nonlocal vector calculus

In the current paper, we develop a nonlocal propagation model, which describes the diffusion wave process.  The main motivation of this work is to apply the nonlocal vector calculus, introduced and developed by Du et al. [1] to such hyperbolic problem.  Moreover, based on some density arguments, some a priori estimates and using the Galerkin approach, we prove existence and uniqueness of a weak solution to the nonlocal wave equation widely adopted in various applications.