Mathematical analysis for the peridynamic nonlocal continuum theory
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 45 (2011) no. 2, pp. 217-234.

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.

DOI : 10.1051/m2an/2010040
Classification : 45A05, 46N20, 74B99
Mots clés : peridynamic model, nonlocal continuum theory, well-posedness, Navier equation
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Du, Qiang; Zhou, Kun. Mathematical analysis for the peridynamic nonlocal continuum theory. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 45 (2011) no. 2, pp. 217-234. doi : 10.1051/m2an/2010040. http://archive.numdam.org/articles/10.1051/m2an/2010040/

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