Oscillation criteria for impulsive parabolic boundary value problem with delay
type: Item
instance of: scholarly article
title: Oscillation criteria for impulsive parabolic boundary value problem with delay
zbMATH Open document ID: 1062.35153
DOI: 10.1016/S0096-3003(03)00659-3
author: Xilin Fu
author: Liejune Shiau
published in: Applied Mathematics and Computation
publication date: 2004-08-06T00:00:00Z
review text: The authors deal with the following impulsive parabolic system with delay \[ \begin{aligned} u_t= a(t)\Delta_xu+ b(t)\Delta_x u(t- \rho,x)- p(t,x) f(u(t- \sigma,x)), &\quad t\neq t_k,\\ u(t^+_k, x)- u(t^-_k, x)= I(t,x,u), &\quad t= t_k,\;k= 1,2,\dots,\end{aligned}\tag{1} \] where \(\Delta_x\) is the Laplacian in \(\mathbb{R}^n\); \(u= u(t,x)\) for \((t,x)\in \mathbb{R}_+\times\Omega\), where \(\Omega\) is a bounded domain in \(\mathbb{R}^n\) with smooth boundary \(\partial\Omega\) and \(\mathbb{R}_+= [0,+\infty)\); \(a(t)\), \(b(t)\), \(p(t,x)\) are piecewise continuous functions of their arguments; \(\rho\) and \(\sigma\) are positive constants with \(I: \mathbb{R}_+\times \overline\Omega\times\mathbb{R}\mapsto \mathbb{R}\). For different kind of boundary conditions the authors study oscillation criteria for (1).
Mathematics Subject Classification ID: 35R10
Mathematics Subject Classification ID: 35B05
Mathematics Subject Classification ID: 35K60
zbMATH DE Number: 2082074
zbMATH Keywords: bounded domain
zbMATH Keywords: smooth boundary
zbMATH Keywords: oscillation criteria
zbMATH Keywords: Eventually positive solution
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
cites work: Comparison principles for impulsive parabolic equations with applications to models of single species growth
cites work: Initial-boundary value problems for impulsive parabolic functional differential equations
cites work: Q4349161
cites work: Q4023219
full work available at URL: s0096-3003(03)00659-3
OpenAlex ID: W2019095634
description: scientific article; zbMATH DE number 2082074