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On a boundary value problem in the theory of linear water waves
Author(s) -
Weck N.
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.1670120504
Subject(s) - mathematics , uniqueness , boundary value problem , mathematical analysis , domain (mathematical analysis) , boundary (topology) , displacement (psychology) , robin boundary condition , laplace operator , mixed boundary condition , psychology , psychotherapist
A body Ω floating in a fluid is subjected to small periodic displacement. Under idealized conditions the resulting wave pattern can be described by a linear boundary value problem for the Laplacian in an unbounded domain with a non‐coercive boundary condition on part of the boundary. Nevertheless uniqueness can be shown if Ω is confined to certain subsets of the fluid which can be described explicitly. This extends a result of V. G. Maz'ja saying that uniqueness holds provided that the exterior normal for ∂Ω avoids certain directions.