@prefix dcat: . @prefix dct: . @prefix foaf: . @prefix vcard: . @prefix xsd: . a dcat:Dataset ; dct:description """ This thesis is devoted to the study of systems of particles undergoing successive coagulations and fragmentations. In the deterministic case, we deal with measure-valued solutions of the coagulation - multifragmentation equation. We also study, on the other hand, its stochastic counterpart: coalescence - multifragmentation Markov processes. In Chapter 1 we only take into account coagulation phenomena. We consider the Smoluchowski equation (which is deterministic) and the Marcus-Lushnikov process (the stochastic version) which can be seen as an approximation of the Smoluchowski equation. We derive a satisfying rate of convergence of the Marcus-Lushnikov process toward the solution to Smoluchowski's coagulation equation. \\noindent The result applies to a class of homogeneous-like coagulation kernels with homogeneity degree ranging in $(-\\infty,1]$. It relies on the use of the Wasserstein-type distance $d_{\\lambda}$, which has shown to be particularly well-adapted to coalescence phenomena. It was introduced and used in preceding works. In Chapter 2 we perform some simulations in order to confirm numerically the rate of convergence deduced in Chapter 1 for the kernels studied in this chapter. Finally, in Chapter 3 we add a fragmentation phenomena and consider a coagulation multiple-fragmentation equation, which describes the concentration $c_t(x)$ of particles of mass $x \\in (0,+\\infty)$ at the instant $t \\geq 0$. We study the existence and uniqueness of measured-valued solutions to this equation for homogeneous-like kernels of homogeneity parameter $\\lambda \\in (0,1]$ and bounded fragmentation kernels, although a non-finite measure giving the mass distribution of fragments and a possibly infinite number of fragments are considered. We also study a stochastic counterpart of this equation where a similar result is shown. We prove existence of such a process for a larger set of fragmentation kernels, namely we relax the boundedness hypothesis. In both cases, the initial state has a finite $\\lambda$-moment. """ ; dct:identifier "tel-00833475" ; dct:issued "2026-05-10T18:05:48.324382"^^xsd:dateTime ; dct:language "en" ; dct:modified "2026-05-10T18:05:48.324386"^^xsd:dateTime ; dct:publisher ; dct:title "Contribution to the probabilistic and numerical study of homogeneous Coagulation - Fragmentation equations" ; dcat:contactPoint [ a vcard:Organization ; vcard:fn "CCSD" ] ; dcat:distribution ; dcat:keyword "coagulation", "coalescence", "fragmentation", "infoeu-reposemanticsdoctoralthesis", "interacting-particle-system", "marcus-lushnikov", "mathmath-apmathematics-mathanalysis-of-pdes-mathap", "mathmath-prmathematics-mathprobability-mathpr", "multi", "smoluchowski", "systeme-de-particules", "theses" ; dcat:landingPage . a dcat:Distribution ; dct:format "HTML" ; dct:issued "2026-05-10T18:05:48.341571"^^xsd:dateTime ; dct:modified "2026-05-10T18:05:48.308728"^^xsd:dateTime ; dct:title "Contribution to the probabilistic and numerical study of homogeneous Coagulation - Fragmentation equations" ; dcat:accessURL . a foaf:Agent ; foaf:name "test_moissonnage_selune" . a foaf:Document .