A qualitative analysis of some models of tissue growth
type: Item
instance of: scholarly article
title: A qualitative analysis of some models of tissue growth
zbMATH Open document ID: 0786.92011
DOI: 10.1016/0025-5564(93)90009-Y
published in: Mathematical Biosciences
publication date: 1993-06-29T00:00:00Z
review text: The authors apply standard maximum principles to a general nonlinear parabolic partial differential equation describing the concentration of the growth inhibitory factor that controls cell mitosis. They show in this way that many of the qualitative features of the solution, which have been obtained from analytical solutions under special conditions on the cell geometry and depletion and source functions, can be obtained in general. They also discuss the applicability of this approach to the inverse problem of describing the source function from the solution.
Mathematics Subject Classification ID: 92C30
Mathematics Subject Classification ID: 92C40
Mathematics Subject Classification ID: 35Q92
Mathematics Subject Classification ID: 92C15
zbMATH DE Number: 219757
zbMATH Keywords: control of mitosis
zbMATH Keywords: maximum principles
zbMATH Keywords: general nonlinear parabolic partial differential equation
zbMATH Keywords: growth inhibitory factor
zbMATH Keywords: cell geometry
zbMATH Keywords: inverse problem
zbMATH Keywords: source function
Wikidata QID: Q52404498
author: N. F. Britton
author: M. A. J. Chaplain
reviewed by: J. M. Cushing
MaRDI profile type: Publication
cites work: A mathematical model of tumor growth. II. Effects of geometry and spatial nonuniformity on stability
cites work: A mathematical model of tumor growth. III. Comparison with experiment
cites work: Q3738973
cites work: Models for the Growth of a Solid Tumor by Diffusion
cites work: Q5533735
cites work: Q4746129
full work available at URL: 0025-5564(93)90009-y
OpenAlex ID: W2022220565
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description: scientific article; zbMATH DE number 219757