Mathematical analysis for the peridynamic nonlocal continuum theory*
Department of Mathematics, Pennsylvania State University, University Park, PA 16802, USA. email@example.com; firstname.lastname@example.org
Revised: 21 March 2010
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.
Mathematics Subject Classification: 45A05 / 46N20 / 74B99
Key words: Peridynamic model / nonlocal continuum theory / well-posedness / Navier equation
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