An inverse hyperbolic obstacle problem
Mourad Choulli, Hiroshi Takase
TL;DR
This paper proves the stability of reconstructing an unknown boundary function of an obstacle in a hyperbolic PDE from boundary measurements, advancing inverse problem theory.
Contribution
It establishes Hölder stability for an inverse hyperbolic obstacle problem, providing new insights into boundary reconstruction from limited measurements.
Findings
Proves Hölder stability in the inverse problem
Reconstructs boundary functions from boundary measurements
Advances understanding of hyperbolic inverse obstacle problems
Abstract
We establish H\"older stability of an inverse hyperbolic obstacle problem. Mainly, we study the problem of reconstructing an unknown function defined on the boundary of the obstacle from two measurements taken on the boundary of a domain surrounding the obstacle.
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Taxonomy
TopicsNumerical methods in inverse problems · Point processes and geometric inequalities · 3D Shape Modeling and Analysis