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 - <p style="text-align: justify;">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 $c_t = 0.$</p>