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N. Duruk Mutlubaş 《Nonlinear Analysis: Real World Applications》2013,14(5):2022-2026
We prove the local well-posedness for a nonlinear equation modeling the evolution of the free surface for waves of moderate amplitude in the shallow water regime. 相似文献
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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. 相似文献
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In one space dimension, a non-local elastic model is based ona single integral law, giving the stress when the strain isknown at all spatial points. In this study, we first derivea higher-order Boussinesq equation using locally non-lineartheory of 1D non-local elasticity and then we are able to showthat under certain conditions the Cauchy problem is globallywell-posed. 相似文献
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In this study we establish global well-posedness of the Cauchy problem for a higher-order Boussinesq equation. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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