Blow-up and global existence for a general class of nonlocal nonlinear coupled wave equations |
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Authors: | N Duruk A Erkip |
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Institution: | a Faculty of Engineering and Natural Sciences, Sabanci University, Tuzla 34956, Istanbul, Turkey b Department of Mathematics, Isik University, Sile 34980, Istanbul, Turkey |
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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. |
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Keywords: | 74H20 74J30 74B20 |
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