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Global existence and blow-up for a class of nonlocal nonlinear Cauchy problems arising in elasticity

Duruk, Nilay and Erbay , Hüsnü A. and Erkip, Albert (2010) Global existence and blow-up for a class of nonlocal nonlinear Cauchy problems arising in elasticity. Nonlinearity, 23 (1). pp. 107-118. ISSN 0951-7715

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Official URL: http://dx.doi.org/10.1088/0951-7715/23/1/006

Abstract

We study the initial-value problem for a general class of nonlinear nonlocal wave equations arising in one-dimensional nonlocal elasticity. The model involves a convolution integral operator with a general kernel function whose Fourier transform is nonnegative. We show that some well-known examples of nonlinear wave equations, such as Boussinesq-type equations, follow from the present model for suitable choices of the kernel function. We establish global existence of solutions of the model assuming enough smoothness on the initial data together with some positivity conditions on the nonlinear term. Furthermore, conditions for finite time blow-up are provided.

Item Type:Article
Subjects:Q Science > QA Mathematics > QA299.6-433 Analysis
ID Code:13902
Deposited By:Albert Erkip
Deposited On:14 Apr 2010 09:27
Last Modified:25 May 2011 14:10

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