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An optimal control problem for the Helmholtz equation in a stratified Shallow ocean
Author(s) -
Xu Yongzhi
Publication year - 1990
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.1670130505
Subject(s) - mathematics , helmholtz equation , galerkin method , representation (politics) , scheme (mathematics) , optimal control , mathematical analysis , mathematical optimization , boundary value problem , finite element method , physics , politics , political science , law , thermodynamics
In this paper we shall consider a kind of optimal control of the Robin problem. First, we discuss the solvability of the Robin problem, which is not uniquely solvable in general. Then we find the representation of the far‐field pattern in terms of the minimal solution to an integral equation. Based on this representation, an optimization problem is discussed and a Galerkin scheme for the solution is presented.