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

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 finite time blow-up and as well as global existence of solutions of the problem.

11 pages. Minor changes and added references

References in corpus (1)

• The hydrodynamical relevance of the Camassa-Holm and Degasperis-Procesi equations

Cited by in corpus (3)

• Initial-value problem for coupled Boussinesq equations and a hierarchy of Ostrovsky equations
• Existence and Stability of Traveling Waves for a Class of Nonlocal Nonlinear Equations
• Incorporating local boundary conditions into nonlocal theories