Modeling and minimization of extinction in Volterra-Lotka type equations with free boundaries (Q678046)

This paper is concerned with modeling and optimal control of Volterra-Lotka type equations with stronger than linear harvesting rates when the size of the population is small. Mathematically, the problem becomes a free boundary problem of the nonlinear elliptic or parabolic obstacle type. The free boundary is the a priori unknown surface in space or in space-time which separates the regions where the species exists and where it is extinct. In this paper, the elliptic problems are studied, and the analytical and numerical results are given. An optimal control problem, in particular, the problem of minimization of the area of extinction of the species is studied.