Dynamic diffusion-type equations on discrete-space domains

Abstract

We consider a class of partial dynamic equations on discrete-space domains which includes, as a special case, the discrete-space versions of the diffusion (heat) equation. We focus on initial-value problems and study the existence and uniqueness of forward and backward solutions.

Moreover, we discuss other topics such as sum and sign preservation, maximum and minimum principles, or symmetry of solutions.

Keywords

• Diffusion equation
• Heat equation
• Semidiscrete equations
• Partial dynamic equations
• Time scales
• Random walk