{"id":{"repo_id":"strathclyde","oai_identifier":"oai:strathclyde:wm117p04t"},"canonical_url":"https://search.dev.ndltd.org/etd/strathclyde/oai:strathclyde:wm117p04t","repository":{"repo_id":"strathclyde","name":"University of Strathclyde","base_url":"https://stax.strath.ac.uk/catalog/oai"},"display":{"title":"The discrete coagulation-fragmentation system","abstract":"In this thesis, we examine an infinite system of ordinary differential equations that models the evolution of fragmenting and coalescing discrete-sized particle clusters.We express this discrete coagulation-fragmentation system as an abstract Cauchy problem posed in an appropriate Banach space of sequences. The theory of operator semigroups is then used to establish the existence and uniqueness of solutions. We also investigate properties of the solutions, such as positivity, mass conservation and asymptotic behaviour. A main aim of this thesis is to relax the assumptions that have previously been required, when using a semigroupapproach, to obtain the existence and uniqueness of physically relevant solutions.Moreover, we consider the case when the infinite system is non-autonomous dueto time-dependent coagulation and fragmentation coefficients.","abstract_html":"In this thesis, we examine an infinite system of ordinary differential equations that models the evolution of fragmenting and coalescing discrete-sized particle clusters.We express this discrete coagulation-fragmentation system as an abstract Cauchy problem posed in an appropriate Banach space of sequences. The theory of operator semigroups is then used to establish the existence and uniqueness of solutions. We also investigate properties of the solutions, such as positivity, mass conservation and asymptotic behaviour. A main aim of this thesis is to relax the assumptions that have previously been required, when using a semigroupapproach, to obtain the existence and uniqueness of physically relevant solutions.Moreover, we consider the case when the infinite system is non-autonomous dueto time-dependent coagulation and fragmentation coefficients.","abstract_has_math":false,"creators":["Kerr, Lyndsay"],"institution":"University of Strathclyde","degree_name":"phd","degree_level":"doctoral-pg","degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Lamb, Wilson","Langer, Matthias"],"committee_chairs":[],"committee_members":[],"year":2020,"date_issued":"2020","date_published":"2020","updated_at":"2026-07-24T04:47:28Z","subjects":[],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier.doi","label":"DOI","values":["10.48730/pa0q-kp60"],"render_values":[{"text":"10.48730/pa0q-kp60","href":"https://doi.org/10.48730/pa0q-kp60","code":true}]},{"key":"dc:identifier","label":"Identifier","values":["T15514"],"render_values":[{"text":"T15514","href":null,"code":true}]},{"key":"dc:creator.authoridentifier","label":"Author Identifier","values":["201669016"],"render_values":[{"text":"201669016","href":null,"code":true}]}]},"links":{"outbound_url":"https://stax.strath.ac.uk/concern/theses/wm117p04t","outbound_label":"Repository record","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Lamb, Wilson","Langer, Matthias"]},{"key":"dc:creator","label":"Author","values":["Kerr, Lyndsay"]},{"key":"dc:creator.authoridentifier","label":"Author Identifier","values":["201669016"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2019"]},{"key":"dc:date.issued","label":"Date","values":["2020"]},{"key":"dc:publisher.department","label":"Dc Publisher Department","values":["Department of Mathematics and Statistics"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["University of Strathclyde"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["doctoral-pg"]},{"key":"dc:type.qualificationname","label":"Dc Type Qualificationname","values":["phd"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["T15514"]},{"key":"dc:identifier.doi","label":"DOI","values":["10.48730/pa0q-kp60"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://stax.strath.ac.uk/concern/theses/wm117p04t"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["In this thesis, we examine an infinite system of ordinary differential equations that models the evolution of fragmenting and coalescing discrete-sized particle clusters.We express this discrete coagulation-fragmentation system as an abstract Cauchy problem posed in an appropriate Banach space of sequences. The theory of operator semigroups is then used to establish the existence and uniqueness of solutions. We also investigate properties of the solutions, such as positivity, mass conservation and asymptotic behaviour. A main aim of this thesis is to relax the assumptions that have previously been required, when using a semigroupapproach, to obtain the existence and uniqueness of physically relevant solutions.Moreover, we consider the case when the infinite system is non-autonomous dueto time-dependent coagulation and fragmentation coefficients."]},{"key":"dc:description.abstract","label":"Abstract","values":["In this thesis, we examine an infinite system of ordinary differential equations that models the evolution of fragmenting and coalescing discrete-sized particle clusters.We express this discrete coagulation-fragmentation system as an abstract Cauchy problem posed in an appropriate Banach space of sequences. The theory of operator semigroups is then used to establish the existence and uniqueness of solutions. We also investigate properties of the solutions, such as positivity, mass conservation and asymptotic behaviour. A main aim of this thesis is to relax the assumptions that have previously been required, when using a semigroupapproach, to obtain the existence and uniqueness of physically relevant solutions.Moreover, we consider the case when the infinite system is non-autonomous dueto time-dependent coagulation and fragmentation coefficients."]},{"key":"dc:title","label":"Title","values":["The discrete coagulation-fragmentation system"]}]}],"canonical_facts":{"dc:contributor.advisor":["Lamb, Wilson","Langer, Matthias"],"dc:creator":["Kerr, Lyndsay"],"dc:creator.authoridentifier":["201669016"],"dc:date":["2019"],"dc:date.issued":["2020"],"dc:description":["In this thesis, we examine an infinite system of ordinary differential equations that models the evolution of fragmenting and coalescing discrete-sized particle clusters.We express this discrete coagulation-fragmentation system as an abstract Cauchy problem posed in an appropriate Banach space of sequences. The theory of operator semigroups is then used to establish the existence and uniqueness of solutions. We also investigate properties of the solutions, such as positivity, mass conservation and asymptotic behaviour. A main aim of this thesis is to relax the assumptions that have previously been required, when using a semigroupapproach, to obtain the existence and uniqueness of physically relevant solutions.Moreover, we consider the case when the infinite system is non-autonomous dueto time-dependent coagulation and fragmentation coefficients."],"dc:description.abstract":["In this thesis, we examine an infinite system of ordinary differential equations that models the evolution of fragmenting and coalescing discrete-sized particle clusters.We express this discrete coagulation-fragmentation system as an abstract Cauchy problem posed in an appropriate Banach space of sequences. The theory of operator semigroups is then used to establish the existence and uniqueness of solutions. We also investigate properties of the solutions, such as positivity, mass conservation and asymptotic behaviour. A main aim of this thesis is to relax the assumptions that have previously been required, when using a semigroupapproach, to obtain the existence and uniqueness of physically relevant solutions.Moreover, we consider the case when the infinite system is non-autonomous dueto time-dependent coagulation and fragmentation coefficients."],"dc:identifier":["T15514"],"dc:identifier.doi":["10.48730/pa0q-kp60"],"dc:identifier.uri":["https://stax.strath.ac.uk/concern/theses/wm117p04t"],"dc:publisher.department":["Department of Mathematics and Statistics"],"dc:publisher.institution":["University of Strathclyde"],"dc:title":["The discrete coagulation-fragmentation system"],"dc:type.qualificationlevel":["doctoral-pg"],"dc:type.qualificationname":["phd"]},"updated_at":"2026-07-24T04:47:28Z"}