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... The initial condition Page 6. 328 M. Eller is (1.14) φ(0) = φ0, ∂tφ(0) = ψ0 and the boundary condition is (1.15) ν · (α∇φ) = g on Σ. The equation (1.13) is transformed into a symmetric hyperbolic system by setting u = (∂tφ, α∇φ)T ,... more
... The initial condition Page 6. 328 M. Eller is (1.14) φ(0) = φ0, ∂tφ(0) = ψ0 and the boundary condition is (1.15) ν · (α∇φ) = g on Σ. The equation (1.13) is transformed into a symmetric hyperbolic system by setting u = (∂tφ, α∇φ)T , Aj∂j = ( 0 −∇T −∇ 0 ) , E = ( 1 0 0 α−1 ) . ...
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We consider Maxwell's system with anisotropic coefficients, i.e., the electric permittivity and the magnetic permeability are assumed to be matrices with non-analytic entries. Under the additional... more
We consider Maxwell's system with anisotropic coefficients, i.e., the electric permittivity and the magnetic permeability are assumed to be matrices with non-analytic entries. Under the additional assumption that one matrix is a scalar multiple of the other we prove unique continuation of the system across non-characteristic surfaces. The proof relies on differential geometry as well as on Carleman estimates.
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Let 0266-5611/12/4/004/img1 be a three-dimensional body with an interior two-dimensional crack 0266-5611/12/4/004/img2. It will be shown that the location and size of the crack is uniquely determined by measurements on the boundary of... more
Let 0266-5611/12/4/004/img1 be a three-dimensional body with an interior two-dimensional crack 0266-5611/12/4/004/img2. It will be shown that the location and size of the crack is uniquely determined by measurements on the boundary of 0266-5611/12/4/004/img1. Moreover, the physical behaviour of the crack will be identified. Our model is the following. Inside the body, with the exception of the crack, we assume
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... optimization for the Maxwell equations under weaker regularity of the data Dérivée par rapport au domaine dans l'équation de Maxwell sous des hypothèses de plus faible régularité des données John Cagnol a,1 , Matthias Eller b,2 a... more
... optimization for the Maxwell equations under weaker regularity of the data Dérivée par rapport au domaine dans l'équation de Maxwell sous des hypothèses de plus faible régularité des données John Cagnol a,1 , Matthias Eller b,2 a École Centrale Paris, laboratoire MAS ...
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ABSTRACT
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. We prove exact controllability for Maxwell's system with variable coefficients in a bounded domain by a current flux in the boundary. The proof relies on a duality argument which... more
. We prove exact controllability for Maxwell's system with variable coefficients in a bounded domain by a current flux in the boundary. The proof relies on a duality argument which reduces the proof of exact controllability to the proof of continuous observability for the homogeneous adjoint system. There is no geometric restriction imposed on the domain.
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Holmgren's theorem guarantees unique continuation across non-characteristic surfaces of class C for solutions to homogeneous linear partial differential equations with analytic coefficients.... more
Holmgren's theorem guarantees unique continuation across non-characteristic surfaces of class C for solutions to homogeneous linear partial differential equations with analytic coefficients. Based on this result a global uniqueness theorem for solutions to hyperbolic differential equations with analytic coefficients in a space-time cylinder Q = (0, T) × Ω is established. Zero Cauchy data on a part of the lateral C -boundary will force every
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We examine the question of stabilization of the (nonstationary) heteregeneousMaxwell's equations in a bounded region with a Lipschitz boundaryby means of nonlinear Silver-Muller boundary condition. This requires thevalidity of some... more
We examine the question of stabilization of the (nonstationary) heteregeneousMaxwell's equations in a bounded region with a Lipschitz boundaryby means of nonlinear Silver-Muller boundary condition. This requires thevalidity of some stability estimate in the linear case that may be checked insome particular situations. As a consequence we get an explicit decay rateof the energy, for instance exponential, polynomial or logarithmic