Functional Analysis and Applications Seminar 

07/04/2010, 11:15 — 12:15 — Room P1, Mathematics Building
Luís Castro, Universidade de Aveiro

Integral equation modelling of electromagnetic scattering by waveguides

We will propose an integral equation analysis of electromagnetic scattering by waveguides based on the characterization of the Fredholm property and Douglis-Nirenberg ellipticity of corresponding integral operators. As a prototype, the scattering of time-harmonic electromagnetic waves by an infinitely long cylindrical orthotropic waveguide iris will be considered in detail. This will be done by using an orthotropic Maxwell system in a cylindrical waveguide iris for plane waves, imbedded in an isotropic infinite medium. This complicated 3D problem is successfully reduced to the solution of a simpler 2D problem. The unique solvability of the associated boundary value problems is proved and regularity of solutions is also obtained in Bessel potential spaces. Part of the talk is based on a joint work with R. Duduchava and D. Kapanadze.