Global existence and blow-up for a class of nonlocal nonlinear Cauchy problems arising in elasticity

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Tarih

2010-01

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Dergi ISSN

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Yayıncı

IOP Publishing

Erişim Hakkı

info:eu-repo/semantics/closedAccess

Araştırma projeleri

Organizasyon Birimleri

Dergi sayısı

Özet

We study the initial-value problem for a general class of nonlinear nonlocal wave equations arising in one-dimensional nonlocal elasticity. The model involves a convolution integral operator with a general kernel function whose Fourier transform is nonnegative. We show that some well-known examples of nonlinear wave equations, such as Boussinesq-type equations, follow from the present model for suitable choices of the kernel function. We establish global existence of solutions of the model assuming enough smoothness on the initial data together with some positivity conditions on the nonlinear term. Furthermore, conditions for finite time blow-up are provided.

Açıklama

Anahtar Kelimeler

Generalized boussinesq equation, Boussinesq equations, Global existence, Global solution

Kaynak

Nonlinearity

WoS Q Değeri

Q2

Scopus Q Değeri

Q1

Cilt

23

Sayı

1

Künye

Duruk, N., Erbay, H. A. & Erkip, A. (2010). Global existence and blow-up for a class of nonlocal nonlinear cauchy problems arising in elasticity. Nonlinearity, 23(1), 107-118. doi:10.1088/0951-7715/23/1/006