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Boundary conditions in acoustic scattering with respect to the reciprocity relation
Author(s) -
Reissinger Jörg
Publication year - 1993
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670161005
Subject(s) - mathematics , boundary value problem , reciprocity (cultural anthropology) , helmholtz equation , uniqueness , mathematical analysis , constructive , unification , scattering , mixed boundary condition , scalar (mathematics) , geometry , physics , optics , computer science , process (computing) , programming language , operating system , psychology , social psychology
A new concept associated with the reciprocity relation in acoustic scattering is introduced. Motivated by this well‐known relation, which holds in all the classical cases, more general boundary value problems for the scalar Helmholtz equation are studied. These generalized boundary conditions are characterized by the validity of the reciprocity relation and seem to be an appropriate unification of a large class of boundary value problems in acoustic scattering. The well‐known results for the classical problems can be extended to this general case and also new connections with the question about existence and uniqueness of solutions to the boundary value problems can be derived. A constructive procedure shows that this approach is applicable for a large class of boundary conditions.