Journal
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Volume 531, Issue 1, Pages -Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2023.127814
Keywords
Inverse boundary obstacle problem; External measurements; Stokes system; Navier slip boundary conditions; Wave equation; Zaremba problem
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This paper presents a numerical study on the inverse problem of identifying an obstruction in a 2D duct, which provides a new approach to solve the life-threatening disease of stenosis in coronary vessels in the medical field.
The problem of identifying an obstruction within a fluid duct has several applications, one of which is in medicine, where the presence of stenosis in coronary vessels poses a life-threatening disease. In this paper, we formulate a continuous setting and study from a numerical perspective the inverse problem of identifying an obstruction contained in a 2D duct where a Stokes flow hits the boundary (subject to Dirichlet and Navier-slip boundary conditions), generating an acoustic wave. To be precise, using acoustic wave measurements at certain points on the exterior of the duct, we can identify the location, extent, and height of the obstruction. Thus, our framework offers an external approach to solving this inverse-obstacle problem. Synthetic examples are used to verify the effectiveness of the proposed numerical formulation.(c) 2023 Elsevier Inc. All rights reserved
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