Measure framework for the pure selection equation: global well posedness and numerical investigations

Abstract

We study the classic pure selection integrodifferential equation, stemming from adaptative dynamics, in a measure framework by mean of duality approach. After providing a well posedness result under fairly general assumptions, we focus on the asymptotic behavior of various cases, illustrated by some numerical simulations.

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• Discrete and continuum models for the evolutionary and spatial dynamics of cancer: a very short introduction through two case studies
• Selection Mutation Differential Equations: Long-time Behavior of Measure-Valued Solutions