Accession Number : ADA185124

Title :   On a Boundary Data Operator and Generalized Exterior Robin Problems for the Helmholtz Equation.

Descriptive Note : Interim rept.,

Corporate Author : NAVAL RESEARCH LAB WASHINGTON DC

Personal Author(s) : Dallas, Allan G

PDF Url : ADA185124

Report Date : 05 Aug 1987

Pagination or Media Count : 40

Abstract : This report deals with boundary-value problems for the equation Delta u + kappa-sq u = 0 in an exterior domain Omega + in euclidean three-space, with a boundary condition of the form del u/del nu + B(u bar gamma) = g; gamma: = del omega + is smooth, nu is the unit normal for gamma, g an element of (2) L 2 (gamma), and B is bounded linear operator in L (2) (gamma) such that i zeta-cap is dissipative for some zeta lying in a certain set depending upon kappa. It is required that the Neumann data del u/del nu and Dirichlet data u bar gamma be taken on in the normal -L (2) sense. The study is based upon the boundary-data operator A in L (2) (gamma), mapping del u/del nu to u bar gamma for appropriate outgoing solutions u in omega plus. By studying the operator I + BA, it is proven that the problem is well-posed and various construction techniques are established.

Descriptors :   *ACOUSTIC SCATTERING, *BOUNDARY VALUE PROBLEMS, OPERATORS(MATHEMATICS), HILBERT SPACE

Subject Categories : Acoustics
      Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE