Structured population equations in metric spaces

• Verfasst von: Gwiazda, Piotr [VerfasserIn]
• Verfasst von: Marciniak-Czochra, Anna [VerfasserIn]
• Titel: Structured population equations in metric spaces
• Verf.angabe: Piotr Gwiazda, Anna Marciniak-Czochra
• Umfang: 41 S.
• Fussnoten: Gesehen am 25.07.2018
• Titel Quelle: Enthalten in: Journal of hyperbolic differential equations
• Jahr Quelle: 2010
• Band/Heft Quelle: 07(2010), 04, S. 733-773
• ISSN Quelle: 1793-6993
• DOI: doi:10.1142/S021989161000227X
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 157794819X

Abstract

In this paper, a framework for the analysis of measure-valued solutions of the nonlinear structured population model is presented. Existence and Lipschitz dependence of the solutions on the model parameters and initial data are shown by proving convergence of a variational approximation scheme, defined in the terms of a suitable metric space. The estimates for a corresponding linear model are used based on the duality formula for transport equations. An extension of a Wasserstein metric to the measures with integrable first moment is proposed to cope with the nonconservative character of the model. This metric is compared with a bounded Lipschitz distance, also called a flat metric, and the results are discussed in the context of applications to biological data.