Cauchy problem for a higher-order boussinesq equation

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Duruk, Nilay (2007) Cauchy problem for a higher-order boussinesq equation. [Thesis]

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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
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

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