Nonlinear impulse evolution systems and applications to population models
type: Item
instance of: scholarly article
title: Nonlinear impulse evolution systems and applications to population models
zbMATH Open document ID: 0876.34011
author: Yuri V. Rogovchneko
published in: Journal of Mathematical Analysis and Applications
publication date: 1997-12-03T00:00:00Z
review text: This article deals with applications to population theory of some results about existence and stability of solutions (in particular, bounded and periodic) of the following impulse differential system: \[ {\textstyle {\frac{dx}{dt}}}+Ax= f(t,x)\qquad (t\in\mathbb{R}\setminus J), \] \[ x(t+0)-x(t-0)= g(t,x(t- 0))\qquad (t\in J), \] where \(J\) is some discrete set, \(A\) a sectorial linear operator in a Banach space \(X\), \(f(t,x)\) and \(g(t,x)\) smooth functions defined on \((\mathbb{R}\setminus J)\times X\) and \(J\times X\), respectively, and taking their values in \(X\); these results were obtained by the author and S. I. Trofimchuk earlier. The basic applications are related with the partial differential equation of type \[ {\textstyle {\frac{\partial u}{\partial t}}}= D\Delta u(t,x)+\varphi(t,x,u(t,x)) \qquad (t\neq t_j) \] (under standard boundary value conditions), which is perturbated with impulse members \[ u(t_j+0,x)- u(t_j-0,x)= g_j(u(t_j-0,x)). \] These systems can be treated as mathematical models for the growth and diffusion of a population subject under abrupt changes (such as disasters, harvesting, heavy immigrations, etc.).
Mathematics Subject Classification ID: 34A37
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 1005681
zbMATH Keywords: population theory
zbMATH Keywords: impulse differential system
zbMATH Keywords: growth and diffusion
reviewed by: Peter P. Zabreĭko
MaRDI profile type: Publication
full work available at URL: jmaa.1997.5245
OpenAlex ID: W1998630347
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DOI: 10.1006/JMAA.1997.5245
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description: scientific article; zbMATH DE number 1005681