A degenerate parabolic equation modelling the spread of an epidemic
type: Item
instance of: scholarly article
title: A degenerate parabolic equation modelling the spread of an epidemic
zbMATH Open document ID: 0617.35066
DOI: 10.1007/BF01769226
author: Maura Ughi
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 1986-01-01T00:00:00Z
review text: This paper concerns the diffusive approximation of a model for the spread of an epidemic in a closed population without remotion: \[ s_ t=s s_{xx}-s(1-s)\quad in\quad {\mathbb{R}}\times (0,T),\quad 0\leq s\leq 1. \] A counterexample for uniqueness of solutions in a natural Lipschitz class is given. The authors formulate a more appropriate definition of solution and prove uniqueness and existence is results. The solution is constructed using \(C^{\infty}\) approximations of initial data. It is also shown that supp s\(=\sup p s_ 0\), \(0\leq t\leq T\), where \(s_ 0\) is the initial data. The main results of this paper hold for equations, \(u_ t=f(u)u_{xx}+g(u)\), under suitable assumptions on f and g.
Mathematics Subject Classification ID: 35K65
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 35D05
Mathematics Subject Classification ID: 35K15
zbMATH DE Number: 4000534
zbMATH Keywords: diffusive approximation
zbMATH Keywords: spread of an epidemic
zbMATH Keywords: closed population without remotion
zbMATH Keywords: uniqueness
zbMATH Keywords: existence
zbMATH Keywords: approximations of initial data
MaRDI profile type: Publication
cites work: Q3311022
cites work: Q4180668
cites work: A generalization of the Kermack-McKendrick deterministic epidemic model
cites work: Q5520962
cites work: Hölder Continuity of Solutions of Parabolic Equations
cites work: Q5562267
cites work: Q4060816
cites work: Q3961832
full work available at URL: https://doi.org/10.1007/bf01769226
OpenAlex ID: W2059915765
description: scientific article; zbMATH DE number 4000534