Parabolic systems in unbounded domains. I: Existence and dynamics
type: Item
instance of: scholarly article
title: Parabolic systems in unbounded domains. I: Existence and dynamics
zbMATH Open document ID: 0895.35046
author: C. V. Pao
published in: Journal of Mathematical Analysis and Applications
publication date: 1998-03-24T00:00:00Z
review text: The systems considered are of the form \[ u^i_{,t} -L^iu^i =f^i(t,x,u^j),\;t>0,\;x\in \Omega,\;u^i(t,x)= h^i(t,x),\;x\in \partial \Omega,\;u^i(0,x)= u^i_0(x), \tag{S} \] where \(\Omega\) is the exterior of a bounded domain of \(\mathbb{R}^n\), \(\mathbb{R}^n\) or a half space, and \(L^i\) are uniformly elliptic operators whose coefficients may depend on \(t\) and \(x\). The solutions considered are classical ones (under the appropriate smoothness conditions on the data). The author proves existence and uniqueness of the solution of (S) and also asymptotic behavior. The main technique used are upper and lower solutions.
Mathematics Subject Classification ID: 35K50
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35K55
zbMATH DE Number: 1115463
zbMATH Keywords: upper and lower solutions
reviewed by: René Sperb
MaRDI profile type: Publication
full work available at URL: jmaa.1997.5706
OpenAlex ID: W2091007074
cites work: Invariant sets and existence theorems for semilinear parabolic and elliptic systems
cites work: Boundedness and decay estimates for a class of reaction-diffusion systems on n
cites work: Dynamics of Interfaces in Competition-Diffusion Systems
cites work: Q4189096
cites work: Q5520962
cites work: Large time behavior of the solutions of a semilinear parabolic equation in \(\mathbb R^ n\)
cites work: Temperature of a semi-infinite rod which radiates both linearly and nonlinearly
cites work: Q3879125
cites work: Instability of stationary solutions for a Lotka-Volterra competition model with diffusion
cites work: The asymptotic behavior of solutions of a system of reaction-diffusion equations which models the Belousov-Zhabotinskii chemical reaction
cites work: Q3807603
cites work: Q4041085
cites work: Nonlinear elliptic boundary-value problems in unbounded domains
cites work: Nonlinear elliptic systems in unbounded domains
cites work: Quasisolutions and global attractor of reaction-diffusion systems
cites work: Optimization of one-dimensional multistage linear processes
cites work: Q5533735
cites work: The asymptotic stability of a traveling wave solution arising from a combustion model
DOI: 10.1006/JMAA.1997.5706
description: scientific article; zbMATH DE number 1115463