Geodesic
Existence of Optimal Stationary States of Exploited Populations with Diffusion
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Selected issues of mathematics and mechanics, Tome 310 (2020), pp. 135-142

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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. 
@article{TM_2020_310_a8,
     author = {A. A. Davydov},
     title = {Existence of {Optimal} {Stationary} {States} of {Exploited} {Populations} with {Diffusion}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {135--142},
     publisher = {mathdoc},
     volume = {310},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2020_310_a8/}
}
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A. A. Davydov. Existence of Optimal Stationary States of Exploited Populations with Diffusion. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Selected issues of mathematics and mechanics, Tome 310 (2020), pp. 135-142. http://geodesic.mathdoc.fr/item/TM_2020_310_a8/