# Mathematical analysis for the peridynamic nonlocal continuum theory*

ESAIM: Mathematical Modelling and Numerical Analysis (2011)

- Volume: 45, Issue: 2, page 217-234
- ISSN: 0764-583X

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topDu, Qiang, and Zhou, Kun. "Mathematical analysis for the peridynamic nonlocal continuum theory*." ESAIM: Mathematical Modelling and Numerical Analysis 45.2 (2011): 217-234. <http://eudml.org/doc/197580>.

@article{Du2011,

abstract = {
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.
},

author = {Du, Qiang, Zhou, Kun},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Peridynamic model; nonlocal continuum theory;
well-posedness; Navier equation; peridynamic model; well-posedness; spring network system; Cauchy problem; classical elastic models},

language = {eng},

month = {1},

number = {2},

pages = {217-234},

publisher = {EDP Sciences},

title = {Mathematical analysis for the peridynamic nonlocal continuum theory*},

url = {http://eudml.org/doc/197580},

volume = {45},

year = {2011},

}

TY - JOUR

AU - Du, Qiang

AU - Zhou, Kun

TI - Mathematical analysis for the peridynamic nonlocal continuum theory*

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2011/1//

PB - EDP Sciences

VL - 45

IS - 2

SP - 217

EP - 234

AB -
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.

LA - eng

KW - Peridynamic model; nonlocal continuum theory;
well-posedness; Navier equation; peridynamic model; well-posedness; spring network system; Cauchy problem; classical elastic models

UR - http://eudml.org/doc/197580

ER -

## References

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