Stabilization and Exact Boundary Controllability for Maxwell’s Equations

Kapitonov, Boris V.

doi:10.1137/s0363012991218487

Cited by 41 publications

(37 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Therefore if the initial data E h0 and H h0 are discrete divergence free then the solution E h and H h of (11)-(15) will be discrete divergence free at all times thanks to (11) and (12). Finally we introduce the discrete integral…”

Section: Discretization By Yee's Scheme Of Maxwell's Systemmentioning

confidence: 99%

“…Recently boundary controllability and stability results of Maxwell's equations have been obtained using different methods, like the multiplier method, the microlocal analysis, the frequency domain method or a combination of them [31,13,14,16,12,25,28,29,33,26,27,4]. Usually these results are based on an observability estimate guaranteeing that the total energy of solutions can be estimated in terms of some local measurements.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Boundary observability of a numerical approximation scheme of Maxwell’s system in a cube

Nicaise

2008

Collect. Math.

View full text Add to dashboard Cite

We consider a numerical space discretization of Maxwell's system by the socalled Yee's scheme. For such a scheme, we first show that the boundary observability estimate is not uniform with respect to the mesh size. Using a discrete multiplier method, we prove an observability estimate that separates the low and high frequency contributions. We then describe one of its consequence to control problem, namely the Tychonoff regularization technique that shows that the discrete system with a discrete boundary control with additional internal controls (tending to zero as the mesh size goes to zero) converges to the continuous system with a boundary control.

show abstract

Section: Discretization By Yee's Scheme Of Maxwell's Systemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Boundary observability of a numerical approximation scheme of Maxwell’s system in a cube

Nicaise

2008

Collect. Math.

View full text Add to dashboard Cite

show abstract

“…In the linear case, for purposes of exact controllability (see for example [4], [5], [7] and the references therein) in order to use Russell's ''controllability via stabilizability'' principle several authors studied such boundary stabilization. However, when the dissipation includes a term of memory type, there are only a few articles considering the transmission problem together with the stabili- zation as t !…”

Section: Dgmentioning

confidence: 99%

Boundary Stabilization and a Problem of Transmission for a System of Propagation of Sound

Kapitonov¹,

Menzala²

2006

View full text Add to dashboard Cite

Abstract. We consider a transmission problem for a model describing the evolution of sound in a compressible fluid. Assuming that dissipative mechanisms of memory type are e¤ective in part of the boundary, the coe‰cients are piecewise constants and suitable geometric conditions on the domain and the interfaces, we prove that the total energy associated with the model decays exponentially fast as t ! þy.

show abstract

“…Stabilization for the Maxwell system with the Silver-Müller absorbing boundary conditions and exact controllability for corresponding initial boundary value problem have been studied by V. Komornik [17], P. Martinez [24] and N. Weck [28]. The uniform exponential decay of solutions of Maxwell's equations with boundary dissipation and exact boundary controllability was proved in [7], [8].…”

Section: Introductionmentioning

confidence: 99%

“…Uniform stabilization and exact control for the Maxwell system in multilayered media were investigated in [8]. The question of boundary controllability in transmission problems for the wave equation has been considered by J.-L. Lions [23], and S. Nicaise [25], [26].…”

Section: Introductionmentioning

confidence: 99%

Simultaneous exact control of piezoelectric systems in multilayered media

Kapitonov¹,

Raupp²

2003

Mat. apl. comput.

View full text Add to dashboard Cite

Abstract. This paper considers a pair of transmission problems for the system of piezoelectricity having piecewise constant coefficients. Under suitable monotonicity conditions on the coefficients and certain geometric conditions on the domain and the interfaces where the coefficients have a jump discontinuity, results on simultaneous boundary observation and simultaneous exact control are established.Mathematical subject classification: 35L50; 35Q60; 35B40.

show abstract

Stabilization and Exact Boundary Controllability for Maxwell’s Equations

Cited by 41 publications

References 12 publications

Boundary observability of a numerical approximation scheme of Maxwell’s system in a cube

Boundary observability of a numerical approximation scheme of Maxwell’s system in a cube

Boundary Stabilization and a Problem of Transmission for a System of Propagation of Sound

Simultaneous exact control of piezoelectric systems in multilayered media

Contact Info

Product

Resources

About