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Volume 20, Issue 4
Well-Posedness and Convergence Analysis of a Nonlocal Model with Singular Matrix Kernel

Mengna Yang & Yufeng Nie

DOI: 10.4208/ijnam2023-1020

Int. J. Numer. Anal. Mod., 20 (2023), pp. 478-496.

Published online: 2023-05

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  • 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 $c_t = 0.$

  • Keywords

Nonlocal model, well-posedness, convergence, singular matrix kernel, coercivity.

  • AMS Subject Headings

45F15, 45K05, 46E40, 74B99

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-20-478, author = {Yang , Mengna and Nie , Yufeng}, title = {Well-Posedness and Convergence Analysis of a Nonlocal Model with Singular Matrix Kernel}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2023}, volume = {20}, number = {4}, pages = {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 $c_t = 0.$

}, issn = {2617-8710}, doi = {https://doi.org/10.4208/ijnam2023-1020}, url = {http://global-sci.org/intro/article_detail/ijnam/21712.html} }
TY - JOUR T1 - Well-Posedness and Convergence Analysis of a Nonlocal Model with Singular Matrix Kernel AU - Yang , Mengna AU - Nie , Yufeng JO - International Journal of Numerical Analysis and Modeling VL - 4 SP - 478 EP - 496 PY - 2023 DA - 2023/05 SN - 20 DO - http://doi.org/10.4208/ijnam2023-1020 UR - https://global-sci.org/intro/article_detail/ijnam/21712.html KW - Nonlocal model, well-posedness, convergence, singular matrix kernel, coercivity. AB -

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 $c_t = 0.$

Mengna Yang & Yufeng Nie. (2023). Well-Posedness and Convergence Analysis of a Nonlocal Model with Singular Matrix Kernel. International Journal of Numerical Analysis and Modeling. 20 (4). 478-496. doi:10.4208/ijnam2023-1020
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