Cauchy problem for a higher-order boussinesq equation
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Duruk, Nilay (2007) Cauchy problem for a higher-order boussinesq equation. [Thesis]
Official URL: http://risc01.sabanciuniv.edu/record=b1164864 (Table of Contents)
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  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.
|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|
|Deposited On:||16 Apr 2008 12:36|
|Last Modified:||25 Mar 2019 16:54|
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