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
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.
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