Functional Differential Equations

Pierre Magal, Shigui Ruan

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

The goal of this chapter is to apply the theories developed in the previous chapters to functional differential equations. In Section 7.1 retarded functional differential equations are rewritten as abstract Cauchy problems and the integrated semigroup theory is used to study the existence of integrated solutions and to establish a general Hopf bifurcation theorem. Section 7.2 deals with neutral functional differential equations. In Section 7.3, firstly it is shown that a delayed transport equation for cell growth and division has asynchronous exponential growth; secondly it is demonstrated that partial functional differential equations can also be set up as abstract Cauchy problems.

Original languageEnglish (US)
Title of host publicationApplied Mathematical Sciences (Switzerland)
PublisherSpringer
Pages309-356
Number of pages48
DOIs
StatePublished - Jan 1 2018

Publication series

NameApplied Mathematical Sciences (Switzerland)
Volume201
ISSN (Print)0066-5452
ISSN (Electronic)2196-968X

Fingerprint

Abstract Cauchy Problem
Functional Differential Equations
Differential equations
Integrated Semigroups
Retarded Functional Differential Equations
Partial Functional Differential Equation
Neutral Functional Differential Equation
Semigroup Theory
Exponential Growth
Transport Equation
Hopf Bifurcation
Division
Hopf bifurcation
Cell
Cell growth
Theorem

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

Magal, P., & Ruan, S. (2018). Functional Differential Equations. In Applied Mathematical Sciences (Switzerland) (pp. 309-356). (Applied Mathematical Sciences (Switzerland); Vol. 201). Springer. https://doi.org/10.1007/978-3-030-01506-0_7

Functional Differential Equations. / Magal, Pierre; Ruan, Shigui.

Applied Mathematical Sciences (Switzerland). Springer, 2018. p. 309-356 (Applied Mathematical Sciences (Switzerland); Vol. 201).

Research output: Chapter in Book/Report/Conference proceedingChapter

Magal, P & Ruan, S 2018, Functional Differential Equations. in Applied Mathematical Sciences (Switzerland). Applied Mathematical Sciences (Switzerland), vol. 201, Springer, pp. 309-356. https://doi.org/10.1007/978-3-030-01506-0_7
Magal P, Ruan S. Functional Differential Equations. In Applied Mathematical Sciences (Switzerland). Springer. 2018. p. 309-356. (Applied Mathematical Sciences (Switzerland)). https://doi.org/10.1007/978-3-030-01506-0_7
Magal, Pierre ; Ruan, Shigui. / Functional Differential Equations. Applied Mathematical Sciences (Switzerland). Springer, 2018. pp. 309-356 (Applied Mathematical Sciences (Switzerland)).
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