Perturbation formula for regular free boundaries in periodic-parabolic equations and minimization of extinction of endangered species

摘要

A periodic-parabolic equation, with discontinuous semi-linearity causing a free boundary of obstacle type, with possible applications in ecology and in modeling population dynamics of an endangered species, is introduced and solved. Optimal control problem for such an equation, and in particular the problem of minimization of the area of extinction of a species, is introduced and solved, by deriving the perturbation formula for the free boundary.