Exponential decay for the fragmentation or cell-division equation
type: Item
instance of: scholarly article
title: Exponential decay for the fragmentation or cell-division equation
zbMATH Open document ID: 1072.35195
published in: Journal of Differential Equations
publication date: 2005-02-22T00:00:00Z
review text: The authors consider the equation \[ \partial n(t, x)/\partial t+\partial n(t, x)/\partial x+ b(x)n(t, x)=4b(2x)n(t, 2x), t>0, x\geq 0 \] with the corresponding initial and boundary conditions. Here \(b\) is a given function. This equation is classical. It arises in various applications as a model for cell-division or fragmentation. In biology, it describes the evolution of the density of cells that grow and divide. The authors prove the existence of a stable steady distribution (first positive eigenvector) under general assumptions in the variable coefficients case. It is also investigated the exponential convergence, for large times, of solutions toward such a steady state.
Mathematics Subject Classification ID: 35R10
Mathematics Subject Classification ID: 92C37
Mathematics Subject Classification ID: 35B35
Mathematics Subject Classification ID: 35B40
zbMATH DE Number: 2136783
zbMATH Keywords: stable steady state
zbMATH Keywords: asymptotic stability
zbMATH Keywords: first positive eigenvector
Wikidata QID: Q60502874
author: Ben{ôı}t Perthame
author: Lenya Ryzhik
reviewed by: Michael I. Gil'
MaRDI profile type: Publication
full work available at URL: j.jde.2004.10.018
OpenAlex ID: W2085503446
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DOI: 10.1016/J.JDE.2004.10.018
description: scientific article; zbMATH DE number 2136783