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Discrete-Space Systems of Partial Dynamic Equations and Discrete-Space Wave Equation

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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.

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Acknowledgments

The paper was supported by Grant No. GA15-076905 of the Czech Science Foundation. The author is grateful to the anonymous referee for several helpful comments.

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  1. Faculty of Mathematics and Physics, Charles University in Prague, Sokolovská 83, 186 75, Praha 8, Czech Republic

    Antonín Slavík

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  1. Antonín Slavík
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Correspondence to Antonín Slavík.

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Slavík, A. Discrete-Space Systems of Partial Dynamic Equations and Discrete-Space Wave Equation. Qual. Theory Dyn. Syst. 16, 299–315 (2017). https://doi.org/10.1007/s12346-016-0193-0

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  • DOI: https://doi.org/10.1007/s12346-016-0193-0

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