Strong unique continuation property for time harmonic Maxwell equations

Okaji, Takashi

doi:10.2969/jmsj/1191593956

Cited by 29 publications

(33 citation statements)

References 7 publications

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“…It is not restrictive to assume that M = 1 and that x 1 = 0. We can write E †,1 = K 1 +Ê †,1 and E †,2 = K 2 +Ê †,2 , where K 1 and K 2 are defined as in (15), with two different polarizations q 0,1 and q 0,2 ; in particular, we know thatÊ †,1 andÊ †,2 belong to H(curl; Ω). Proceeding as before, the unique continuation principle yields E †,1 = E †,2 in Ω\B r (0) for each r > 0, therefore…”

Section: Theorem 42 Assuming That Conditionmentioning

confidence: 99%

Inverse source problems for eddy current equations

2011

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Abstract. We study the inverse source problem for the eddy current approximation of Maxwell equations. As for the full system of Maxwell equations, we show that a volume current source cannot be uniquely identified by the knowledge of the tangential components of the electromagnetic fields on the boundary, and we characterize the space of non-radiating sources. On the other hand, we prove that the inverse source problem has a unique solution if the source is supported on the boundary of a subdomain or if it is the sum of a finite number of dipoles. We address the applicability of this result for the localization of brain activity from electroencephalography and magnetoencephalography measurements.

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Section: Theorem 42 Assuming That Conditionmentioning

confidence: 99%

Inverse source problems for eddy current equations

2011

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“…The coefficients c and a are assumed to be piecewise C1 functions and any surfaces of discontinuity are assumed to be smooth. The latter assumption is made so that we can apply the unique continuation results of [21] (in [19] it is commented that the continuation property extends to piecewise C 1 functions under even more general conditions on the interface between regions where the coefficients are smooth). Given a current density J supported in £, the resulting electromagnetic field described by the electric field E and magnetic field H satisfies the following Maxwell system where w > 0 is the frequency of the time harmonic field:…”

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confidence: 99%

The inverse source problem for Maxwell's equations

Albanese¹,

Monk²

2006

Inverse Problems

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Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for resiewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing this collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden to Department of Defense, Washington Headquarters Services, Directorate for Information Operations and Reports (0704-0188), 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302, Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. REPORT DATE (DD-MM-YYYY)2 SUPPLEMENTARY NOTESFinal report delivered by the AFOSR contractor (Monk) to the government (AFRL/HEX members contributing) based upon EEG data supplied by Dr. James Kroger, New Mexico State University.10-26-06: Cleared for public release; PA-06-382 14. ABSTRACT The inverse source problem for Maxwell's equations is considered. We show that the problem of finding a volume current density from surface measurements does not have a unique solution, and we characterize the nonuniqueness. We also show that if further information is available the inverse source problem may have a unique solution. The method is useful for the quantitative determination of interior brain currents from surface electroencephalographic measurements. The application is to prosthesis control. Abstract. The inverse source problem for Maxwell's equations is considered. We show that the problem of finding a volume current density from surface measurements does not have a unique solution, and characterize the non-uniqueness. We also show that if further a priori information is available, the inverse source problem may have a unique solution (in particular for surface currents or dipole sources). SUBJECT

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“…There are not so many articles in the mathematical literature giving rigorous results on the anisotropic case for Maxwell's equations. Let us mention some of them: V. Vogelsang [16] and T. Okaji [14] proved strong unique continuation for time-harmonic anisotropic Maxwell's equations, V. G. Yakhno [17] gave a construction of a Green's function for the time-dependent anisotropic Maxwell's system, M. Eller [4,5] proved a unique continuation of the system across non-characteristic surfaces and also a boundary observability inequality for the anisotropic case. This result implies the exact boundary controllability of an electromagnetic field in Ω, M. Eller and M. Yamamoto [8] obtained a Carleman estimate for the time-harmonic anisotropic Maxwell system.…”

Section: Cleverson R Da Luz and Gustavo P Menzalamentioning

confidence: 99%

Uniform stabilization of anisotropic Maxwell's equations with boundary dissipation

Luz¹,

Menzala²

2009

Discrete &Amp; Continuous Dynamical Systems - S

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We consider the Maxwell system with variable anisotropic coefficients in a bounded domain Ω of R 3 . The boundary conditions are of Silver-Muller's type. We proved that the total energy decays exponentially fast to zero as time approaches infinity. This result is well known in the case of isotropic coefficients. We make use of modified multipliers with the help of an elliptic problem and some technical assumptions on the permittivity and permeability matrices.2000 Mathematics Subject Classification. Primary: 35Q99, 35Q60, 35L99.

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Strong unique continuation property for time harmonic Maxwell equations

Cited by 29 publications

References 7 publications

Inverse source problems for eddy current equations

Inverse source problems for eddy current equations

The inverse source problem for Maxwell's equations

Uniform stabilization of anisotropic Maxwell's equations with boundary dissipation

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