Blow-up and global existence for a general class of nonlocal nonlinear coupled wave equations
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CitationDuruk, N., Erbay, H. A. & Erkip, A. (2011). Blow-up and global existence for a general class of nonlocal nonlinear coupled wave equations. Journal of Differential Equations, 250(3), 1448-1459. doi: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 finite-time blow-up and as well as global existence of solutions of the problem.