a1 Department of Mathematics, Pennsylvania State University, University Park, PA 16802, USA. firstname.lastname@example.org; email@example.com
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 provided.
(Received September 3 2009)
(Revised March 21 2010)
(Online publication August 2 2010)
Mathematics Subject Classification:
* This work is supported in part by NSF through grant DMS-0712744, and by DOE/Sandia Lab through grants 926627 and 961673.