TY - JOUR

T1 - Asymptotic properties of the spectrum in the problem on waves in a bounded volume on a two-layer fluid

AU - Nazarov, S. A.

PY - 2013/12/1

Y1 - 2013/12/1

N2 - The asymptotic of eigen frequencies and corresponding waves on the free surface and interface of a two-layer ideal heavy fluid is constructed in two cases: the fluid is almost uniform and the upper layer has a low density. The asymptotic formulae are jusitified under the condition that the volume of the fluid is bounded. For the problem of surface waves, travelling in a submerged or surface-piercing infinite cylinder, the sufficient conditions for localized solutions of the limit problems to exist are indicated, and the hypothesis on the inevitable trapping of a wave by the body, which does not intersect both surfaces, is also formulated.

AB - The asymptotic of eigen frequencies and corresponding waves on the free surface and interface of a two-layer ideal heavy fluid is constructed in two cases: the fluid is almost uniform and the upper layer has a low density. The asymptotic formulae are jusitified under the condition that the volume of the fluid is bounded. For the problem of surface waves, travelling in a submerged or surface-piercing infinite cylinder, the sufficient conditions for localized solutions of the limit problems to exist are indicated, and the hypothesis on the inevitable trapping of a wave by the body, which does not intersect both surfaces, is also formulated.

UR - http://www.scopus.com/inward/record.url?scp=84896700498&partnerID=8YFLogxK

U2 - 10.1016/j.jappmathmech.2013.12.005

DO - 10.1016/j.jappmathmech.2013.12.005

M3 - Article

AN - SCOPUS:84896700498

VL - 77

SP - 494

EP - 507

JO - Journal of Applied Mathematics and Mechanics

JF - Journal of Applied Mathematics and Mechanics

SN - 0021-8928

IS - 5

ER -