A non-expanding transport distance for some structured equations
Nicolas Fournier (LPSM (UMR\_8001)), Beno\^it Perthame (LJLL, (UMR\_7598))
TL;DR
This paper introduces a new transport distance related to the Monge-Kantorovich distance that remains non-expanding for certain structured equations in mathematical biology, aiding in the analysis of measure solutions.
Contribution
It proposes a novel non-expanding transport distance tailored for structured equations, enhancing the mathematical toolkit for their analysis.
Findings
The transport distance is non-expanding for several linear structured equations.
It provides a new perspective on measure solutions in mathematical biology.
The approach could facilitate stability analysis of solutions.
Abstract
Structured equations are a standard modeling tool in mathematical biology. They areintegro-differential equations where the unknown depends on one or several variables, representing the state or phenotype of individuals. A large literature has been devoted to many aspects of these equations and in particular to the study of measure solutions.Here we introduce a transport distance closely related to the Monge-Kantorovich distance,which appears to be non-expanding for several (mainly linear) examples of structured equations.
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Taxonomy
TopicsStochastic processes and statistical mechanics · Geometry and complex manifolds · Mathematical and Theoretical Epidemiology and Ecology Models