The inverse problem consists of finding {ε[x]−ε0,σ[x]} from the knowledge of the wave fronts τk[x] on ∂B and of the tangential components {FH[x,t,v(k),FE[x,t,v(k)]}≡{F(k)H,F(k)E} of the four electromagnetic fields {H(k),E(k)} on S[v(k)], k=1,2,3,4. Reviewer's remarks: 1. To the extent to which both the dependence of {ε,σ} on frequency and the Kramers-Kronig relations can be neglected, these results can be applied to inverse problems for penetrable obstacles in the time domain. 2. The idea of "identifying coefficients'' (in quite general terms) by means of multiple data sets and by solving algebraic systems derived therefrom is another basic joint contribution by the author [M. M. Lavrentʹev, V. G. Romanov and S. P. Šišatskiĭ, Ill-posed problems of mathematical physics and analysis (Russian), "Nauka'', Moscow, 1980; MR0591674 (82g:65003) (Chapter VII, Section 2)]: this paper further demonstrates how fruitful such a scheme still is, even in complex situations.

Crosta, G. (2006). Mathematical Review: MR2123298 (2006b:35347) Romanov, V. G. An estimate for the stability of the solution of a three-dimensional inverse problem for a system of Maxwell equations. (Russian). MATHEMATICAL REVIEWS.

Mathematical Review: MR2123298 (2006b:35347) Romanov, V. G. An estimate for the stability of the solution of a three-dimensional inverse problem for a system of Maxwell equations. (Russian)

CROSTA, GIOVANNI FRANCO FILIPPO
2006

Abstract

The inverse problem consists of finding {ε[x]−ε0,σ[x]} from the knowledge of the wave fronts τk[x] on ∂B and of the tangential components {FH[x,t,v(k),FE[x,t,v(k)]}≡{F(k)H,F(k)E} of the four electromagnetic fields {H(k),E(k)} on S[v(k)], k=1,2,3,4. Reviewer's remarks: 1. To the extent to which both the dependence of {ε,σ} on frequency and the Kramers-Kronig relations can be neglected, these results can be applied to inverse problems for penetrable obstacles in the time domain. 2. The idea of "identifying coefficients'' (in quite general terms) by means of multiple data sets and by solving algebraic systems derived therefrom is another basic joint contribution by the author [M. M. Lavrentʹev, V. G. Romanov and S. P. Šišatskiĭ, Ill-posed problems of mathematical physics and analysis (Russian), "Nauka'', Moscow, 1980; MR0591674 (82g:65003) (Chapter VII, Section 2)]: this paper further demonstrates how fruitful such a scheme still is, even in complex situations.
Recensione in rivista
Maxwell equations; inverse permittivity and conductivity; stability estimates; multiple data sets
English
2006
none
Crosta, G. (2006). Mathematical Review: MR2123298 (2006b:35347) Romanov, V. G. An estimate for the stability of the solution of a three-dimensional inverse problem for a system of Maxwell equations. (Russian). MATHEMATICAL REVIEWS.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/29895
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