Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
840040 | Nonlinear Analysis: Theory, Methods & Applications | 2014 | 10 Pages |
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 LL and BB. 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.