Structured population equations in metric spaces
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, defi...
Gespeichert in:
| Hauptverfasser: | , |
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| Dokumenttyp: | Article (Journal) |
| Sprache: | Englisch |
| Veröffentlicht: |
2010
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| In: |
Journal of hyperbolic differential equations
Year: 2010, Jahrgang: 07, Heft: 04, Pages: 733-773 |
| ISSN: | 1793-6993 |
| DOI: | 10.1142/S021989161000227X |
| Online-Zugang: | Resolving-System, Volltext: http://dx.doi.org/10.1142/S021989161000227X Verlag, Volltext: https://www.worldscientific.com/doi/10.1142/S021989161000227X 
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| Verfasserangaben: | Piotr Gwiazda, Anna Marciniak-Czochra |
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| 520 | |a 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. | ||
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