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.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.