Title: Structure of a Parabolic Partial Differential Equation on Graphs and Digital spaces. Solution of PDE on Digital Spaces: a Klein Bottle, a Projective Plane, a 4D Sphere and a Moebius Band,
Abstract: This paper studies the structure of a parabolic partial differential equation
on graphs and digital n-dimensional manifolds, which are digital models of
continuous n-manifolds. Conditions for the existence of solutions of equations
are determined and investigated. Numerical solutions of the equation on a Klein
bottle, a projective plane, a 4D sphere and a Moebius strip are presented.