{"title":"具有强破碎且无平衡条件的离散混凝方程的指数趋向平衡","authors":"N. Fournier, S. Mischler","doi":"10.1098/rspa.2004.1294","DOIUrl":null,"url":null,"abstract":"The coagulation–fragmentation equation describes the concentration fi(t) of particles of size i ∈ N/{0} at time t ⩾ 0 in a spatially homogeneous infinite system of particles subjected to coalescence and break–up. We show that when the rate of fragmentation is sufficiently stronger than that of coalescence, (fi(t))i ∈ N/{0} tends to a unique equilibrium as t tends to infinity. Although we suppose that the initial datum is sufficiently small, we do not assume a detailed balance (or reversibility) condition. The rate of convergence we obtain is, furthermore, exponential.","PeriodicalId":20722,"journal":{"name":"Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences","volume":"1 1","pages":"2477 - 2486"},"PeriodicalIF":0.0000,"publicationDate":"2004-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"23","resultStr":"{\"title\":\"Exponential trend to equilibrium for discrete coagulation equations with strong fragmentation and without a balance condition\",\"authors\":\"N. Fournier, S. Mischler\",\"doi\":\"10.1098/rspa.2004.1294\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The coagulation–fragmentation equation describes the concentration fi(t) of particles of size i ∈ N/{0} at time t ⩾ 0 in a spatially homogeneous infinite system of particles subjected to coalescence and break–up. We show that when the rate of fragmentation is sufficiently stronger than that of coalescence, (fi(t))i ∈ N/{0} tends to a unique equilibrium as t tends to infinity. Although we suppose that the initial datum is sufficiently small, we do not assume a detailed balance (or reversibility) condition. The rate of convergence we obtain is, furthermore, exponential.\",\"PeriodicalId\":20722,\"journal\":{\"name\":\"Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences\",\"volume\":\"1 1\",\"pages\":\"2477 - 2486\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2004-09-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"23\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1098/rspa.2004.1294\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1098/rspa.2004.1294","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Exponential trend to equilibrium for discrete coagulation equations with strong fragmentation and without a balance condition
The coagulation–fragmentation equation describes the concentration fi(t) of particles of size i ∈ N/{0} at time t ⩾ 0 in a spatially homogeneous infinite system of particles subjected to coalescence and break–up. We show that when the rate of fragmentation is sufficiently stronger than that of coalescence, (fi(t))i ∈ N/{0} tends to a unique equilibrium as t tends to infinity. Although we suppose that the initial datum is sufficiently small, we do not assume a detailed balance (or reversibility) condition. The rate of convergence we obtain is, furthermore, exponential.
期刊介绍:
Proceedings A publishes articles across the chemical, computational, Earth, engineering, mathematical, and physical sciences. The articles published are high-quality, original, fundamental articles of interest to a wide range of scientists, and often have long citation half-lives. As well as established disciplines, we encourage emerging and interdisciplinary areas.