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Main Title: Stability analysis in the inverse Robin transmission problem
Author(s): Meftahi, Houcine
Type: Article
Language Code: en
Abstract: In this paper, we consider the conductivity problem with piecewise‐constant conductivity and Robin‐type boundary condition on the interface of discontinuity. When the quantity of interest is the jump of the conductivity, we perform a local stability estimate for a parameterized non‐monotone family of domains. We give also a quantitative stability result of local optimal solution with respect to a perturbation of the Robin parameter. In order to find an optimal solution, we propose a Kohn–Vogelius‐type cost functional over a class of admissible domains subject to two boundary values problems. The analysis of the stability involves the computation of first‐order and second‐order shape derivative of the proposed cost functional, which is performed rigorously by means of shape‐Lagrangian formulation without using the shape sensitivity of the states variables.
Issue Date: 2016
Date Available: 7-Feb-2019
DDC Class: 510 Mathematik
Subject(s): stability analysis
second-order shape derivative
Lagrange formulation
Journal Title: Mathematical Methods in the Applied Sciences
Publisher: Wiley
Publisher Place: Chichester
Volume: 40
Issue: 7
Publisher DOI: 10.1002/mma.4173
Page Start: 2505
Page End: 2521
EISSN: 1099-1476
ISSN: 0170-4214
Appears in Collections:Inst. Mathematik » Publications

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