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

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, utt−Luxx=B(−|u|p−1u)xx,(p>1), where the nonlocality enters through two pseudo-differential operators L and B. We establish thresholds for g...

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Veröffentlicht in:Nonlinear analysis 2014-01, Vol.95, p.313-322
Hauptverfasser: Erbay, H.A., Erbay, S., Erkip, A.
Format: Artikel
Sprache:eng
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Zusammenfassung: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, utt−Luxx=B(−|u|p−1u)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.
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2013.09.013