The Cauchy problem for a class of two-dimensional nonlocal nonlinear wave equations governing anti-plane shear motions in elastic materials
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Dosyalar
Tarih
2011-04
Yazarlar
Dergi Başlığı
Dergi ISSN
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Yayıncı
IOP Publishing Ltd
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
This paper is concerned with the analysis of the Cauchy problem of a general class of two-dimensional nonlinear nonlocal wave equations governing anti-plane shear motions in nonlocal elasticity. The nonlocal nature of the problem is reflected by a convolution integral in the space variables. The Fourier transform of the convolution kernel is nonnegative and satisfies a certain growth condition at infinity. For initial data in L-2 Sobolev spaces, conditions for global existence or finite time blow-up of the solutions of the Cauchy problem are established.
Açıklama
This work has been supported by the Scientific and Technological Research Council of Turkey (TUBITAK) under the project TBAG-110R002. The authors are grateful to the anonymous referees for the insightful comments and suggestions.
Anahtar Kelimeler
Global existence, Blow-up, Mechanics, Boussinesq equations, Global solution
Kaynak
Nonlinearity
WoS Q Değeri
Q2
Scopus Q Değeri
Q2
Cilt
24
Sayı
4
Künye
Erbay, H. A., Erbay, S. & Erkip, A. (2011). The cauchy problem for a class of two-dimensional nonlocal nonlinear wave equations governing anti-plane shear motions in elastic materials. Nonlinearity, 24(4), 1347-1359. doi:10.1088/0951-7715/24/4/017
