Research output: Contribution to journal › Article
Spectrum of the linear water model for a two-layer liquid with cuspidal geometries at the interface. / Martin, J.; Nazarov, S.A.; Taskinen, J.
In: ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik, No. 8, 2015, p. 859-876.Research output: Contribution to journal › Article
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TY - JOUR
T1 - Spectrum of the linear water model for a two-layer liquid with cuspidal geometries at the interface
AU - Martin, J.
AU - Nazarov, S.A.
AU - Taskinen, J.
PY - 2015
Y1 - 2015
N2 - © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.We show that the linear water wave problem in a bounded liquid domain may have continuous spectrum, if the interface of a two-layer liquid touches the basin walls at zero angle. The reason for this phenomenon is the appearance of cuspidal geometries of the liquid phases. We calculate the exact position of the continuous spectrum. We also discuss the physical background of wave propagation processes, which are enabled by the continuous spectrum. Our approach and methods include constructions of a parametrix for the problem operator and singular Weyl sequences.
AB - © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.We show that the linear water wave problem in a bounded liquid domain may have continuous spectrum, if the interface of a two-layer liquid touches the basin walls at zero angle. The reason for this phenomenon is the appearance of cuspidal geometries of the liquid phases. We calculate the exact position of the continuous spectrum. We also discuss the physical background of wave propagation processes, which are enabled by the continuous spectrum. Our approach and methods include constructions of a parametrix for the problem operator and singular Weyl sequences.
U2 - 10.1002/zamm.201300212
DO - 10.1002/zamm.201300212
M3 - Article
SP - 859
EP - 876
JO - ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik
JF - ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik
SN - 0044-2267
IS - 8
ER -
ID: 4012022