Applications of improved duality lemmas to the discrete\n coagulation-fragmentation equations with diffusion

2016/06/24 by Maxime Breden, Breden, Maxime
Mathematics · Medicine · #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Biology Tumor Growth #Trauma, Hemostasis, Coagulopathy, Resuscitation

paper · pdf · doi:10.48550/arxiv.1606.07661

openalex publication_date 2016/06/24 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

In this paper, we investigate the use of so called "duality lemmas" to study\nthe system of discrete coagulation-fragmentation equations with diffusion. When\nthe fragmentation is strong enough with respect to the coagulation, we show\nthat we have creation and propagation of superlinear moments. In particular\nthis implies that strong enough fragmentation can prevent gelation even for\nsuperlinear coagulation, a statement which was only known up to now in the\nhomogeneous setting. We also use this control of superlinear moments to extend\na recent result about the regularity of the solutions in the pure coagulation\ncase, to strong fragmentation models.\n

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• A note on mass-conserving solutions to the coagulation-fragmentation\n equation by using non-conservative approximation
• Global solutions of continuous coagulation-fragmentation equations with unbounded coefficients
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