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Journal Articles SIAM Journal on Mathematical Analysis Year : 2021

A non-expanding transport distance for some structured equations

Abstract

Structured equations are a standard modeling tool in mathematical biology. They are integro-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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Dates and versions

hal-03133608 , version 1 (06-02-2021)

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Nicolas Fournier, Benoît Perthame. A non-expanding transport distance for some structured equations. SIAM Journal on Mathematical Analysis, 2021, 53 (6), pp.6847-6872. ⟨10.1137/21M1397313⟩. ⟨hal-03133608⟩
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