Publicación:
THE DUBOVITSKII AND MILYUTIN METHODOLOGY APPLIED TO AN OPTIMAL CONTROL PROBLEM ORIGINATING IN AN ECOLOGICAL SYSTEM

dc.creatorESPERANZA LOZADA GUIDICHI
dc.creatorANÍBAL CORONEL PÉREZ
dc.date2021
dc.date.accessioned2025-01-10T15:25:32Z
dc.date.available2025-01-10T15:25:32Z
dc.date.issued2021
dc.description.abstractWE RESEARCH A CONTROL PROBLEM FOR AN ECOLOGICAL MODEL GIVEN BY A REACTION?DIFFUSION SYSTEM. THE ECOLOGICAL MODEL IS GIVEN BY A NONLINEAR PARABOLIC PDE SYSTEM OF THREE EQUATIONS MODELLING THE INTERACTION OF THREE SPECIES BY CONSIDERING THE STANDARD LOTKA-VOLTERRA ASSUMPTIONS. THE OPTIMAL CONTROL PROBLEM CONSISTS OF THE DETERMINATION OF A COEFFICIENT SUCH THAT THE POPULATION DENSITY OF PREDATOR DECREASES. WE REFORMULATE THE CONTROL PROBLEM AS AN OPTIMAL CONTROL PROBLEM BY INTRODUCING AN APPROPRIATE COST FUNCTION. THEN, WE INTRODUCE AND PROVE THREE TYPES OF RESULTS. A FIRST CONTRIBUTION OF THE PAPER IS THE WELL-POSEDNESS FRAMEWORK OF THE MATHEMATICAL MODEL BY CONSIDERING THAT THE INTERACTION OF THE SPECIES IS GIVEN BY A GENERAL FUNCTIONAL RESPONSES. SECOND, WE STUDY THE DIFFERENTIABILITY PROPERTIES OF A COST FUNCTION. THE THIRD RESULT IS THE EXISTENCE OF OPTIMAL SOLUTIONS, THE EXISTENCE OF AN ADJOINT STATE, AND A CHARACTERIZATION OF THE CONTROL FUNCTION. THE FIRST RESULT IS PROVED BY THE APPLICATION OF SEMIGROUP THEORY AND THE SECOND AND THIRD RESULT ARE PROVED BY THE APPLICATION OF DUBOVITSKII AND MILYUTIN FORMALISM.
dc.formatapplication/pdf
dc.identifier.doi10.3390/math9050479
dc.identifier.issn2227-7390
dc.identifier.urihttps://repositorio.ubiobio.cl/handle/123456789/11954
dc.languagespa
dc.publisherMATHEMATICS
dc.relation.uri10.3390/math9050479
dc.rightsPUBLICADA
dc.titleTHE DUBOVITSKII AND MILYUTIN METHODOLOGY APPLIED TO AN OPTIMAL CONTROL PROBLEM ORIGINATING IN AN ECOLOGICAL SYSTEM
dc.typeARTÍCULO
dspace.entity.typePublication
ubb.EstadoPUBLICADA
ubb.Otra ReparticionDEPARTAMENTO DE CIENCIAS BASICAS
ubb.Otra ReparticionDEPARTAMENTO DE CIENCIAS BASICAS
ubb.SedeCHILLÁN
ubb.SedeCHILLÁN
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