The Cauchy problem for a class of two-dimensional nonlocal nonlinear wave equations governing anti-plane shear motions in elastic materials
Erbay, Hüsnü A. and Erbay , Saadet and Erkip, Albert (2011) The Cauchy problem for a class of two-dimensional nonlocal nonlinear wave equations governing anti-plane shear motions in elastic materials. Nonlinearity, 24 (4). pp. 1347-1359. ISSN 0951-7715
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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
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