The Cauchy problem for a one dimensional nonlinear elastic peridynamic model
Erbay, Hüsnü A. and Erkip, Albert and Muslu, Gülçin M. (2012) The Cauchy problem for a one dimensional nonlinear elastic peridynamic model. Journal of Differential Equations, 252 (8). pp. 4392-4409. ISSN 0022-0396
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Official URL: http://dx.doi.org/10.1016/j.jde.2012.01.008
This paper studies the Cauchy problem for a one-dimensional nonlinear peridynamic model describing the dynamic response of an innitely long elastic bar. The issues of local well-posedness and smoothness of the solutions are discussed. The existence of a global solution is proved rst in the sublinear case and then for nonlinearities of degree at most three. The conditions for nite-time blow-up of solutions are established.
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