Affiliation:
1. Université de Tunis El Manar, Ecole Nationale d'Ingénieurs de Tunis Tunis Tunisia
2. Institut Supérieur des Mathématiques Appliquées et de l'Informatique de Kairouan Avenue Assad Iben Fourat Kairouan Tunisia
Abstract
In this work, we establish a local stability estimate for a problem involving the reconstruction of a domain
in the time‐fractional diffusion equation with an order of
:
from the knowledge of a Neumann additional data on a part of the boundary. This problem is motivated by several applications in anomalous diffusion phenomena. The stability estimate is obtained through a straightforward approach utilizing shape optimization techniques. To reconstruct the domain
, we formulate the inverse problem as a shape optimization one by minimizing a least‐squares cost function. Using the topological derivative method, we perform a noniterative algorithm for numerically recovering the location and shape of the unknown domain. Finally, we demonstrate the effectiveness of our approach in reconstructing multiple subdomains of varying shapes and sizes, considering noisy data, through numerical experiments.
Subject
General Engineering,General Mathematics
Cited by
1 articles.
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