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| Dirac Concentrations in a Chemostat Model of Adaptive Evolution |
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Citation： |
Alexander LORZ,Beno^ i t PERTHAME,C'ecile TAING.Dirac Concentrations in a Chemostat Model of Adaptive Evolution[J].Chinese Annals of Mathematics B,2017,38(2):513~538 |
| Page view： 929
Net amount： 472 |
Authors： |
Alexander LORZ; Beno^ i t PERTHAME;C'ecile TAING |
Foundation： |
This work was supported by ANR-13-BS01-0004 funded by
the French Ministry of Research (ANR Kibord). |
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| Abstract： |
This paper deals with a non-local parabolic equation of
Lotka-Volterra type that describes the evolution of phenotypically
structured populations. Nonlinearities appear in these systems to
model interactions and competition phenomena leading to selection.
In this paper, the equation on the structured population is coupled
with a differential equation on the nutrient concentration that
changes as the total population varies.
Different methods aimed at showing the convergence of the solutions
to a moving Dirac mass are reviewed. Using either weak or strong
regularity assumptions, the authors study the concentration of the
solution. To this end, $BV$ estimates in time on appropriate
quantities are stated, and a constrained Hamilton-Jacobi equation to
identify where the solutions concentrates as Dirac masses is
derived. |
Keywords： |
Adaptive evolution, Asymptotic behaviour, Chemostat, Diracconcentrations, Hamilton-Jacobi equations, Lotka-Volterra equations,Viscosity solutions |
Classification： |
35B25, 35K57, 47G20, 49L25, 92D15 |
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