The Cauchy problem for a class of two-dimensional nonlocal nonlinear wave equations governing anti-plane shear motions in elastic materials

Official URL: http://dx.doi.org/10.1088/0951-7715/24/4/017

This paper is concerned with the analysis of the Cauchy problem of a general class of two-dimensional nonlinear nonlocal wave equations governing antiplane shear motions in nonlocal elasticity. The nonlocal nature of the problem is reflected by a convolution integral in the space variables. The Fourier transform of the convolution kernel is nonnegative and satisfies a certain growth condition at infinity. For initial data in L^2 Sobolev spaces, conditions for global existence or finite time blow-up of the solutions of the Cauchy problem are established. Mathematics Subject Classification: 74H20, 74J30, 74B20