Blow-up and global existence for a general class of nonlocal nonlinear coupled wave equations

Duruk Mutlubaş, Nilay and Erbay, Hüsnü Ata and Erkip, Albert (2011) Blow-up and global existence for a general class of nonlocal nonlinear coupled wave equations. Journal of Differential Equations, 250 (3). pp. 1448-1459. ISSN 0022-0396

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Official URL: http://dx.doi.org/10.1016/j.jde.2010.09.002

Abstract

We study the initial-value problem for a general class of nonlinear nonlocal coupled wave equations. The problem involves convolution operators with kernel functions whose Fourier transforms are nonnegative. Some well-known examples of nonlinear wave equations, such as coupled Boussinesq-type equations arising in elasticity and in quasi-continuum approximation of dense lattices, follow from the present model for suitable choices of the kernel functions. We establish local existence and sufficient conditions for finitetime blow-up and as well as global existence of solutions of the problem.

Item Type:	Article
Uncontrolled Keywords:	Nonlocal Cauchy problem; Boussinesq equation; Global existence; Blow-up; Nonlocal elasticity
Subjects:	Q Science > QA Mathematics > QA299.6-433 Analysis
ID Code:	16281
Deposited By:	Albert Erkip
Deposited On:	07 Jan 2011 14:27
Last Modified:	25 May 2011 14:11

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Blow-up and global existence for a general class of nonlocal nonlinear coupled wave equations. (deposited 19 Oct 2010 11:33)
- Blow-up and global existence for a general class of nonlocal nonlinear coupled wave equations. (deposited 07 Jan 2011 14:27) [Currently Displayed]

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