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The Helmholtz equation in a quadrant with Robin's conditions
Author(s) -
Penzel F.,
Teixeira F. S.
Publication year - 1999
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/(sici)1099-1476(199902)22:3<201::aid-mma32>3.0.co;2-t
Subject(s) - mathematics , helmholtz equation , boundary value problem , quadrant (abdomen) , mathematical analysis , equivalence (formal languages) , robin boundary condition , mixed boundary condition , pure mathematics , medicine , pathology
The boundary value problem for the Helmholtz equation in a quadrant with different Robin's or impedance‐type conditions is considered by the use of variational methods and boundary pseudodifferential equations. The coerciveness of the underlying sesquilinear form in dependence of the impedance parameters is proved. The equivalence between the boundary value problem and a scalar uniquely solvable Wiener–Hopf–Hankel equation is obtained. Copyright © 1999 John Wiley & Sons, Ltd.