Open AccessA STUDY OF THE PROFITABILITY FOR AN OPTIMAL CONTROL PROBLEM WHEN THE SIZE OF THE DOMAIN CHANGES
Author(s) -
MONTERO J.A.
Publication year - 2001
Publication title -
natural resource modeling
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.28
H-Index - 32
eISSN - 1939-7445
pISSN - 0890-8575
DOI - 10.1111/j.1939-7445.2001.tb00053.x
Subject(s) - bounded function , profitability index , domain (mathematical analysis) , neumann boundary condition , mathematics , boundary (topology) , dirichlet distribution , work (physics) , dirichlet boundary condition , stochastic game , quadratic equation , boundary value problem , control (management) , maximum principle , mathematical analysis , optimal control , mathematical optimization , mathematical economics , computer science , economics , finance , physics , geometry , thermodynamics , artificial intelligence
. In this work we consider the increase in benefit for a control problem when the size of domain increases. Our control problem involves the study of the profitability of a biological growing species whose growth is confined to a bounded domain Ω? R N and is modeled by a logistic elliptic equation with different boundary conditions (Dirichlet or Neumann). The payoff‐cost functional considered, J , is of quadratic type. We prove that, under Dirichlet boundary conditions, the optimal benefit (sup J ) increases when the domain ? increases. This is not true under Neumann boundary conditions.