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Cauchy problem for a higher-order boussinesq equation /

Duruk, Nilay (2006) Cauchy problem for a higher-order boussinesq equation /. [Thesis]

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Official URL: http://risc01.sabanciuniv.edu/record=b1164864 (Table of Contents)

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
Uncontrolled Keywords:Higher-Order Boussinesq equation -- Global existence -- Cauchy problem -- Generalized double dispersion equation
Subjects:Q Science > QA Mathematics
ID Code:8351
Deposited By:IC-Cataloging
Deposited On:16 Apr 2008 12:36
Last Modified:27 Dec 2008 14:28

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