Published January 1, 2014
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Thresholds for global existence and blow-up in a general class of doubly dispersive nonlocal wave equations
Creators
- 1. Ozyegin Univ, Fac Engn, Dept Nat & Math Sci, TR-34794 Istanbul, Turkey
- 2. Sabanci Univ, Fac Engn & Nat Sci, TR-34956 Istanbul, Turkey
Description
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 nonlinearities, u(tt) - Lu-xx = 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. (C) 2013 Elsevier Ltd. All rights reserved.
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