TY - JOUR

T1 - On a nonlinear partial differential equation arising in magnetic resonance electrical impedance tomography

AU - Kim, Sungwhan

AU - Kwon, Ohin

AU - Seo, Jin Keun

AU - Yoon, Jeong Rock

N1 - Copyright:
Copyright 2004 Elsevier Science B.V., Amsterdam. All rights reserved.

PY - 2003

Y1 - 2003

N2 - This paper considers the fundamental questions, such as existence and uniqueness, of a mathematical model arising in the MREIT system, which is an electrical impedance tomography technique integrated with magnetic resonance imaging. The mathematical model for MREIT is the Neumann problem of a nonlinear elliptic partial differential equation ∇ · (a(x)/|∇u(x)| ∇u(x)) = 0. We show that this Neumann problem belongs to one of two cases: either infinitely many solutions exist or no solution exists. This explains rigorously the reason why we have used the modified model in [O. Kwon, E. J. Woo, J. R. Yoon, and J. K. Seo, IEEE Trans. Biomed. Engrg., 49 (2002), pp. 160-167], which is a system of the Neumann problem associated with two different Neumann data. For this modified system, we prove a uniqueness result on the edge detection of a piecewise continuous conductivity distribution.

AB - This paper considers the fundamental questions, such as existence and uniqueness, of a mathematical model arising in the MREIT system, which is an electrical impedance tomography technique integrated with magnetic resonance imaging. The mathematical model for MREIT is the Neumann problem of a nonlinear elliptic partial differential equation ∇ · (a(x)/|∇u(x)| ∇u(x)) = 0. We show that this Neumann problem belongs to one of two cases: either infinitely many solutions exist or no solution exists. This explains rigorously the reason why we have used the modified model in [O. Kwon, E. J. Woo, J. R. Yoon, and J. K. Seo, IEEE Trans. Biomed. Engrg., 49 (2002), pp. 160-167], which is a system of the Neumann problem associated with two different Neumann data. For this modified system, we prove a uniqueness result on the edge detection of a piecewise continuous conductivity distribution.

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U2 - 10.1137/S0036141001391354

DO - 10.1137/S0036141001391354

M3 - Article

AN - SCOPUS:0037512368

VL - 34

SP - 511

EP - 526

JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

SN - 0036-1410

IS - 3

ER -