High frequency limit of the Transport Cross Section and boundedness of the Total Cross Section in scattering by an obstacle with impedance boundary conditions

TL;DR

This paper proves the uniform boundedness of the total cross section for all frequencies and derives the high frequency limit of the transport cross section for scalar wave scattering by convex obstacles with impedance boundaries.

Contribution

It establishes the boundedness of the total cross section across all frequencies and calculates the high frequency limit of the transport cross section using variational methods.

Findings

Total cross section is uniformly bounded for all frequencies.

High frequency limit of the transport cross section is explicitly derived.

Results apply to scattering by convex obstacles with impedance boundary conditions.

Abstract

The scalar scattering of the plane wave by a strictly convex obstacle with impedance boundary conditions is considered. The uniform boundedness of the Total Cross Section for all values of frequencies is proved. The high frequency limit of the Transport Cross Section is founded and presented as a classical functional of the variational theory.