Coagulation and fragmentation processes with evolving size and shape profiles: a semigroup approach

Wilson Lamb; Adam McBride; Ann Louise Smith

doi:10.3934/dcds.2013.33.5177

Coagulation and fragmentation processes with evolving size and shape profiles: a semigroup approach

Wilson Lamb, Adam McBride, Ann Louise Smith

Mathematics And Statistics

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Abstract

We investigate a class of bivariate coagulation-fragmentation equations. These equations describe the evolution of a system of particles that are characterised not only by a discrete size variable but also by a shape variable which can be either discrete or continuous. Existence and uniqueness of strong solutions to the associated abstract Cauchy problems are established by using the theory of substochastic semigroups of operators.

Original language	English
Pages (from-to)	5177-5187
Number of pages	11
Journal	Discrete and Continuous Dynamical Systems - Series A
Volume	33
Issue number	11/12
Early online date	16 May 2013
DOIs	https://doi.org/10.3934/dcds.2013.33.5177
Publication status	Published - Nov 2013

Keywords

fragmentation process
coagulation–fragmentation
size profiles
semigroup approach
semilinear Cauchy problems
multicomponent coagulation-fragmentation processes
semigroups of operators

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10.3934/dcds.2013.33.5177

LMcS DCDS 2013Submitted manuscript, 108 KB

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title = "Coagulation and fragmentation processes with evolving size and shape profiles: a semigroup approach",

abstract = "We investigate a class of bivariate coagulation-fragmentation equations. These equations describe the evolution of a system of particles that are characterised not only by a discrete size variable but also by a shape variable which can be either discrete or continuous. Existence and uniqueness of strong solutions to the associated abstract Cauchy problems are established by using the theory of substochastic semigroups of operators.",

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Y1 - 2013/11

N2 - We investigate a class of bivariate coagulation-fragmentation equations. These equations describe the evolution of a system of particles that are characterised not only by a discrete size variable but also by a shape variable which can be either discrete or continuous. Existence and uniqueness of strong solutions to the associated abstract Cauchy problems are established by using the theory of substochastic semigroups of operators.

AB - We investigate a class of bivariate coagulation-fragmentation equations. These equations describe the evolution of a system of particles that are characterised not only by a discrete size variable but also by a shape variable which can be either discrete or continuous. Existence and uniqueness of strong solutions to the associated abstract Cauchy problems are established by using the theory of substochastic semigroups of operators.

KW - fragmentation process

KW - coagulation–fragmentation

KW - size profiles

KW - semigroup approach

KW - semilinear Cauchy problems

KW - multicomponent coagulation-fragmentation processes

KW - semigroups of operators

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DO - 10.3934/dcds.2013.33.5177

M3 - Article

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VL - 33

SP - 5177

EP - 5187

JO - Discrete and Continuous Dynamical Systems - Series A

JF - Discrete and Continuous Dynamical Systems - Series A

IS - 11/12

ER -

Coagulation and fragmentation processes with evolving size and shape profiles: a semigroup approach

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Keywords

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