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JOURNALS // Trudy Matematicheskogo Instituta imeni V.A. Steklova // Archive

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

This article is cited in 12 papers

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.

UDC: 517.97

Received: February 25, 2020
Revised: June 5, 2020
Accepted: June 5, 2020

DOI: 10.4213/tm4143


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

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© Steklov Math. Inst. of RAS, 2025