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In this article we study global existence and blow-up of solutions for ageneral class of nonlocal nonlinear wave equations with power-typenonlinearities, $u_{tt}-Lu_{xx}=B(- |u|^{p-1}u)_{xx}, ~(p>1)$, where thenonlocality enters through two pseudo-differential operators $L$ and $B$. Weestablish thresholds for global existence versus blow-up using the potentialwell method which relies essentially on the ideas suggested by Payne andSattinger. Our results improve the global existence and blow-up results givenin the literature for the present class of nonlocal nonlinear wave equationsand cover those given for many well-known nonlinear dispersive wave equationssuch as the so-called double-dispersion equation and the traditionalBoussinesq-type equations, as special cases.

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