Boundary value contact acoustic problems

Abstract

Boundary value contact problems are the problems of mathematical physics, whose statement contains some conditions at particular points or lines of the boundary. The purpose of this paper is to discuss some mathematical aspects of the BVCP, such as the correct functional classes and Fredholm type equations for the solution, the completeness of eigenfunctions, the connection between the BVCP and supersymmetric quantum mechanic, paritial radiation conditions, limiting absorption principle, existence of eigenfunctions in infinite domains, uniqueness of the solution, “optical” theorem, and so on.

Keywords:

• Helmholtz equation
• eigenfunctions
• radiation conditions
• uniqueness theorem
• operator pencils