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

H. A. Erbay; A. Erkip; G. M. Muslu

doi:10.1016/j.jde.2012.01.008

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

H. A. Erbay, A. Erkip, G. M. Muslu^*

^*Corresponding author for this work

Department of Mathematics Engineering

Research output: Contribution to journal › Article › peer-review

25 Citations (Scopus)

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.

Original language	English
Pages (from-to)	4392-4409
Number of pages	18
Journal	Journal of Differential Equations
Volume	252
Issue number	8
DOIs	https://doi.org/10.1016/j.jde.2012.01.008
Publication status	Published - 15 Apr 2012

Funding

This work has been supported by the Scientific and Technological Research Council of Turkey (TUBITAK) under the project TBAG-110R002.

Funders	Funder number
TUBITAK	TBAG-110R002
Türkiye Bilimsel ve Teknolojik Araştirma Kurumu

Keywords

Blow-up
Global existence
Nonlinear peridynamic equation
Nonlocal Cauchy problem

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10.1016/j.jde.2012.01.008

Cite this

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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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AU - Erkip, A.

AU - Muslu, G. M.

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Y1 - 2012/4/15

N2 - 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.

AB - 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.

KW - Blow-up

KW - Global existence

KW - Nonlinear peridynamic equation

KW - Nonlocal Cauchy problem

UR - https://www.scopus.com/pages/publications/84856769497

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DO - 10.1016/j.jde.2012.01.008

M3 - Article

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EP - 4409

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 8

ER -

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

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Keywords

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