Recursive representations for the unique solution of the transport equation on isolated time scales. Issue 1 (10th February 2011)

• Record Type: Journal Article
• Authors: Ahrendt, C.
• Is Part Of: International journal of dynamical systems and differential equations. Volume 3:Issue 1/2(2011)
• Page Start: 206
• Page End: 233
• Publication Date: 2011-02-10
• Subjects: transport equation -- time scales; Differential equations -- Periodicals; 515.35
• Languages: English
• ISSNs: 1752-3583

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.