Repositorio
Institucional

Lecaros, Rodrigo

Montecinos, Gino

Ortega, Jaime H.

Ramirez-Ganga, Javier

CGO SOLUTIONS FOR COUPLED CONDUCTIVITY EQUATIONS

EDITURA ACAD ROMANE

MATHEMATICAL REPORTS

en

This paper is devoted to study of complex geometrical optics (CGO) solutions to the coupled conductivity equations written in a matrix form div (Q center dot del U) - 0 in R-2 for symmetric, positive definite matrix functions Q. The CGO solutions were introduced by Faddeev in 1966 [8] to prove the uniqueness in the inverse potential scattering problem for Schodinger equation, later Sylvester and Uhlmann in 1987 [26] use the CGO functions to study the uniqueness of the Calderon's inverse problem. Following the ideas of Astala and Paivarinta [3], we compute CGO solutions considering the vectorial solutions of an associated Beltrami system. In this work, we first prove the existence of CGO solution and then use a numerical strategy based on the method introduced by Huhtanem and Peramaki in [12] for the Beltrami equation. Numerical experiments are considered to show the influence of coupled equations.

artículo original

This work was partially supported by Centro de Modelamiento Matematico (CMM) Grant ANID ACE210010 and Basal FB210005. R. Lecaros was partially supported by FONDECYT (Chile) Grant 11180874. G. Montecinos was partially supported by FONDECYT (Chile), in the frame of the research project for Initiation in Research Grant 11180926. J. H. Ortega was partially supported by FONDECYT (Chile) Grant 1201125.

Este trabajo fue parcialmente apoyado por la Beca ANID ACE210010 del Centro de Modelamiento Matemático (CMM) y Basal FB210005. R. Lecaros fue parcialmente apoyado por FONDECYT (Chile) Beca 11180874. G. Montecinos fue parcialmente apoyado por FONDECYT (Chile), en el marco del proyecto de investigación de Iniciación a la Investigación Beca 11180926. J. H. Ortega fue parcialmente apoyado por FONDECYT (Chile) Subvención 1201125.

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inverse problems

inverse conductivity problem

complex geometrical optics

electrical impedance tomography

dbar-equation

numerical solution of PDEs

CALDERONS INVERSE PROBLEM

GLOBAL UNIQUENESS

IDENTIFICATION

Matemáticas

problemas inversos

problema de conductividad inversa

óptica geométrica compleja

tomografía de impedancia eléctrica

ecuación de dbar

solución numérica de PDEs

PROBLEMA INVERSO DE CALDERONES

SINGICIDAD GLOBAL

IDENTIFICACIÓN

CGO SOLUTIONS FOR COUPLED CONDUCTIVITY EQUATIONS

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artículo original

version publicada

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acceso abierto

acceso abierto

ANID ACE210010

ANID FB210005

ANID-FONDECYT 1201125

ANID-FONDECYT 11180874

ANID-FONDECYT 11180926