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A nonlinear structured population model: Global existence and structural stability of measure-valued solutions

Lorenz, Thomas ; Marciniak-Czochra, Anna ; Gwiazda, Piotr

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This paper is devoted to the study of the global existence and structural stability of measure-valued solutions to a nonlinear structured population model given in the form of a nonlocal first-order hyperbolic problem on positive real numbers. In distinction to previous studies, where the L^1 norm was used, we apply the flat metric, similar to the Wasserstein W^1 distance. We argue that stability using this metric, in addition to mathematical advantages, is consistent with intuitive understanding of empirical data. Structural stability and the uniqueness of the weak solutions are shown under the assumption about the Lipschitz continuity of the kinetic functions. The stability result is based on the duality formula and the Gronwall-type argument. Using a framework of mutational equations, existence of solutions to the equations of the model is also shown under weaker assumptions, i.e., without assuming Lipschitz continuity of the kinetic functions.

Item Type: Preprint
Date Deposited: 11 Jun 2008 14:14
Date: 2008
Faculties / Institutes: Service facilities > Uni-externe Einrichtungen
The Faculty of Mathematics and Computer Science > Department of Applied Mathematics
Service facilities > Interdisciplinary Center for Scientific Computing
Subjects: 510 Mathematics
Controlled Keywords: Populationsdynamik, Radon-Maß, Metrischer Raum, Nichtlineares dynamisches System
Uncontrolled Keywords: structural stability , Radon measures , population dynamics , structured population model , mutational equations
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