Existence and uniqueness for the population dynamics with nonlinear diffusion
type: Item
instance of: scholarly article
title: Existence and uniqueness for the population dynamics with nonlinear diffusion
zbMATH Open document ID: 0752.92020
published in: Differential and Integral Equations
publication date: 1992-06-25T00:00:00Z
review text: The author treats the existence and uniqueness problem for an age structured population equation with nonlinear spatial diffusion. The equation is \[ u_ t+u_ a+\mu(a)u-\Delta_ x\beta(u)=f,\quad 0<a<A,\quad x\in\Omega,\quad 0<t<T, \] \[ \beta(u(a,x,t))=0,\quad 0<a<A,\quad x\in\partial\Omega,\quad 0<t<T, \] \[ u(0,x,t)=\int^ A_ 0 b(a)u(a,x,t)da,\quad x\in\Omega,\quad 0<t<T, \] \[ u(a,x,0)=u_ 0(a,x),\qquad 0<a<A,\qquad x\in\Omega. \] Here \(\Omega\) is a bounded open set in \(\mathbb{R}^ N\) with sufficiently smooth boundary. The method used involves nonlinear dissipative operator theory. The particular case that \(\beta(u)=| u|^{m-1} u\), \(m>(N-2)/N\) is also considered.
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 35K65
Mathematics Subject Classification ID: 35Q92
Mathematics Subject Classification ID: 35D99
Mathematics Subject Classification ID: 47H06
zbMATH DE Number: 11962
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: age structured population
zbMATH Keywords: nonlinear spatial diffusion
zbMATH Keywords: smooth boundary
zbMATH Keywords: nonlinear dissipative operator theory
author: Sebastian Aniţa
reviewed by: Glenn Webb
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 11962