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STATIONARY SOLUTIONS OF A SELECTION MUTATION MODEL: THE PURE MUTATION CASE

ÀNGEL CALSINA

Departament d'Informàtica i Matemàtica Aplicada, Campus Montilivi Universitat de Girona, E-17071, Girona, Spain

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and

SÍLVIA CUADRADO

Departament de Matemàtiques, Universitat Autònoma de, Barcelona 08193 Bellaterra, Barcelona, Spain

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https://doi.org/10.1142/S0218202505000637Cited by:16 (Source: Crossref)

Abstract

A selection mutation equations model for the distribution of individuals with respect to the age at maturity is considered. In this model we assume that a mutation, perhaps very small, occurs in every reproduction where the noncompactness of the domain of the structuring variable and the two-dimensionality of the environment are the main features. Existence of stationary solutions is proved using the theory of positive semigroups and the infinite-dimensional version in Banach lattices of the Perron Frobenius theorem. The behavior of these stationary solutions when the mutation is small is studied.

This work was partially supported by DGI BMF2002-04613-C03.

Keywords:

AMSC: 45K05, 92D15, 92D25

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