The well-posedness and regularity of a peridynamic model with a special kernel is studied. The differential-integral equation describing the model is first converted to an operator valued Volterra integral equation. Then the existence and regularity of the solution of the peridynamics problem are established through the study of the Volterra integral equation. The regularity results improve the previous known results for more general peridynamics models.
"On the problems of peridynamics with special convolution kernels." J. Integral Equations Applications 26 (3) 301 - 321, FALL 2014. https://doi.org/10.1216/JIE-2014-26-3-301