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

Mengna Yang, Yufeng Nie

科研成果: 期刊稿件文章同行评审

摘要

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 rut(r> 0) , the existence results in Lp , 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.

源语言英语
文章编号189
期刊Zeitschrift fur Angewandte Mathematik und Physik
74
5
DOI
出版状态已出版 - 10月 2023

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