Oscillations of solutions of vector differential equations of parabolic type with functional arguments
type: Item
instance of: scholarly article
title: Oscillations of solutions of vector differential equations of parabolic type with functional arguments
zbMATH Open document ID: 1034.35143
DOI: 10.1016/S0377-0427(02)00740-9
author: Norio Yoshida
author: Emil Minchev
published in: Journal of Computational and Applied Mathematics
publication date: 2003-03-16T00:00:00Z
review text: This paper is devoted to the oscillatory properties of solutions of the vector parabolic differential equation with functional arguments \[ \begin{multlined} \frac{\partial} {\partial t} \left(U(x,t)+ \sum^\ell_{i=1} h_i(t)U \bigl(x,\rho_i(t)\bigr)\right) -a(t)\Delta U(x,t)-\sum^k_{i=1} b_i(t)\Delta U\bigl(x,\tau_i(t)\bigr)+\\ +\sum^m_{i=1} c_i \biggl(x,t,U \bigl(x, \sigma_i(t)\bigr) \biggr)U\bigl(x,\sigma_i(t)\bigr)=F(x,t),\;(x,t)\in \Omega =G\times(0,\infty)\end{multlined}\tag{1} \] where \(G\) is a bounded domain in \(\mathbb{R}^n\) with piecewise smooth boundary \(\partial G\) and \(h_i,b_i,a, \rho_i,\tau_i, \sigma_i\), \(c_{ix}\) are given functions. Under some natural assumptions on the data of (1), the authors reduce the multi-dimensional oscillation problem (1) to one-dimensional oscillation problems for scalar functional differential inequalities. As a result they present sufficient conditions for every solution of boundary value problems for (1) with functional arguments to be \(H\)-oscillatory in a cylindrical domain.
Mathematics Subject Classification ID: 35R10
Mathematics Subject Classification ID: 35B05
zbMATH DE Number: 1882243
zbMATH Keywords: oscillations
zbMATH Keywords: vector differential equations
zbMATH Keywords: parabolic type
zbMATH Keywords: functional arguments
zbMATH Keywords: parabolic differential equation with functional arguments
zbMATH Keywords: bounded domain
zbMATH Keywords: oscillation problems for scalar functional differential inequalities
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1882243