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Global existence and blow-up of solutions for a general class of doubly dispersive nonlocal nonlinear wave equations

Babaoğlu, Ceni and Erbay, Hüsnü A. and Erkip, Albert (2013) Global existence and blow-up of solutions for a general class of doubly dispersive nonlocal nonlinear wave equations. Nonlinear Analysis: Theory, Methods & Applications, 77 . pp. 82-93. ISSN 0362-546X

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Official URL: http://dx.doi.org/10.1016/j.na.2012.09.001

Abstract

This study deals with the analysis of the Cauchy problem of a general class of nonlocal nonlinear equations modeling the bi-directional propagation of dispersive waves in various contexts. The nonlocal nature of the problem is reflected by two different elliptic pseudodifferential operators acting on linear and nonlinear functions of the dependent variable, respectively. The well-known doubly dispersive nonlinear wave equation that incorporates two types of dispersive effects originated from two different dispersion operators falls into the category studied here. The class of nonlocal nonlinear wave equations also covers a variety of well-known wave equations such as various forms of the Boussinesq equation. Local existence of solutions of the Cauchy problem with initial data in suitable Sobolev spaces is proven and the conditions for global existence and finite-time blow-up of solutions are established.

Item Type:Article
Uncontrolled Keywords:Nonlocal Cauchy problem; Double dispersion equation; Global existence; Blow-up; Boussinesq equation
Subjects:Q Science > QA Mathematics > QA299.6-433 Analysis
ID Code:19913
Deposited By:Albert Erkip
Deposited On:04 Nov 2012 23:04
Last Modified:08 Dec 2012 21:09

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