On a mathematical model for body tissue inflammation
type: Item
instance of: scholarly article
title: On a mathematical model for body tissue inflammation
zbMATH Open document ID: 0727.92009
DOI: 10.1007/BF00276951
published in: Journal of Mathematical Biology
publication date: 1989-01-01T00:00:00Z
review text: A mathematical analysis is made of a model of inflammatory response to bacterial invasion of body tissue proposed by \textit{D. A. Lauffenburger} and \textit{C. R. Kennedy} [ibid. 16, 141-163 (1983; Zbl 0537.92007)]. The model is a system of two coupled nonlinear parabolic partial differential equations. A positivity theorem, an existence theorem and a uniqueness theorem are proved. The main part of the proof of the existence theorem is to establish the existence of a semiclassical solution (belonging to \(L^ 2\) and with derivatives in the Sobolev sense) by obtaining a priori estimates and then using the Leray-Schauder method.
Mathematics Subject Classification ID: 92C50
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 35K60
Mathematics Subject Classification ID: 92C30
Mathematics Subject Classification ID: 35Q92
zbMATH DE Number: 4202082
zbMATH Keywords: tissue inflammation
zbMATH Keywords: bacterial inflammation
zbMATH Keywords: inflammatory response to bacterial invasion of body tissue
zbMATH Keywords: system of two coupled nonlinear parabolic partial differential equations
zbMATH Keywords: positivity theorem
zbMATH Keywords: existence theorem
zbMATH Keywords: uniqueness theorem
zbMATH Keywords: existence of a semiclassical solution
zbMATH Keywords: a priori estimates
zbMATH Keywords: Leray-Schauder method
Wikidata QID: Q52545539
author: Paola Cerrai
MaRDI profile type: Publication
cites work: Q5520962
cites work: Localized bacterial infection in a distributed model for tissue inflammation
cites work: Q5815802
full work available at URL: https://doi.org/10.1007/bf00276951
OpenAlex ID: W2038107159
description: scientific article; zbMATH DE number 4202082