2,058 research outputs found
A singular perturbation problem in exact controllability of the Maxwell system
Abstract. This paper studies the exact controllability of the Maxwell system in a bounded domain, controlled by a current flowing tangentially in the boundary of the region, as well as the exact con-trollability the same problem but perturbed by a dissipative term multiplied by a small parameter in the boundary condition. This boundary perturbation improves the regularity of the problem and is therefore a singular perturbation of the original problem. The purpose of the paper is to examine the connection, for small values of the perturbation parameter, between observability estimates for the two systems, and between the optimality systems corresponding to the problem of norm minimum exact control of the solutions of the two systems from the rest state to a specied terminal state
Global Well-Posedness and Exponential Stability for Heterogeneous Anisotropic Maxwell's Equations under a Nonlinear Boundary Feedback with Delay
We consider an initial-boundary value problem for the Maxwell's system in a
bounded domain with a linear inhomogeneous 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 assumptions and geometric conditions, we show
the system is exponentially stable.Comment: updated and improved versio
Controllability of a viscoelastic plate using one boundary control in displacement or bending
In this paper we consider a viscoelastic plate (linear viscoelasticity of the
Maxwell-Boltzmann type) and we compare its controllability properties with the
(known) controllability of a purely elastic plate (the control acts on the
boundary displacement or bending). By combining operator and moment methods, we
prove that the viscoelastic plate inherits the controllability properties of
the purely elastic plate
On the controllability of the 2-D Vlasov-Stokes system
In this paper we prove an exact controllability result for the Vlasov-Stokes
system in the two-dimensional torus with small data by means of an internal
control. We show that one can steer, in arbitrarily small time, any initial
datum of class C 1 satisfying a smallness condition in certain weighted spaces
to any final state satisfying the same conditions. The proof of the main result
is achieved thanks to the return method and a Leray-Schauder fixed-point
argument
Lack of controllability of the heat equation with memory
We consider a model for the heat equation with memory, which has infinite propagation speed, like the standard heat equation. We prove that, in spite of this, for every T > 0 there exist square integrable initial data which cannot be steered to hit zero at time T , using square integrable controls. We show that the counterexample we present complies with the restrictions imposed by the second principle of thermodynamic
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