Modeling and Minimization of Extinction in Volterra–Lotka Type Equations with Free Boundaries

An equation of the distributed Volterra–Lotka type, with free boundary of the obstacle type, with possible applications in ecology, when extinction of the biological species is of particular concern, is introduced and solved. An optimal control problem for such an equation, and in particular the problem of minimization of the area of extinction of the species, is introduced and to some extent solved.