Discrete-space systems of partial dynamic equations and discrete-space wave equation

Abstract

We study the well-posedness of initial-value problems for systems of partial dynamic equations with discrete space and arbitrary time domain. We also present the superposition principle for infinite linear combinations of solutions.

As an example, we consider the discrete-space wave equation, which is equivalent to a pair of first-order equations. We provide a general method for finding fundamental solutions and illustrate it on several examples of time scales.

Keywords

• wave equation
• lattice equation
• time scale
• well-posedness
• superposition principle
• fundamental solution