Global existence and blow-up for a class of nonlocal nonlinear Cauchy problems arising in elasticity
Yükleniyor...
Dosyalar
Tarih
2010-01
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
IOP Publishing
Erişim Hakkı
info:eu-repo/semantics/closedAccess
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
