Please use this identifier to cite or link to this item: https://hdl.handle.net/20.500.11851/1685
Title: On a class of nonlocal wave equations from applications
Authors: Beyer, Horst Reinhard
Aksoylu, Burak
Çeliker, Fatih
29230
Keywords: Finite-Element-Method
 Long-Range Forces
 Peridynamic Theory
 Linear Elasticity
 Global Existence
 Navier Equation
 Blow-Up
 Diffusion
 Models
 Approximation
Issue Date: Jun-2016
Publisher: American Institute of Physics Inc.
Source: Beyer, H. R., Aksoylu, B., & Celiker, F. (2016). On a class of nonlocal wave equations from applications. Journal of Mathematical Physics, 57(6), 062902.
Abstract: We study equations from the area of peridynamics, which is a nonlocal extension of elasticity. The governing equations form asystem of nonlocal wave equations. We take a novel approach by applying operator theory methods in a systematic way. On the unbounded domain Rn, we present three main results. As main result 1, we find that the governing operator is a bounded function of the governing operator of classical elasticity. As main result 2, a consequence of main result 1, we prove that the peridynamic solutions strongly converge to the classical solutions by utilizing, for the first time, strong resolvent convergence. In addition, main result 1 allows us to incorporate local boundary conditions, in particular, into peridynamics. This avenue of research is developed in companion papers, providing a remedy for boundary effects. As main result 3, employing spherical Bessel functions, we give a new practical series representation of the solution which allows straightforward numerical treatment with symbolic computation.
URI: https://doi.org/10.1063/1.4953252
https://hdl.handle.net/20.500.11851/1685
ISSN: 0022-2488
Appears in Collections:Matematik Bölümü / Department of Mathematics
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

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