ESAIM: M2AN 45 (2011) 217-234
Mathematical analysis for the peridynamic nonlocal continuum theory*
Qiang Du and Kun Zhou
Department of Mathematics, Pennsylvania State University, University Park, PA 16802, USA. email@example.com; firstname.lastname@example.org
We develop a functional analytical framework for a linear
peridynamic model of a spring network system in any space dimension.
Various properties of the peridynamic operators are examined for
general micromodulus functions. These properties are utilized to
establish the well-posedness of both the stationary peridynamic
model and the Cauchy problem of the time dependent peridynamic
model. The connections to the classical elastic models are also
Mathematics Subject Classification: 45A05 / 46N20 / 74B99
Key words: Peridynamic model / nonlocal continuum theory /
well-posedness / Navier equation
This work is supported in part by NSF through grant DMS-0712744, and by DOE/Sandia Lab through grants 926627 and
© EDP Sciences, SMAI, 2010
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