Oscillation of a class of functional parabolic differential equations
type: Item
instance of: scholarly article
title: Oscillation of a class of functional parabolic differential equations
zbMATH Open document ID: 0973.35191
DOI: 10.1016/S0893-9659(00)00081-1
author: Peiguang Wang
author: Weigao Ge
published in: Applied Mathematics Letters
publication date: 2000-11-13T00:00:00Z
review text: The authors of this interesting paper investigate a class of nonlinear parabolic equations with distributed deviating arguments, \[ u_t= a(t)\Delta u+ \sum^n_{i=1} a_i(t)\Delta u(x,\tau_i(t))- p(x,t)u- \int^b_a q(x,t,\xi) f(u[x, g(t,\xi)]) d\sigma(\xi)+ h(x, t), \] \((x,t)\in \Omega\times \mathbb{R}_+\equiv G\), the integral is a Stieltjes integral. Given one of the boundary conditions \(u= \varphi(x,t)\), \(\partial u/\partial n= \psi(x,t)\), \(\partial u/\partial n+\nu(x,t)u= 0\) on \(\partial\Omega\times \mathbb{R}_+\). Here \(\Delta\) is the Laplacian operator in \(\mathbb{R}^n\), \(\Omega\) is a bounded domain in \(\mathbb{R}^n\) with piecewise smooth boundary \(\partial\Omega\). The functions \(a(t)\), \(a_i(t)\), \(\tau_i(t)\), \(p\), \(q\), \(g\), \(f\) are continuous with respect to their arguments. Interesting oscillatory criteria for the considered problem under each one of the three boundary conditions are established.
Mathematics Subject Classification ID: 35R10
Mathematics Subject Classification ID: 35B05
Mathematics Subject Classification ID: 35K60
zbMATH DE Number: 1528557
zbMATH Keywords: oscillation
zbMATH Keywords: nonlinear parabolic equations with distributed deviating arguments
reviewed by: Drumi Bainov
MaRDI profile type: Publication
cites work: Q3700135
cites work: Allowable delays for positive diffusion processes
cites work: Oscillation of nonlinear parabolic equations with functional arguments
cites work: Forced oscillations of solutions of parabolic equations
cites work: Q4326775
cites work: Q3944531
full work available at URL: s0893-9659(00)00081-1
OpenAlex ID: W2040942776
description: scientific article; zbMATH DE number 1528557