On the scattered field generated by a ball inhomogeneity of constant index

Article type: Research Article

Authors: Capdeboscq, Yves

Affiliations: Mathematical Institute, 24-29 St. Giles, Oxford OX1 3LB, UK. E-mail: yves.capdeboscq@maths.ox.ac.uk

Abstract: We consider the solution of a scalar Helmholtz equation where the potential (or index) takes two positive values, one inside a disk of radius ε and another one outside. We derive sharp estimates of the size of the scattered field caused by this disk inhomogeneity, for any frequencies and any contrast. We also provide a broadband estimate, that is, a uniform bound for the scattered field for any contrast, and any frequencies outside of a set which tends to zero with ε.

Keywords: uniform scattering estimates, Helmholtz equation, Bessel function

DOI: 10.3233/ASY-2011-1080

Journal: Asymptotic Analysis, vol. 77, no. 3-4, pp. 197-246, 2012