ESAIM: Mathematical Modelling and Numerical Analysis

Research Article

Mathematical analysis for the peridynamic nonlocal continuum theory*

Du, Qianga1 and Zhou, Kuna1

a1 Department of Mathematics, Pennsylvania State University, University Park, PA 16802, USA.;


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)

Key Words:

  • Peridynamic model;
  • nonlocal continuum theory;
  • well-posedness;
  • Navier equation

Mathematics Subject Classification:

  • 45A05;
  • 46N20;
  • 74B99


*  This work is supported in part by NSF through grant DMS-0712744, and by DOE/Sandia Lab through grants 926627 and 961673.