This article is cited in 14 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.

MSC: Primary 49J15; Secondary 34H05, 93C15, 93C95

Received: July 19, 2011; in revised form December 29, 2011

Language: English

DOI: 10.17323/1609-4514-2012-12-2-269-273

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