Blow-up and global existence for a general class of nonlocal nonlinear coupled wave equations

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.Comment: 11 pages. Minor changes and added reference

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

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

The Cauchy Problem for a One Dimensional Nonlinear Peridynamic Model

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.Comment: To appear in Journal of Differential Equations (added references, corrected typos, minor revision in Section 2, 18 pages

A higher-order Boussinesq equation in locally non-linear theory of one-dimensional non-local elasticity

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

An analysis of functional moves in the introduction sections of research articles written by Turkish scholars

Tez (doktora) - Anadolu ÜniversitesiAnadolu Üniversitesi, Eğitim Bilimleri Enstitüsü, Yabancı Diller Eğitimi Anabilim DalıKayıt no: 1035572Akademik ortamda İngilizcenin temel iletişim aracı olması nedeni ile uluslararası dergilerde yayın yapmak ana dili İngilizce olmayan araştırmacılar arasında yaygınlaşan ortak bir hedef ve bunun sonucunda karşılaştıkları bir zorluk olarak ortaya çıkmaktadır. Bugüne kadar yapılmış olan çalışmalarda İngilizce ve başka dillerde yazılan bilimsel makalelerdeki metinsel yapı özellikleri incelenmiştir. Bununla birlikte, yabancı bir dil olarak İngilizce yazılmış metinlerin kültürlerarası incelendiği çalışmalar- özellikle de akademik ortama yeni adım atan yazarlar için zorlayıcı olarak bilinen giriş bölümlerine odaklanan çalışmalar- oldukça azdır (Ahmed, 2004; Jogthong, 2001).Buna ek olarak, günümüzde akademik yazıda öz bölümleri dikkat çekerkençok az araştırma giriş bölümlerini incelemiştir; disiplinler arası farklılık da dâhil olmak üzere bu bölümlerin adım yapısını inceleyen çok az betimsel çalışma vardır. Araştırma makalelerinin giriş bölümleri önemlidir çünkü bu bölümlerde yazarlar bilgi sahibi olduklarını iddia etmek için sözbilimsel yapı oluştururlar. Giriş bölümlerini ele alan göreceli az sayıda olan çalışmalardan yola çıkarak bu çalışmada Türklerin iki disiplin olarak okul öncesi öğretmenliği ve özel eğitim bölümlerinde Türkçe ve İngilizcede yazdıkları makalelerin giriş bölümlerinin Swales'ın (2004) CARS Modelini kullanarak adım yapılarının incelenmesi amaçlanmıştır. Verilerin incelenmesi sonucunda gruplar arasında önemli benzerlik ve farklılıkların olduğu gözlenmiştir. Bulgular ana dili İngilizce olan yazarlar ile ana dili Türkçe olan yazarların araştırma makalelerinin giriş bölümlerini yazarken Swales (2004) tarafından sunulan adım yapılarının farkında olduklarını göstermiştir. Bulgular çalışmada incelenmiş olan makalelerin yarısından azında 1-2-3 diziliminde adım yapısı olduğunu göstermiştir; ancak, dizilim göz önünde bulundurulmadığında araştırma makalelerinin giriş bölümlerinde adım yapılarının hepsinin yüksek bir miktarda kullanıldığını göstermiştir.Bu çalışmada elde edilen sonuçlar göz önüne alınarak genel olarak ikinci dilde yazma dersleri ve ileri seviyede İngilizce bilen Türk öğrenciler ile Türk akademisyenler için akademik yazma dersleri öğretimine yönelik yansımalar üzerinde durulmuş ve önerilerde bulunulmuştur

A CEFR Based evaluation of B1+ level preparatory program at A Turkish State University: The application of the foreign language skills scale

Despite the centrality of the Common European Framework of Reference for Languages (CEFR) in language teaching and assessment, studies investigating its learning outcomes in language program evaluations are quite scarce. This paper aims to evaluate the effectiveness of a modular English preparatory school program through the Foreign Language Skills Scale. The research sample consists of 357 preparatory school students having attained B1+ level of proficiency in the program. The results revealed that while the language program designed to be in line with the CEFR guidelines, in general, serves for the needs of the students, there are still some discrepancies between the learning outcomes of B1+ and opinions of students about their competencies, especially in listening sub-skills

The Camassa-Holm equation as the long-wave limit of the improved Boussinesq equation and of a class of nonlocal wave equations

In the present study we prove rigorously that in the long-wave limit, the unidirectional solutions of a class of nonlocal wave equations to which the improved Boussinesq equation belongs are well approximated by the solutions of the Camassa-Holm equation over a long time scale. This general class of nonlocal wave equations model bidirectional wave propagation in a nonlocally and nonlinearly elastic medium whose constitutive equation is given by a convolution integral. To justify the Camassa-Holm approximation we show that approximation errors remain small over a long time interval. To be more precise, we obtain error estimates in terms of two independent, small, positive parameters $\epsilon$ and $\delta$ measuring the effect of nonlinearity and dispersion, respectively. We further show that similar conclusions are also valid for the lower order approximations: the Benjamin-Bona-Mahony approximation and the Korteweg-de Vries approximation.Comment: 24 pages, to appear in Discrete and Continuous Dynamical System

The Cauchy problem for a class of two-dimensional nonlocal nonlinear wave equations governing anti-plane shear motions in elastic materials

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.Comment: 15 pages. "Section 6 The Anisotropic Case" added and minor changes. Accepted for publication in Nonlinearit