Upper-lower solutions for nonlinear parabolic systems and their applications
type: Item
instance of: scholarly article
title: Upper-lower solutions for nonlinear parabolic systems and their applications
zbMATH Open document ID: 1237.35091
author: Mufid Abudiab
author: Inkyung Ahn
author: Lige Li
published in: Journal of Mathematical Analysis and Applications
publication date: 2011-03-29T00:00:00Z
review text: A method of upper and lower-solutions for nonlinear time-dependent reaction-diffusion systems of the type \[ \begin{cases} {\partial \over {\partial t}} u_i(x,t) - d_i \Delta u_i(x,t)= f_i(u_1,\dots,u_m, x) \quad \text{ for } x\in \Omega \subset \mathbb R^m \\ \alpha_i u_i(x,t) + \beta_i {\partial \over \partial n} u_i(x,t) = \psi_i(u_1,\dots,u_{i-1},u_{i+1}, \dots, u_m, x) \quad \text{ on } \partial\Omega\\ u_i(x,0)=u_i^\circ(x) \end{cases} \] is employed, without assuming the quasi-monotonicity on the reaction term. As an application, a mathematical model of interaction between immune cells and a virus arising from biological and medical sciences is investigated. For this model the authors obtain the existence of positive solutions and the \(\omega\)-limit.
reviewed by: Cristina Marcelli
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35B09
Mathematics Subject Classification ID: 35Q92
zbMATH DE Number: 5871219
zbMATH Keywords: reaction-diffusion systems
zbMATH Keywords: nonlinear parabolic systems
zbMATH Keywords: nonlinear boundary conditions
zbMATH Keywords: positive solutions
zbMATH Keywords: non-quasi-monotonicity
MaRDI profile type: Publication
full work available at URL: j.jmaa.2011.01.003
OpenAlex ID: W2088168633
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DOI: 10.1016/J.JMAA.2011.01.003
description: scientific article; zbMATH DE number 5871219