Thresholds for global existence and blow-up in a general class of doubly dispersive nonlocal wave equations
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
Full text not available from this repository.
Official URL: http://dx.doi.org/10.1016/j.na.2013.09.013
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.
Repository Staff Only: item control page