Title: Recursive representations for the unique solution of the transport equation on isolated time scales

Authors: C. Ahrendt

Addresses: Department of Mathematics, University of Wisconsin-Eau Claire, Eau Claire, WI 54702-4004, USA

Abstract: In this paper, we develop two recursive representations for the unique solution of the transport partial dynamic equation on an isolated time scale. We then use these representations to explicitly find the solution of the transport equation in several specific cases. Finally, we compare and contrast the behaviour with that of the well-known behaviour of the solution to the transport partial difference equation in the case where 𝕋 = ℤ.

Keywords: transport equations; time scales; partial dynamic equations.

DOI: 10.1504/IJDSDE.2011.038503

International Journal of Dynamical Systems and Differential Equations, 2011 Vol.3 No.1/2, pp.206 - 233

Published online: 09 Feb 2011 *

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