The Cauchy problem for a one-dimensional nonlinear elastic peridynamic model

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:252

Article

Erbay, H. A.²  Erkip, A.³  Muslu, G. M.¹ 

[1] Istanbul Tech Univ, Dept Math, TR-34469 Istanbul, Turkey

[2] Ozyegin Univ, Fac Arts & Sci, TR-34794 Istanbul, Turkey

[3] Sabanci Univ, Fac Engn & Nat Sci, TR-34956 Istanbul, Turkey

关键词: Nonlocal Cauchy problem;    Nonlinear peridynamic equation;    Global existence;    Blow-up;   

DOI  :  10.1016/j.jde.2012.01.008

来源: Elsevier

【 摘 要 】

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. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free