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 |
Keywords: | Finite-Element-Method Long-Range Forces Peridynamic Theory Linear Elasticity Global Existence Navier Equation Blow-Up Diffusion Models Approximation |
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 |
Files in This Item:
File | Description | Size | Format | |
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BurakAksoylu_1.pdf | 4.97 MB | Adobe PDF | ![]() View/Open |
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