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The Cauchy problem for a one-dimensional nonlinear elastic peridynamic model |
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| Authors: | HA Erbay A Erkip GM Muslu |
| Institution: | 1. Faculty of Arts and Sciences, Ozyegin University, Cekmekoy 34794, Istanbul, Turkey;2. Faculty of Engineering and Natural Sciences, Sabanci University, Tuzla 34956, Istanbul, Turkey;3. Department of Mathematics, Istanbul Technical University, Maslak 34469, Istanbul, Turkey |
| Abstract: | This paper studies the Cauchy problem for a one-dimensional nonlinear peridynamic model describing the dynamic response of an infinitely long elastic bar. The issues of local well-posedness and smoothness of the solutions are discussed. The existence of a global solution is proved first in the sublinear case and then for nonlinearities of degree at most three. The conditions for finite-time blow-up of solutions are established. |
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