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

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

2010-09-07

arxiv.org/abs/1009.1263v2

Journal of Differential Equations 250, 1448-1459 (2011)

Mathematics

Analysis of PDEs

11 pages. Minor changes and added references

Scientific paper

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.

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