This article is cited in 5 scientific papers (total in 5 papers)
Optimal stationary solution in forest management model by accounting intra-species competition
A. A. Davydov, A. S. Platov
Department of Functional Analysis and its Applications, Vladimir State University named after Alexander and Nikolay Stoletovs, Gorkii street 87, 600000 Vladimir, Russia
We consider a model of exploitation of a size-structured population when the birth, growth and mortality rates depend on the individual size and interspecies competition, while the exploitation intensity is a function of the size only. For a given exploitation intensity and under natural assumptions on the rates, we establish existence and uniqueness of a nontrivial stationary state of the population. In addition, we prove existence of an exploitation intensity which maximises a selected profit functional of exploitation.
Key words and phrases:
Calculus of variations and optimal control, stationary solution.
MSC: Primary 49J15; Secondary 34H05, 93C15, 93C95
Received: July 19, 2011; in revised form December 29, 2011
A. A. Davydov, A. S. Platov, “Optimal stationary solution in forest management model by accounting intra-species competition”, Mosc. Math. J., 12:2 (2012), 269–273
Citation in format AMSBIB
\by A.~A.~Davydov, A.~S.~Platov
\paper Optimal stationary solution in forest management model by accounting intra-species competition
\jour Mosc. Math.~J.
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This publication is cited in the following articles:
A. A. Davydov, A. S. Platov, “Optimal exploitation of two competing size-structured populations”, Proc. Steklov Inst. Math. (Suppl.), 287, suppl. 1 (2014), 49–54
A. A. Davydov, A. F. Nassar, “On a stationary state in the dynamics of a population with hierarchical competition”, Russian Math. Surveys, 69:6 (2014), 1126–1128
Davydov A.A., Platov A.S., “Optimal Stationary Exploitation of Size-Structured Population With Intra-Specific Competition”, Geometric Control Theory and Sub-Riemannian Geometry, Springer Indam Series, 4, eds. Stefani G., Boscain U., Gauthier J., Sarychev A., Sigalotti M., Springer Int Publishing Ag, 2014, 123–132
A. A. Davydov, A. F. Nassar, “On the uniqueness of a positive stationary state in the dynamics of a population with asymmetric competition”, Proc. Steklov Inst. Math., 291 (2015), 78–86
A. A. Belavin, D. Gepner, Ya. A. Kononov, “Flat coordinates for Saito Frobenius manifolds and string theory.”, Theoret. and Math. Phys., 189:3 (2016), 1775–1789
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