On the convergence of the nonlocal nonlinear model to the classical elasticity equation

Name: On the convergence of the nonlocal nonlinear model to the classical elasticity equation
Author: Erbay, Hüsnü Ata, Erbay, Saadet, Erkip, A.

İsim	On the convergence of the nonlocal nonlinear model to the classical elasticity equation
Yazar	Erbay, Hüsnü Ata, Erbay, Saadet, Erkip, A.
Basım Tarihi:	2021-12
Basım Yeri	- Elsevier
Konu	Nonlocal elasticity, Long wave limit, Discrete-to-continuum convergence, Lattice dynamics
Tür	Süreli Yayın
Dil	İngilizce
Dijital	Evet
Yazma	Hayır
Kütüphane:	Özyeğin Üniversitesi
Demirbaş Numarası	0167-2789
Kayıt Numarası	c5a47cce-92db-4eed-bfee-578e31762b71
Lokasyon	Natural and Mathematical Sciences
Tarih	2021-12
Örnek Metin	We consider a general class of convolution-type nonlocal wave equations modeling bidirectional propagation of nonlinear waves in a continuous medium. In the limit of vanishing nonlocality we study the behavior of solutions to the Cauchy problem. We prove that, as the kernel functions of the convolution integral approach the Dirac delta function, the solutions converge strongly to the corresponding solutions of the classical elasticity equation. An energy estimate with no loss of derivative plays a critical role in proving the convergence result. As a typical example, we consider the continuous limit of the discrete lattice dynamic model (the Fermi–Pasta–Ulam–Tsingou model) and show that, as the lattice spacing approaches zero, solutions to the discrete lattice equation converge to the corresponding solutions of the classical elasticity equation.
DOI	10.1016/j.physd.2021.133010
Cilt	427

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On the convergence of the nonlocal nonlinear model to the classical elasticity equation

Yazar Erbay, Hüsnü Ata, Erbay, Saadet, Erkip, A.

Basım Tarihi 2021-12

Basım Yeri - Elsevier

Konu Nonlocal elasticity, Long wave limit, Discrete-to-continuum convergence, Lattice dynamics

Tür Süreli Yayın

Dil İngilizce

Dijital Evet

Yazma Hayır

Kütüphane Özyeğin Üniversitesi

Demirbaş Numarası 0167-2789

Kayıt Numarası c5a47cce-92db-4eed-bfee-578e31762b71

Lokasyon Natural and Mathematical Sciences

Tarih 2021-12

Örnek Metin We consider a general class of convolution-type nonlocal wave equations modeling bidirectional propagation of nonlinear waves in a continuous medium. In the limit of vanishing nonlocality we study the behavior of solutions to the Cauchy problem. We prove that, as the kernel functions of the convolution integral approach the Dirac delta function, the solutions converge strongly to the corresponding solutions of the classical elasticity equation. An energy estimate with no loss of derivative plays a critical role in proving the convergence result. As a typical example, we consider the continuous limit of the discrete lattice dynamic model (the Fermi–Pasta–Ulam–Tsingou model) and show that, as the lattice spacing approaches zero, solutions to the discrete lattice equation converge to the corresponding solutions of the classical elasticity equation.

DOI 10.1016/j.physd.2021.133010

Cilt 427