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Conditioning analysis of nonlocal integral operators in fractional Sobolev spaces
(Society for Industrial and Applied Mathematics Publications, 2014-03)
We study the conditioning of nonlocal integral operators with singular and integrable kernels in fractional Sobolev spaces. These operators are used, for instance, in peridynamics formulation and nonlocal diffusion. In one ...
On a class of nonlocal wave equations from applications
(American Institute of Physics Inc., 2016-06)
We study equations from the area of peridynamics, which is a nonlocal extension of elasticity. The governing equations form asystem of nonlocal wave equations. We take a novel approach by applying operator theory methods ...