Global Attractivity and Oscillations in a Nonlinear Impulsive Parabolic Equation with Delay

• Journal title : Kyungpook mathematical journal
• Volume 48, Issue 4,  2008, pp.593-611
• Publisher : Department of Mathematics, Kyungpook National University
• DOI : 10.5666/KMJ.2008.48.4.593
Title & Authors
Global Attractivity and Oscillations in a Nonlinear Impulsive Parabolic Equation with Delay
Wang, Xiao; Li, Zhixiang;

Abstract
Global attractivity and oscillatory behavior of the following nonlinear impulsive parabolic differential equation which is a general form of many population models $\small{\array{\{{{\frac {{\partial}u(t,x)}{{\partial}t}=\Delta}u(t,x)-{\delta}u(t,x)+f(u(t-\tau,x)),\;t{\neq}t_k,\\u(t^+_k,x)}$$\small{-u(t_k,x)=g_k(u(t_k,x)),\;k{\in}I_\infty,}\;\;\;\;\;\;\;\;(*)}$ are considered. Some new sufficient conditions for global attractivity and oscillation of the solutions of (*) with Neumann boundary condition are established. These results no only are true but also improve and complement existing results for (*) without diffusion or impulses. Moreover, when these results are applied to the Nicholson's blowflies model and the model of Hematopoiesis, some new results are obtained.
Keywords
impulsive parabolic equation;global attractivity;oscillation;
Language
English
Cited by
1.
Complex Dynamic Behaviors of an Impulsively Controlled Predator-prey System with Watt-type Functional Response, Kyungpook mathematical journal, 2016, 56, 3, 831
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