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Mosc. Math. J., 2012, Volume 12, Number 2, Pages 269–273 (Mi mmj466)  

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

Abstract: 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.

Full text: http://www.ams.org/.../abst12-2-2012.html
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Document Type: Article
MSC: Primary 49J15; Secondary 34H05, 93C15, 93C95
Received: July 19, 2011; in revised form December 29, 2011
Language: English

Citation: 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
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\by A.~A.~Davydov, A.~S.~Platov
\paper Optimal stationary solution in forest management model by accounting intra-species competition
\jour Mosc. Math.~J.
\yr 2012
\vol 12
\issue 2
\pages 269--273
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2978756}
\zmath{https://zbmath.org/?q=an:1255.49004}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. 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  mathnet  crossref  mathscinet  isi  elib
    2. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. 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  crossref  mathscinet  zmath  isi  scopus
    4. 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  mathnet  crossref  crossref  isi  elib
    5. 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  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
  • Moscow Mathematical Journal
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