Global existence and blow-up for a class of nonlocal nonlinear Cauchy problems arising in elasticity
We study the initial-value problem for a general class of nonlinear nonlocal wave equations arising in one-dimensional nonlocal elasticity. The model involves a convolution integral operator with a general kernel function whose Fourier transform is nonnegative. We show that some well-known examples...
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| Veröffentlicht in: | Nonlinearity 2010-01, Vol.23 (1), p.107-118 |
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| container_title | Nonlinearity |
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| creator | Duruk, N Erbay, H A Erkip, A |
| description | We study the initial-value problem for a general class of nonlinear nonlocal wave equations arising in one-dimensional nonlocal elasticity. The model involves a convolution integral operator with a general kernel function whose Fourier transform is nonnegative. We show that some well-known examples of nonlinear wave equations, such as Boussinesq-type equations, follow from the present model for suitable choices of the kernel function. We establish global existence of solutions of the model assuming enough smoothness on the initial data together with some positivity conditions on the nonlinear term. Furthermore, conditions for finite time blow-up are provided. |
| doi_str_mv | 10.1088/0951-7715/23/1/006 |
| format | Article |
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| ispartof | Nonlinearity, 2010-01, Vol.23 (1), p.107-118 |
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| source | Institute of Physics Journals; Institute of Physics (IOP) Journals - HEAL-Link |
| subjects | Exact sciences and technology Global analysis, analysis on manifolds Mathematical analysis Mathematical methods in physics Mathematics Numerical analysis Numerical analysis. Scientific computation Other topics in mathematical methods in physics Partial differential equations Partial differential equations, initial value problems and time-dependant initial-boundary value problems Physics Sciences and techniques of general use Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds |
| title | Global existence and blow-up for a class of nonlocal nonlinear Cauchy problems arising in elasticity |
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