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This paper studies the structure of a parabolic partial differential equationon graphs and digital n-dimensional manifolds, which are digital models ofcontinuous n-manifolds. Conditions for the existence of solutions of equationsare determined and investigated. Numerical solutions of the equation on a Kleinbottle, a projective plane, a 4D sphere and a Moebius strip are presented.

cornell university

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