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 Trudy Mat. Inst. Steklova, 2020, Volume 310, Pages 135–142 (Mi tm4143)

Existence of Optimal Stationary States of Exploited Populations with Diffusion

A. A. Davydovabc

a National University of Science and Technology MISIS, Leninskii pr. 4, Moscow, 119049 Russia
b Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Leninskie Gory 1, Moscow, 119991 Russia
c International Institute for Applied Systems Analysis (IIASA), Schlossplatz 1, A-2361 Laxenburg, Austria

Abstract: We study population dynamics with diffusion described by a parabolic equation with a logistic reaction term in the presence of exploitation consisting in constant harvesting of a part of the population density. Under natural constraints on the parameters of the model, we prove that there exists a stable stationary state of the population that provides the maximum profit of exploitation in the natural form.

 Funding Agency Grant Number Russian Science Foundation 19-11-00223 This work is supported by the Russian Science Foundation under grant 19-11-00223.

DOI: https://doi.org/10.4213/tm4143

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English version:
Proceedings of the Steklov Institute of Mathematics, 2020, 310, 124–130

Bibliographic databases:

UDC: 517.97
Revised: June 5, 2020
Accepted: June 5, 2020

Citation: A. A. Davydov, “Existence of Optimal Stationary States of Exploited Populations with Diffusion”, Selected issues of mathematics and mechanics, Collected papers. On the occasion of the 70th birthday of Academician Valery Vasil'evich Kozlov, Trudy Mat. Inst. Steklova, 310, Steklov Math. Inst., Moscow, 2020, 135–142; Proc. Steklov Inst. Math., 310 (2020), 124–130

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/tm4143
• https://doi.org/10.4213/tm4143
• http://mi.mathnet.ru/eng/tm/v310/p135

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This publication is cited in the following articles:
1. A. A. Davydov, D. A. Melnik, “Optimalnye sostoyaniya raspredelennykh ekspluatiruemykh populyatsii s periodicheskim impulsnym otborom”, Tr. IMM UrO RAN, 27, no. 2, 2021, 99–107
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