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On the Spectral Stability of Internal Solitary Waves in Fluids with Density Stratification

On the Spectral Stability of Internal Solitary Waves in Fluids with Density Stratification

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KLAIBER, Andreas, 2013. On the Spectral Stability of Internal Solitary Waves in Fluids with Density Stratification

@phdthesis{Klaiber2013Spect-25443, title={On the Spectral Stability of Internal Solitary Waves in Fluids with Density Stratification}, year={2013}, author={Klaiber, Andreas}, address={Konstanz}, school={Universität Konstanz} }

2013 Klaiber, Andreas Frequently encountered in nature, internal solitary waves in stratified fluids are well-observed and well-studied objects from the experimental, the theoretical and the numerical perspective. Contrasting with a rich theory for their existence and the development of methods for computing these waves, their stability analysis has received less attention at a rigorous mathematical level.<br /><br />In this thesis, we propose a method for investigating the spectral stability of internal solitary waves which consists of five steps:<br /><br />(i) reformulation of the eigenvalue problem as an infinite-dimensional spatial-dynamical system,<br /><br />(ii) procedure to obtain finite-dimensional truncations,<br /><br />(iii) definition of an Evans function for the finite-dimensional problems,<br /><br />(iv) investigation of the Evans functions for zeros with positive real part,<br /><br />(v) identification or preclusion of eigenvalues with positive real part of the infinite-dimensional system.<br /><br />While steps (i)-(iv) are carried out within this thesis, step (v) is left to future work. eng 2013-12-18T12:32:06Z Zur spektralen Stabilität interner Solitärwellen in Fluiden mit Dichteschichtung 2013-12-18T12:32:06Z On the Spectral Stability of Internal Solitary Waves in Fluids with Density Stratification deposit-license Klaiber, Andreas

Dateiabrufe seit 01.10.2014 (Informationen über die Zugriffsstatistik)

dissertation-aklaiber_flat.pdf 190

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