Regularity and convergence results for nonlocal peridynamic equations with truncated tensor kernels

This paper is concerned with some properties of solutions for a two-dimensional linear nonlocal peridynamic model involving a smooth truncated integrable tensor kernel. For the stationary Dirichlet-type problem with zero boundary data, the higher integrability and H¹ regularity of its weak solution are established. On the other hand, for the nonstationary problem with a local damping term 2 ru_t(r> 0) , the existence results in L^p , Lβp and Hölder spaces are obtained via successive approximation methods, Bessel potential theory and standard ODE arguments, respectively. Further, under certain suitable assumptions on kernels, we can recover the corresponding local problem in the limit of δ→ 0 and prove that the limit of nonlocal solutions is a weak solution of the local counterparts exactly.