Existence and uniqueness of density conserving solutions to the coagulation-fragmentation equations with strong fragmentation
type: Item
instance of: scholarly article
title: Existence and uniqueness of density conserving solutions to the coagulation-fragmentation equations with strong fragmentation
zbMATH Open document ID: 0839.34015
published in: Journal of Mathematical Analysis and Applications
publication date: 1996-06-16T00:00:00Z
full work available at URL: http://hdl.handle.net/10400.2/1466
review text: The paper investigates the coagulation-fragmentation equations \[ C_j(t) = {1 \over 2} \sum^{j - 1}_{k = 1} W_{j - k,k} \bigl( C(t) \bigr) - \sum^\infty_{k = 1} W_{j,k} \bigl( C(t)\bigr), \quad j = 1,2,3, \dots, \] where \(W_{j,k} (C(t)) = a_{j,k} \cdot C_j(t) C_k(t) - b_{j,k} \cdot C_{j + k} (t)\). The author proves the existence and uniqueness of admissible solutions for coagulation coefficients \(a_{j,k}\) satisfying \(a_{j,k} \leq K_\alpha \cdot (j \cdot k)^\alpha\) with \(\alpha \in ({1 \over 2}, 1]\), and for fragmentation coefficients satisfying a strong fragmentation condition.
Mathematics Subject Classification ID: 34A35
Mathematics Subject Classification ID: 34A12
Mathematics Subject Classification ID: 92C15
zbMATH DE Number: 811169
zbMATH Keywords: coagulation-fragmentation equations
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
author: F. P. Da Costa
reviewed by: A. Yu. Timofeev
MaRDI profile type: Publication
OpenAlex ID: W2276210967
DOI: 10.1006/JMAA.1995.1210
description: scientific article; zbMATH DE number 811169