Communications in Mathematical Analysis

A Note on Embedded Trapped Modes for a Two-layer Fluid over a Rectangular Barrier

M. I. Romero Rodriguez and P. Zhevandrov

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

We prove that the system of equations describing waves in a two-layer fluid over a rectangular barrier of small height possesses embedded trapped modes (eigenvalues submerged in the continuous spectrum) for certain values of the width of the barrier and that these eigenvalues are analytic in the small parameter characterizing the height of the barrier. We do this by means of purely elementary considerations constructing explicit solutions and thus confirm the results of [7] obtained for general perturbations of the depth of the fluid in the particular case of a rectangular barrier.

Article information

Source
Commun. Math. Anal., Volume 17, Number 2 (2014), 338-343.

Dates
First available in Project Euclid: 18 December 2014

Permanent link to this document
https://projecteuclid.org/euclid.cma/1418919774

Mathematical Reviews number (MathSciNet)
MR3292978

Zentralblatt MATH identifier
1326.76025

Subjects
Primary: 76B70: Stratification effects in inviscid fluids 34L40: Particular operators (Dirac, one-dimensional Schrödinger, etc.)

Keywords
embedded eigenvalues two-layer fluid

Citation

Romero Rodriguez, M. I.; Zhevandrov, P. A Note on Embedded Trapped Modes for a Two-layer Fluid over a Rectangular Barrier. Commun. Math. Anal. 17 (2014), no. 2, 338--343. https://projecteuclid.org/euclid.cma/1418919774


Export citation