A doubly nonlocal Laplace operator and its connection to the classical Laplacian

DOI10.1216/JIE-2019-31-3-379zbMath1429.35189OpenAlexW2977127122MaRDI QIDQ2290672

Petronela Radu, Kelsey Wells

Publication date: 29 January 2020

Published in: Journal of Integral Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.jiea/1572660076

zbMATH Keywords

convergenceconvolutionstate-based peridynamicsnonlocal modelsnonlocal Laplacianhorizon of interaction

Mathematics Subject Classification ID

Theories of fracture and damage (74A45) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Integral operators (45P05) Linear integral equations (45A05) PDEs in connection with mechanics of deformable solids (35Q74) Integro-partial differential equations (35R09)

Related Items (4)

A new nonlocal calculus framework. Helmholtz decompositions, properties, and convergence for nonlocal operators in the limit of the vanishing horizon ⋮ Nonlocal gradient operators with a nonspherical interaction neighborhood and their applications ⋮ A fast convolution-based method for peridynamic transient diffusion in arbitrary domains ⋮ Towards a unified theory of fractional and nonlocal vector calculus

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