ANALYSIS OF A SCALAR NONLOCAL PERIDYNAMIC MODEL WITH A SIGN CHANGING KERNEL

In this paper, a scalar peridynamic model is analyzed. The study extends earlier works in the literature on scalar nonlocal diffusion and nonlocal peridynamic models to include a sign changing kernel. We prove the well-posedness of both variational problems with nonlocal constraints and time-dependent equations with or without damping. The analysis is based on some nonlocal Poincare type inequalities and compactness of the associated nonlocal operators. It also offers careful characterizations of the associated solution spaces such as compact embedding, separability and completeness along with regularity properties of solutions for different types of kernels.