Florin Bobaru
University of Nebraska-Lincoln, Lincoln, Nebraska, USA

Peridynamic models are described by integro-differential equations (IDEs) with associated initial and nonlocal boundary conditions. I will present some recent results on obtaining analytical solutions to transient diffusion (heat and mass transfer, etc.) and elastodynamics problems using the idea of separation of variables employed in the classical partial differential equations (PDEs) problems. We show that, formally, the solutions to the initial and boundary values problems for IDEs are identical to those of the corresponding PDEs-based problems with the exception of the presence of a "nonlocal factor" which becomes equal to one in the PDE case. The discussion covers both 1D and 2D cases, and extensions to 3D problems are immediate. For a number of examples we prove uniform convergence of the series solutions. If time permits, I will also discuss some interesting connections between analytical classical solutions and approximate nonlocal solutions. This work is in collaboration with Prof. Z. Chen (Huazhong University of Science and Technology, China) and Dr. S. Jafarzadeh (Lehigh University, USA), and is detailed in https://doi.org/10.1007/s42102-022-00080-7 (for diffusion) and a paper to appear in Int. J. of Engineering Science.