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

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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2020, Volume 310, Pages 135–142
DOI: https://doi.org/10.4213/tm4143 (Mi tm4143)

This article is cited in 12 scientific papers (total in 12 papers)

Existence of Optimal Stationary States of Exploited Populations with Diffusion

A. A. Davydov^abc

^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

Full-text PDF (138 kB) Citations (12)

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

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.

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

English version:
Proceedings of the Steklov Institute of Mathematics, 2020, Volume 310, Pages 124–130
DOI: https://doi.org/10.1134/S0081543820050090

Bibliographic databases:

Document Type: Article

UDC: 517.97

Language: Russian

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

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https://doi.org/10.4213/tm4143

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This publication is cited in the following 12 articles:

S. V. Aleshin, D. S. Glyzin, S. A. Kaschenko, “Wave propagation in the Kolmogorov–Petrovsky–Piscounov–Fisher equation with delay”, Theoret. and Math. Phys., 220:3 (2024), 1411–1428
S.V. Aleshin, S.D. Glyzin, S.A. Kashchenko, “Wave propagation in the Kolmogorov–Petrovskii–Piskunov–Fischer equation with time delay and spatial deviation”, Partial Differential Equations in Applied Mathematics, 11 (2024), 100855
A. A. Davydov, Kh. A. Khachatryan, “Stationary States in Population Dynamics with Migration and Distributed Offspring”, J Math Sci, 2024
A. A. Bazulkina, “Otsenka summarnogo dokhoda s uchetom diskontirovaniya dlya veroyatnostnykh modelei dinamiki populyatsii”, Vestnik rossiiskikh universitetov. Matematika, 28:143 (2023), 217–226
A. A. Davydov, Kh. A. Khachatryan, “Statsionarnye sostoyaniya v dinamike populyatsii s migratsiei i raspredelennym potomstvom”, SMFN, 69, no. 4, Rossiiskii universitet druzhby narodov, M., 2023, 578–587
E. V. Vinnikov, A. A. Davydov, D. V. Tunitsky, “Existence of maximum of time averaged harvesting in the KPP-model on sphere with permanent and impulse collection”, Dokl. Math., 108:3 (2023), 472–476
M. S. Woldeab, L. I. Rodina, “About the methods of biological resourse extraction, that provide the maximum average time benefit”, Russian Math. (Iz. VUZ), 66:1 (2022), 8–18
M. S. Voldeab, L. I. Rodina, “O sposobakh dobychi vozobnovlyaemogo resursa iz strukturirovannoi populyatsii”, Vestnik rossiiskikh universitetov. Matematika, 27:137 (2022), 16–26
A. A. Rodin, L. I. Rodina, A. V. Chernikova, “O sposobakh ekspluatatsii populyatsii, zadannoi raznostnym uravneniem so sluchainymi parametrami”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 32:2 (2022), 211–227
A. Davydov, E. Vinnikov, “Optimal cyclic dynamic of distributed population under permanent and impulse harvesting”, Dynamic Control and Optimization, Springer Proceedings in Mathematics & Statistics, 407, 2022, 101–112
A. A. Davydov, D. A. Melnik, “Optimal states of distributed exploited populations with periodic impulse selection”, Proc. Steklov Inst. Math. (Suppl.), 315, suppl. 1 (2021), S81–S88
A. O. Belyakov, A. A. Davydov, “Optimal Cyclic Harvesting of a Distributed Renewable Resource with Diffusion”, Proc. Steklov Inst. Math., 315 (2021), 56–64

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Труды Математического института имени В. А. Стеклова

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