Year: 2023
Author: Mengna Yang, Yufeng Nie
International Journal of Numerical Analysis and Modeling, Vol. 20 (2023), Iss. 4 : pp. 478–496
Abstract
In this paper, we consider a two-dimensional linear nonlocal model involving a singular matrix kernel. For the initial value problem, we first give well-posedness results and energy conservation via Fourier transform. Meanwhile, we also discuss the corresponding Dirichlet-type nonlocal boundary value problems in the cases of both positive and semi-positive definite kernels, where the core is the coercivity of bilinear forms. In addition, in the limit of vanishing nonlocality, the solution of the nonlocal model is seen to converge to a solution of its classical elasticity local model provided that $c_t = 0.$
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ijnam2023-1020
International Journal of Numerical Analysis and Modeling, Vol. 20 (2023), Iss. 4 : pp. 478–496
Published online: 2023-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 19
Keywords: Nonlocal model well-posedness convergence singular matrix kernel coercivity.