WELL-POSEDNESS AND CONVERGENCE ANALYSIS OF A NONLOCAL MODEL WITH SINGULAR MATRIX KERNEL

Mengna Yang; Yufeng Nie

doi:10.4208/ijnam2023-1020

WELL-POSEDNESS AND CONVERGENCE ANALYSIS OF A NONLOCAL MODEL WITH SINGULAR MATRIX KERNEL

Mengna Yang, Yufeng Nie

School of Mathematics and Statistics

Northwestern Polytechnical University Xian

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	478-496
Number of pages	19
Journal	International Journal of Numerical Analysis and Modeling
Volume	20
Issue number	4
DOIs	https://doi.org/10.4208/ijnam2023-1020
State	Published - 2023

Keywords

coercivity
convergence
Nonlocal model
singular matrix kernel
well-posedness

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

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10.4208/ijnam2023-1020

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title = "WELL-POSEDNESS AND CONVERGENCE ANALYSIS OF A NONLOCAL MODEL WITH SINGULAR MATRIX KERNEL",

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 ct = 0.",

keywords = "coercivity, convergence, Nonlocal model, singular matrix kernel, well-posedness",

author = "Mengna Yang and Yufeng Nie",

note = "Publisher Copyright: {\textcopyright} 2023 Institute for Scientific Computing and Information.",

year = "2023",

doi = "10.4208/ijnam2023-1020",

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AU - Yang, Mengna

AU - Nie, Yufeng

PY - 2023

Y1 - 2023

N2 - 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 ct = 0.

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 ct = 0.

KW - coercivity

KW - convergence

KW - Nonlocal model

KW - singular matrix kernel

KW - well-posedness

UR - http://www.scopus.com/inward/record.url?scp=85161006422&partnerID=8YFLogxK

U2 - 10.4208/ijnam2023-1020

DO - 10.4208/ijnam2023-1020

M3 - 文章

AN - SCOPUS:85161006422

SN - 1705-5105

VL - 20

SP - 478

EP - 496

JO - International Journal of Numerical Analysis and Modeling

JF - International Journal of Numerical Analysis and Modeling

IS - 4

ER -

WELL-POSEDNESS AND CONVERGENCE ANALYSIS OF A NONLOCAL MODEL WITH SINGULAR MATRIX KERNEL

Abstract

Keywords

UN SDGs

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