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An integro-differential equation from population genetics and perturbations of differentiable semigroups in Fréchet spaces

Published online by Cambridge University Press:  14 November 2011

Reinhard Bürger
Reinhard Bürger
Affiliation:
Institut für Mathematik, Universität Wien, Strudlhofgasse 4, A-1090 Wien, Austria
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Synopsis

Existence and uniqueness of solutions of an integro-differential equation that arises in population genetics are proved. This equation describes the evolution of type densities in a population that is subject to mutation and directional selection on a quantitative trait. It turns out that a certain Fréchet space is the natural framework to show existence and uniqueness. One of the main steps in the proof is the investigation of perturbations of generators of differentiable semigroups in Fréchet spaces.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 118 , Issue 1-2 , 1991 , pp. 63 - 73
Copyright
Copyright © Royal Society of Edinburgh 1991

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