Delay differential equations

Document type: Journal Articles
Article type: Original article
Peer reviewed: Yes
Author(s): Yurii Grigoriev, Nail H. Ibragimov, Vladimir Kovalev, Sergey Meleshko
Title: Delay differential equations
Journal: Lecture Notes in Physics
Year: 2010
Volume: 806
Pagination: 251-292
ISSN: 0075-8450
Publisher: Springer
URI/DOI: 10.1007/978-90-481-3797-8_6
Organization: Blekinge Institute of Technology
Department: School of Engineering - Dept. of Mathematics & Natural Sciences (Sektionen för ingenjörsvetenskap - Avd.för matematik och naturvetenskap)
School of Engineering S-371 79 Karlskrona
+46 455 38 50 00
Language: English
Abstract: In this chapter, applications of group analysis to delay differential equations are considered. Many mathematical models in biology, physics and engineering, where there is a time lag or aftereffect, are described by delay differential equations. These equations are similar to ordinary differential equations, but their evolution involves past values of the state variable. For the sake of completeness the chapter is started with a short introduction into the theory of delay differential equations. The mathematical background of these equations is followed by the section which deals with the definition of an admitted Lie group for them and some examples. The purpose of the next section is to give a complete group classification with respect to admitted Lie groups of a second-order delay ordinary differential equation. The reasonable generalization of the definition of an equivalence Lie group for delay differential equations is considered in the next section. The last section of the chapter is devoted to application of the developed theory to the reaction-diffusion equation with a delay.
Subject: Mathematics\General