Download or read book Periodic-parabolic Boundary Value Problems and Positivity written by Peter Hess and published by Longman. This book was released on 1991 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: In these notes we give a unified treatment of semilinear nonautonomous diffusion equations and systems thereof, which satisfy a comparison principle, and whose coefficient functions depend periodically on time. Such equations arise naturally, e. g. in biomathematics if one admits dependence of the data on daily, monthly, or seasonal variations. Typical examples considered are the logistic equation with diffusion, Fisher's equation of population genetics, and Volterra-Lotka systems (with diffusion) of competition and of the predator-prey type. The existence and qualitative properties of periodic solutions, and the asymptotic behaviour of solutions of the initial-value problem are studied. Basic underlying concepts are strongly order-preserving discrete semigroups and the principal eigenvalue of a periodic-parabolic operator.