TY - JOUR

T1 - The enclosure method for a generalized anisotropic complex conductivity equation

AU - Kuan, Rulin

N1 - Publisher Copyright:
© 2021 IOP Publishing Ltd.

PY - 2021/5

Y1 - 2021/5

N2 - We study how to apply the enclosure method to reconstruct an unknown inclusion within a medium in a domain in ℝn which satisfies the conductivity equation ∇ ⋅ ((σ 0 + iϵ 0)∇u) = 0 with σ 0 and ϵ 0 being real matrix functions. Motivated by some real world applications, we assume the unknown inclusion satisfies an equation of the more general form ∇ ˙ ((σ + iϵ) ∇ u+ ζ ∇ u)= 0, where σ, ϵ, ζ are also real matrix functions. Due to the anisotropy, it is in general difficult to find complex geometric optics solutions. Therefore, we construct the oscillating decaying solutions, which is used to test whether a given half-space intersects the unknown inclusion or not.

AB - We study how to apply the enclosure method to reconstruct an unknown inclusion within a medium in a domain in ℝn which satisfies the conductivity equation ∇ ⋅ ((σ 0 + iϵ 0)∇u) = 0 with σ 0 and ϵ 0 being real matrix functions. Motivated by some real world applications, we assume the unknown inclusion satisfies an equation of the more general form ∇ ˙ ((σ + iϵ) ∇ u+ ζ ∇ u)= 0, where σ, ϵ, ζ are also real matrix functions. Due to the anisotropy, it is in general difficult to find complex geometric optics solutions. Therefore, we construct the oscillating decaying solutions, which is used to test whether a given half-space intersects the unknown inclusion or not.

UR - http://www.scopus.com/inward/record.url?scp=85104928425&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85104928425&partnerID=8YFLogxK

U2 - 10.1088/1361-6420/abf163

DO - 10.1088/1361-6420/abf163

M3 - Article

AN - SCOPUS:85104928425

VL - 37

JO - Inverse Problems

JF - Inverse Problems

SN - 0266-5611

IS - 5

M1 - 055010

ER -