Publication
Mathematical aspects of coagulation-fragmentation equations
| Summary: | We give an overview of the mathematical literature on the coagulation-like equations, from an analytic deterministic perspective. In Section 1 we present the coagulation type equations more commonly encountered in the scientific and mathematical literature and provide a brief historical overview of relevant works. In Section 2 we present results about existence and uniqueness of solutions in some of those systems, namely the discrete Smoluchowski and coagulation-fragmentation: we start by a brief description of the functional spaces, and then review the results on existence of solutions with a brief description of the main ideas of the proofs. This part closes with the consideration of uniqueness results. In Sections 3 and 4 we are concerned with several aspects of the solutions behaviour.We pay special attention to the long time convergence to equilibria, self-similar behaviour, and density conservation or lack thereof. |
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| Main Authors: | Costa, Fernando Pestana da |
| Subject: | Coagulation equations Coagulation-fragmentation equations |
| Year: | 2015 |
| Country: | Portugal |
| Document type: | book part |
| Access type: | open access |
| Associated institution: | Universidade Aberta |
| Language: | English |
| Origin: | Repositório Aberto da Universidade Aberta |
| Summary: | We give an overview of the mathematical literature on the coagulation-like equations, from an analytic deterministic perspective. In Section 1 we present the coagulation type equations more commonly encountered in the scientific and mathematical literature and provide a brief historical overview of relevant works. In Section 2 we present results about existence and uniqueness of solutions in some of those systems, namely the discrete Smoluchowski and coagulation-fragmentation: we start by a brief description of the functional spaces, and then review the results on existence of solutions with a brief description of the main ideas of the proofs. This part closes with the consideration of uniqueness results. In Sections 3 and 4 we are concerned with several aspects of the solutions behaviour.We pay special attention to the long time convergence to equilibria, self-similar behaviour, and density conservation or lack thereof. |
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