Oscillation of hyperbolic partial differential equations with impulses
type: Item
instance of: scholarly article
title: Oscillation of hyperbolic partial differential equations with impulses
zbMATH Open document ID: 1024.35089
DOI: 10.1016/S0096-3003(01)00217-X
published in: Applied Mathematics and Computation
publication date: 2003-01-28T00:00:00Z
review text: This is an interesting paper which deals with the oscillation of solutions of impulsive hyperbolic equations \[ u_{tt}(t,x) = a(t) \Delta u(t,x) - p(t,x)u(t,x), \quad t \neq t_k, x \in \Omega, \] together with the boundary condition \[ \frac{\partial u}{\partial n} (t,x) + \gamma (t,x) u(t,x) = 0, \quad t \neq t_k, x \in \partial \Omega \] and the impulsive condition \[ u(t_k^+,x) = g(t_k,x,u(t_k,x)), \quad x \in \bar{\Omega}, \;k = 1,2,\dots , \] where \(t_1 < t_2 < \dots < t_k < \dots \) are given numbers such that \(\lim_{k \to \infty} t_k = \infty\). The author obtains sufficient conditions for oscillation of the solution using averaging technique and considering adequate impulsive ordinary differential inequalities.
Mathematics Subject Classification ID: 35R12
Mathematics Subject Classification ID: 35L20
Mathematics Subject Classification ID: 35B05
zbMATH DE Number: 1861256
zbMATH Keywords: sufficient conditions for oscillation
zbMATH Keywords: averaging technique
author: Jiaowan Luo
reviewed by: Emil Minchev
MaRDI profile type: Publication
cites work: Oscillation of the solutions of impulsive parabolic equations
cites work: Exponential stability of the solutions of the initial value problem for systems with an impulse effect
cites work: Q4280625
cites work: Q4317041
cites work: Comparison principles for impulsive parabolic equations with applications to models of single species growth
cites work: Q3995625
cites work: Q2970111
cites work: Oscillation of solutions of hyperbolic equations of neutral type
description: scientific article; zbMATH DE number 1861256