115570284MaRDI QIDQ2633736

Michael Pokojovy, Andrii Anikushyn

Publication date: 10 May 2019

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1807.00098

zbMATH Keywords

exponential stabilitywell-posednessMaxwell's equationsnonlinear boundary feedbackinstantaneous dampingtime-localized delay

Mathematics Subject Classification ID

Feedback control (93B52) Stability in context of PDEs (35B35) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Maxwell equations (35Q61) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (8)

Bifurcation analysis of a coupled system between a transport equation and an ordinary differential equation with time delay ⋮ Bifurcation theory of a coupled system modelling the blood flow control in the kidney ⋮ Finite element approximation for Maxwell's equations with Debye memory under a nonlinear boundary feedback with delay ⋮ Global well-posedness and exponential stability for Maxwell's equations under delayed boundary condition in metamaterials ⋮ Normal trace inequalities and decay of solutions to the nonlinear Maxwell system with absorbing boundary ⋮ A three-dimensional Petrov-Galerkin finite element interface method for solving inhomogeneous anisotropic Maxwell's equations in irregular regions ⋮ Active manipulation of exterior electromagnetic fields by using surface sources ⋮ Exponential decay of quasilinear Maxwell equations with interior conductivity

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• General decay rate estimate for the energy of a weak viscoelastic equation with an internal time-varying delay term
• Boundary regularity for Maxwell's equations with applications to shape optimization
• Existence and asymptotic stability of a viscoelastic wave equation with a delay
• Global existence and energy decay of solutions to a viscoelastic wave equation with a delay term in the non-linear internal feedback
• Partially delayed stabilizing feedbacks for Maxwell's system
• Exact boundary controllability of Maxwell's equations with weak conductivity in the heterogeneous medium inside a general domain
• Uniform boundary stabilization of semilinear wave equations with nonlinear boundary damping
• Exponential decay of solutions of Maxwell's equations coupled with a first-order ordinary differential equation for the polarization.
• Exponential decay for Maxwell equations with a boundary memory condition
• Decay rates for solutions of a Maxwell system with nonlinear boundary damping
• Internal and boundary observability estimates for the heterogeneous Maxwell's system
• Internal stabilization of Maxwell's equations in heterogeneous media
• Continuous observability for the anisotropic Maxwell system
• The Linear Sampling Method in Inverse Electromagnetic Scattering
• Stability and Instability Results of the Wave Equation with a Delay Term in the Boundary or Internal Feedbacks
• An Example on the Effect of Time Delays in Boundary Feedback Stabilization of Wave Equations
• Exact Boundary Controllability of Maxwell’s Equations in a General Region
• Un résultat de densité pour les équations de Maxwell régularisées dans un domaine lipschitzien
• Stabilization and Exact Boundary Controllability for Maxwell’s Equations
• Two examples of ill-posedness with respect to time delays revisited
• Boundary stabilization of Maxwell's equations with space-time variable coefficients
• Exact Boundary Controllability of Maxwell's Equations in Heterogeneous Media and an Application to an Inverse Source Problem
• Strong and Mild Extrapolated $L^{2}$-Solutions to the Heat Equation with Constant Delay
• Nonlinear Differential Equations of Monotone Types in Banach Spaces
• Exact internal controllability of Maxwell's equations
• Exact internal controllability of Maxwell's equations
• Exact boundary controllability of electromagnetic fields in a general region
• Semigroups and linear partial differential equations with delay

This page was built for publication: Global well-posedness and exponential stability for heterogeneous anisotropic Maxwell's equations under a nonlinear boundary feedback with delay