Existence and uniqueness results for the continuous coagulation and fragmentation equation

W. Lamb

Research output: Contribution to journalArticle

33 Citations (Scopus)

Abstract

A non-linear integro-differential equation modelling coagulation and fragmentation is investigated using the theory of strongly continuous semigroups of operators. Under the assumptions that the coagulation kernel is bounded and the overall rate of fragmentation satisfies a linear growth condition, global existence and uniqueness of mass-conserving solutions are established. This extends similar results obtained in earlier investigations. In the case of pure fragmentation, when no coagulation occurs, a precise characterization of the generator of the associated semigroup is also obtained by using perturbation results for substochastic semigroups due to Banasiak (Taiwanese J. Math. 2001; 5: 169-191) and Voigt (Transport Theory Statist. Phys. 1987; 16: 453-466).
LanguageEnglish
Pages703-721
Number of pages18
JournalMathematical Methods in the Applied Sciences
Volume27
Issue number6
DOIs
Publication statusPublished - 16 Mar 2004

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Coagulation
Existence and Uniqueness Results
Fragmentation
Semigroup
Semigroups of Operators
Nonlinear Integro-differential Equations
Strongly Continuous Semigroups
Transport Theory
Integrodifferential equations
Growth Conditions
Global Existence
Existence and Uniqueness
Generator
kernel
Perturbation
Modeling

Keywords

  • semigroups of operators
  • semilinear Cauchy problem
  • coagulation
  • fragmentation

Cite this

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Existence and uniqueness results for the continuous coagulation and fragmentation equation. / Lamb, W.

In: Mathematical Methods in the Applied Sciences, Vol. 27, No. 6, 16.03.2004, p. 703-721.

Research output: Contribution to journalArticle

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