Stability for a class of equilibrium solutions to the coagulation-fragmentation equation

Wilson Lamb, Iain W. Stewart

Research output: Chapter in Book/Report/Conference proceedingChapter

36 Downloads (Pure)

Abstract

We consider the behaviour of solutions to the continuous constant-rate coagulation-fragmentation equation in the vicinity of an equilibrium solution. Semigroup methods are used to show that the governing linear equation for a perturbation epsilon(x,t) has a unique globally defined solution for suitable initial conditions. In addition, Laplace transforms and the method of characteristics lead to an explicit formula for epsilon. The long-term behavior of epsilon is also discussed.
Original languageEnglish
Title of host publicationNumerical Analysis and Applied Mathematics
Subtitle of host publicationInternational Conference on Numerical Analysis and Applied Mathematics
Pages942-945
Number of pages4
Volume1048
Edition1
DOIs
Publication statusPublished - 20 Sep 2008
EventInternational Conference on Numerical Analysis and Applied Mathematics 2008 - Kos, Greece
Duration: 16 Sep 200820 Sep 2008

Publication series

NameAIP Conference Proceedings
PublisherAmerican Institute of Physics

Conference

ConferenceInternational Conference on Numerical Analysis and Applied Mathematics 2008
CountryGreece
CityKos
Period16/09/0820/09/08

Fingerprint

Method of Characteristics
Coagulation
Equilibrium Solution
Behavior of Solutions
Fragmentation
Rate Constant
Laplace transform
Explicit Formula
Governing equation
Linear equation
Initial conditions
Semigroup
Perturbation
Class

Keywords

  • coagulation–fragmentation
  • stability of equilibria
  • numerical analysis
  • applied mathematics

Cite this

Lamb, W., & Stewart, I. W. (2008). Stability for a class of equilibrium solutions to the coagulation-fragmentation equation. In Numerical Analysis and Applied Mathematics: International Conference on Numerical Analysis and Applied Mathematics (1 ed., Vol. 1048, pp. 942-945). (AIP Conference Proceedings). https://doi.org/10.1063/1.2991091
Lamb, Wilson ; Stewart, Iain W. / Stability for a class of equilibrium solutions to the coagulation-fragmentation equation. Numerical Analysis and Applied Mathematics: International Conference on Numerical Analysis and Applied Mathematics. Vol. 1048 1. ed. 2008. pp. 942-945 (AIP Conference Proceedings).
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Lamb, W & Stewart, IW 2008, Stability for a class of equilibrium solutions to the coagulation-fragmentation equation. in Numerical Analysis and Applied Mathematics: International Conference on Numerical Analysis and Applied Mathematics. 1 edn, vol. 1048, AIP Conference Proceedings, pp. 942-945, International Conference on Numerical Analysis and Applied Mathematics 2008, Kos, Greece, 16/09/08. https://doi.org/10.1063/1.2991091

Stability for a class of equilibrium solutions to the coagulation-fragmentation equation. / Lamb, Wilson; Stewart, Iain W.

Numerical Analysis and Applied Mathematics: International Conference on Numerical Analysis and Applied Mathematics. Vol. 1048 1. ed. 2008. p. 942-945 (AIP Conference Proceedings).

Research output: Chapter in Book/Report/Conference proceedingChapter

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N2 - We consider the behaviour of solutions to the continuous constant-rate coagulation-fragmentation equation in the vicinity of an equilibrium solution. Semigroup methods are used to show that the governing linear equation for a perturbation epsilon(x,t) has a unique globally defined solution for suitable initial conditions. In addition, Laplace transforms and the method of characteristics lead to an explicit formula for epsilon. The long-term behavior of epsilon is also discussed.

AB - We consider the behaviour of solutions to the continuous constant-rate coagulation-fragmentation equation in the vicinity of an equilibrium solution. Semigroup methods are used to show that the governing linear equation for a perturbation epsilon(x,t) has a unique globally defined solution for suitable initial conditions. In addition, Laplace transforms and the method of characteristics lead to an explicit formula for epsilon. The long-term behavior of epsilon is also discussed.

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KW - stability of equilibria

KW - numerical analysis

KW - applied mathematics

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Lamb W, Stewart IW. Stability for a class of equilibrium solutions to the coagulation-fragmentation equation. In Numerical Analysis and Applied Mathematics: International Conference on Numerical Analysis and Applied Mathematics. 1 ed. Vol. 1048. 2008. p. 942-945. (AIP Conference Proceedings). https://doi.org/10.1063/1.2991091