TY - JOUR

T1 - Perturbation analysis of embedded eigenvalues for water-waves

AU - Kemppainen, J.T.

AU - Nazarov, S.A.

AU - Ruotsalainen, K.M.

PY - 2015

Y1 - 2015

N2 - © 2015 Elsevier Inc.The starting point of our study is the knowledge that certain surface piercing bodies support a trapped mode, i.e. an embedded eigenvalue in the continuous spectrum. In the framework of the two-dimensional theory of linear water waves, we investigate the question whether a trapped mode still exists after the small perturbation of the body contours. The perturbation of the obstacle is performed by a linear combination of appropriate profile functions. The coefficients of the profile functions and a perturbation parameter of the eigenvalue form a parameter space which controls the embedded eigenvalue as well as the geometry of the water domain. Based on the concept of enforced stability of embedded eigenvalues in the continuous spectrum, we will show that the trapped mode is preserved in the small perturbation, if the profile functions fulfil problem dependent orthogonalisation and normalisation conditions. The argumentation relies on a sufficient condition for the existence of a trapped mod

AB - © 2015 Elsevier Inc.The starting point of our study is the knowledge that certain surface piercing bodies support a trapped mode, i.e. an embedded eigenvalue in the continuous spectrum. In the framework of the two-dimensional theory of linear water waves, we investigate the question whether a trapped mode still exists after the small perturbation of the body contours. The perturbation of the obstacle is performed by a linear combination of appropriate profile functions. The coefficients of the profile functions and a perturbation parameter of the eigenvalue form a parameter space which controls the embedded eigenvalue as well as the geometry of the water domain. Based on the concept of enforced stability of embedded eigenvalues in the continuous spectrum, we will show that the trapped mode is preserved in the small perturbation, if the profile functions fulfil problem dependent orthogonalisation and normalisation conditions. The argumentation relies on a sufficient condition for the existence of a trapped mod

U2 - 10.1016/j.jmaa.2015.02.050

DO - 10.1016/j.jmaa.2015.02.050

M3 - Article

SP - 399

EP - 427

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 1

ER -