On a degenerate diffusion equation of the form \(c(z)_ t=\phi (z_ x)_ x\) with application to population dynamics
type: Item
instance of: scholarly article
title: On a degenerate diffusion equation of the form \(c(z)_ t=\phi (z_ x)_ x\) with application to population dynamics
zbMATH Open document ID: 0624.35049
DOI: 10.1016/0022-0396(87)90139-2
author: Morton E. Gurtin
author: Michiel Bertsch
author: Danielle Hilhorst
published in: Journal of Differential Equations
publication date: 1987-01-01T00:00:00Z
review text: We study the equation \(c(z)_ t=\phi (z_ x)_ x\), where \(\phi (s)=| s|^{m-1}s\) \((m>1)\) and where the positive derivative c'(z) has a discontinuity at \(z=0\). In particular we analyze the level set \({\mathcal J}=\{(x,t):\) \(z(x,t)=0\}\) and prove that after some well- defined time T, \({\mathcal J}\) becomes a smooth curve. The equation arises in a theory for two interacting populations which disperse in response to population pressure. If the populations are initially segregated, they remain segregated for all later times, and the level set \({\mathcal J}\) represents the segregation front.
Mathematics Subject Classification ID: 35K65
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 35B40
zbMATH DE Number: 4013159
zbMATH Keywords: discontinuity
zbMATH Keywords: level set
zbMATH Keywords: interacting populations
MaRDI profile type: Publication
full work available at URL: 0022-0396(87)90139-2
OpenAlex ID: W2024948945
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description: scientific article; zbMATH DE number 4013159