Reconstructing unknown inclusions for the biharmonic equation

2020/07/13 by Hwang, Gyeongha, Kar, Manas
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2007.06147

Abstract

Herein, we study an inverse problem for detecting unknown obstacles by the enclosure method using the Dirichlet--to--Neumann map for measurements. We justify the method for an penetrable obstacle case involving a biharmonic equation. We use complex geometrical optics solutions with a logarithmic phase to reconstruct some non--convex parts of the obstacle.

Related

• Revisiting the probe and enclosure methods
• The obstacle scattering for the biharmonic equation
• Inverse obstacle problem for the non-stationary wave equation with an unknown background
• An inverse obstacle problem with a single pair of Cauchy data: Laplace's equation case
• Reconstruction of penetrable obstacles in the anisotropic acoustic scattering