Boundedness, global existence and continuous dependence for nonlinear dynamical systems describing physiologically structured populations

23Citations
Citations of this article
15Readers
Mendeley users who have this article in their library.

Abstract

The paper is aimed as a contribution to the general theory of nonlinear infinite dimensional dynamical systems describing interacting physiologically structured populations. We carry out continuation of local solutions to maximal solutions in a functional analytic setting. For maximal solutions we establish global existence via exponential boundedness and by a contraction argument, adapted to derive uniform existence time. Moreover, within the setting of dual Banach spaces, we derive results on continuous dependence with respect to time and initial state. To achieve generally the paper is organized top down, in the way that we first treat abstract nonlinear dynamical systems under very few but rather strong hypotheses and thereafter work our way down towards verifiable assumptions in terms of more basic biological modelling ingredients that guarantee that the high level hypotheses hold. © 2004 Elsevier Inc. All rights reserved.

Cite

CITATION STYLE

APA

Diekmann, O., & Getto, P. (2005). Boundedness, global existence and continuous dependence for nonlinear dynamical systems describing physiologically structured populations. Journal of Differential Equations, 215(2), 268–319. https://doi.org/10.1016/j.jde.2004.10.025

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free