Nonlocal operators with local boundary conditions in higher dimensions

摘要: We present novel nonlocal governing operators in 2D/3D for wave propagation and diffusion. The are inspired by peridynamics. They agree with the original peridynamics operator bulk of domain simultaneously enforce local boundary conditions (BC). main ingredients periodic, antiperiodic, mixed extensions separable kernel functions together even odd parts bivariate on rectangular/box domains. bounded self-adjoint. all possible 36 different types BC 2D which include pure combinations Neumann, Dirichlet, antiperiodic BC. Our construction is systematic easy to follow. provide numerical experiments that verify our theoretical findings. also compare solutions classical heat equations their counterparts.