Inverse problem for a physiologically structured population model with variable-effort harvesting

• Main Author: Andrusyak Ruslan V.
• Format: Article
• Language: English
• Published: De Gruyter 2017-04-01
• Series: Open Mathematics
• Subjects: inverse problem; physiologically structured population model; conservation law; time-dependent harvesting; the method of characteristics; contraction mapping; the picard iteration; 35l04; 35q92; 35r30
• Online Access: https://doi.org/10.1515/math-2017-0040
• ISSN: 2391-5455

We consider the inverse problem of determining how the physiological structure of a harvested population evolves in time, and of finding the time-dependent effort to be expended in harvesting, so that the weighted integral of the density, which may be, for example, the total number of individuals or the total biomass, has prescribed dynamics. We give conditions for the existence of a unique, global, weak solution to the problem. Our investigation is carried out using the method of characteristics and a generalization of the Banach fixed-point theorem.