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arXiv · 1309.2385

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

Saadet Erbay·Husnu A. Erbay·Albert Erkip
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Abstract

In this article we study 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.

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Saadet Erbay, Husnu A. Erbay, Albert Erkip. 2013-09-10. Thresholds for global existence and blow-up in a general class of doubly dispersive nonlocal wave equations. https://arxiv.org/abs/1309.2385

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