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Thresholds for global existence and blow-up in a general class of doubly dispersive nonlocal wave equations

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Erbay, H. A. and Erbay, S. and Erkip, Albert (2014) Thresholds for global existence and blow-up in a general class of doubly dispersive nonlocal wave equations. Nonlinear Analysis: Theory, Methods & Applications, 95 . pp. 313-322. ISSN 0362-546X

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Official URL: http://dx.doi.org/10.1016/j.na.2013.09.013

Abstract

In this paper we study the global existence and blow-up of solutions for a general class of nonlocal nonlinear wave equations with power-type onlinearities, utt − Luxx = B(−|u|^(p−1)u)_xx, (p > 1), where the nonlocality enters through two pseudo-differential operators L and B. We establish thresholds for global existence versus blow-up using the potential well method which relies essentially on the ideas suggested by Payne and Sattinger. Our results improve the global existence and blow-up results given in the literature for the present class of nonlocal nonlinear wave equations and cover those given for many well-known nonlinear dispersive wave equations such as the so-called double-dispersion equation and the traditional Boussinesq-type equations, as special cases.

Item Type:Article
Uncontrolled Keywords:Nonlocal Cauchy problem; Global existence; Blow-up; Potential well; Boussinesq equation; Double dispersion equation
Subjects:Q Science > QA Mathematics > QA299.6-433 Analysis
ID Code:21984
Deposited By:Albert Erkip
Deposited On:07 Nov 2013 16:19
Last Modified:01 Aug 2019 11:34

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