Necessary optimality conditions for three species reaction–diffusion system

✍ Scribed by N.C. Apreutesei

• Publisher: Elsevier Science
• Year: 2011
• Tongue: English
• Weight: 220 KB
• Volume: 24
• Category: Article
• ISSN: 0893-9659
• DOI: 10.1016/j.aml.2010.10.008

✦ Synopsis

An optimal control problem is studied for an ecosystem composed by one predator and two prey populations. Its dynamics is modelled by a reaction-diffusion system of Volterra type. Two control variables are introduced in the system; their meaning is the mixture rates between predator and each prey population. The goal of this paper is to maximize the total density of the three populations at a fixed time moment. The existence of the optimal control is established and necessary optimality conditions are found with the aid of a maximum principle.