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^*

^*Bu çalışma için yazışmadan sorumlu yazar

Matematik Bölümü

Ozyegin University
Sabanci University

Araştırma sonucu: Dergiye katkı › Makale › bilirkişi

25 Atıf (Scopus)

Özet

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.

Orijinal dil	İngilizce
Sayfa (başlangıç-bitiş)	4392-4409
Sayfa sayısı	18
Dergi	Journal of Differential Equations
Hacim	252
Basın numarası	8
DOI'lar	https://doi.org/10.1016/j.jde.2012.01.008
Yayın durumu	Yayınlandı - 15 Nis 2012

Finansman

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

Finansörler	Finansör numarası
TUBITAK	TBAG-110R002
Türkiye Bilimsel ve Teknolojik Araştirma Kurumu

Belgeye Erişim

10.1016/j.jde.2012.01.008

Diğer Dosyalar ve Linkler

Link to publication in Scopus

Alıntı Yap

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title = "The Cauchy problem for a one-dimensional nonlinear elastic peridynamic model",

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.",

keywords = "Blow-up, Global existence, Nonlinear peridynamic equation, Nonlocal Cauchy problem",

author = "Erbay, \{H. A.\} and A. Erkip and Muslu, \{G. M.\}",

year = "2012",

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doi = "10.1016/j.jde.2012.01.008",

language = "English",

volume = "252",

pages = "4392--4409",

journal = "Journal of Differential Equations",

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TY - JOUR

T1 - The Cauchy problem for a one-dimensional nonlinear elastic peridynamic model

AU - Erbay, H. A.

AU - Erkip, A.

AU - Muslu, G. M.

PY - 2012/4/15

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

U2 - 10.1016/j.jde.2012.01.008

DO - 10.1016/j.jde.2012.01.008

M3 - Article

AN - SCOPUS:84856769497

SN - 0022-0396

VL - 252

SP - 4392

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

Özet

Finansman

Belgeye Erişim

Diğer Dosyalar ve Linkler

Parmak izi

Alıntı Yap