Yazar "Erkip, Albert" seçeneğine göre listele

Listeleniyor 1 - 4 / 4
  • Küçük Resim
    Yayın
    Blow-up and global existence for a general class of nonlocal nonlinear coupled wave equations
    (Academic Press Inc Elsevier Science, 2011-02-01) Duruk, Nilay; Erbay, Hüsnü Ata; Erkip, Albert
    We study the initial-value problem for a general class of nonlinear nonlocal coupled wave equations. The problem involves convolution operators with kernel functions whose Fourier transforms are nonnegative. Some well-known examples of nonlinear wave equations, such as coupled Boussinesq-type equations arising in elasticity and in quasi-continuum approximation of dense lattices, follow from the present model for suitable choices of the kernel functions. We establish local existence and sufficient conditions for finite-time blow-up and as well as global existence of solutions of the problem.
  • Küçük Resim
    Yayın
    The Cauchy problem for a class of two-dimensional nonlocal nonlinear wave equations governing anti-plane shear motions in elastic materials
    (IOP Publishing Ltd, 2011-04) Erbay, Hüsnü Ata; Erbay, Saadet; Erkip, Albert
    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.
  • Küçük Resim
    Yayın
    Global existence and blow-up for a class of nonlocal nonlinear Cauchy problems arising in elasticity
    (IOP Publishing, 2010-01) Duruk, Nilay; Erbay, Hüsnü Ata; Erkip, Albert
    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.
  • Küçük Resim
    Yayın
    A Higher-order Boussinesq equation in locally non-linear theory of one-dimensional non-local elasticity
    (Oxford Univ Press, 2009-02) Duruk, Nilay; Erkip, Albert; Erbay, Hüsnü Ata
    In one space dimension, a non-local elastic model is based on a single integral law, giving the stress when the strain is known at all spatial points. In this study, we first derive a higher-order Boussinesq equation using locally non-linear theory of 1D non-local elasticity and then we are able to show that under certain conditions the Cauchy problem is globally well-posed.