Measure-transmission metric and stability of structured population models

作者：Jamroz G^*

来源：Nonlinear Analysis: Real World Applications , 2015, 25: 9-30.

DOI：10.1016/j.nonrwa.2015.02.008

• Transport equation
• Measure-valued solutions
• Metrics on measures
• Structured population models
• Cell differentiation
• Stability

In Gwiazda, et al. (2012) a framework for studying cell differentiation processes based on measure-valued solutions of transport equations was introduced. Under application of the so-called measure-transmission conditions it enabled to describe processes involving both discrete and continuous transitions. This framework, however, admits solutions which lack continuity with respect to initial data. In this paper, we modify the framework from Gwiazda, et al. (2012) by replacing the flat metric, known also as bounded Lipschitz distance, by a new Wasserstein-type metric. We prove, that the new metric provides stability of solutions with respect to perturbations of initial data while preserving their continuity in time. The stability result is important for numerical applications.

• 出版日期2015-10