Duruk, Nilay (2007) Cauchy problem for a higher-order boussinesq equation. [Thesis]
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Abstract
In this thesis, we establish global well-posedness of the Cauchy problem for a particular higher-order Boussinesq equation. At the microscopic level this sixth order Boussinesq equation was derived in [11] for the longitudinal vibrations of a dense lattice, in which a unit length of the lattice contains a large number of lattice points. We take the initial data in the Sobolev space Hs with s > 1 2 . With smoothness assumptions on the nonlinear term, we establish local existence and uniqueness of the solution. Under further assumptions, we prove the global existence for s 1. Finally, we show continuous dependence of the solution on the initial data.
Item Type: | Thesis |
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Uncontrolled Keywords: | Higher-Order Boussinesq equation. -- Global existence. -- Cauchy problem. -- Generalized double dispersion equation. -- Yüksek mertebeden Boussinesq denklemi. -- Global varlık. -- Cauchy problemi. -- Genelleştirilmiş çift dağılma denklemi. |
Subjects: | Q Science > QA Mathematics |
Divisions: | Faculty of Engineering and Natural Sciences > Basic Sciences > Mathematics Faculty of Engineering and Natural Sciences |
Depositing User: | IC-Cataloging |
Date Deposited: | 16 Apr 2008 12:36 |
Last Modified: | 26 Apr 2022 09:47 |
URI: | https://research.sabanciuniv.edu/id/eprint/8351 |