TY - JOUR
T1 - On uniqueness in the problem of gravity–capillary water waves above submerged bodies
JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science
JO - PROC R SOC A
M3 - 10.1098/rspa.2009.0012
AU - Motygin, Oleg V
AU - McIver, Philip
Y1 - 2009/01/01
UR - http://rspa.royalsocietypublishing.org/content/early/2009/03/06/rspa.2009.0012.abstract
N2 - In this paper, we consider the two-dimensional linear problem of wave–body interaction with surface tension effects being taken into account. We suggest a criterion for unique solvability of the problem based on symmetrization of boundary integral equations. The criterion allows us to develop an algorithm for detecting non-uniqueness (finding trapped modes) for given geometries of bodies; examples of numerical computation of trapped modes are given. We also prove a uniqueness theorem that provides simple bounds for the possible non-uniqueness parameters.
ER -