Stability of solutions of kinetic equations corresponding to the replicator dynamics

Mirosław Lachowicz; Andrea Quartarone; Tatiana V. Ryabukha

doi:10.3934/krm.2014.7.109

Article Contents

2014, Volume 7, Issue 1: 109-119. Doi: 10.3934/krm.2014.7.109

This issue Previous Article Long time asymptotics of a degenerate linear kinetic transport equation Next Article Decay of solutions to generalized plate type equations with memory

Stability of solutions of kinetic equations corresponding to the replicator dynamics

1.
Faculty of Mathematics, Informatics and Mechanics, Institute of Applied Mathematics and Mechanics, University of Warsaw, ul. Banacha 2, 02-097 Warszawa
2.
Scienze Matematiche e Informatiche, Universitá di Messina, Dipartimento di Matematica, Viale F. Stagno D’Alcontres, Messina 98166

Received: December 31, 2012

Revised: March 31, 2013

Published: February 2014

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Abstract

In the present paper we propose a class of kinetic type equations that describes the replicator dynamics at the mesoscopic level. The equations are highly nonlinear due to the dependence of the transition rates of distribution function. Under suitable assumptions we show the asymptotic (exponential) stability of the solutions to such kinetic equations.

Keywords:

Mathematics Subject Classification: 60J75, 92D25, 35Q92, 35R09, 37N25, 45K05.

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