Periodic Parabolic Boundary Value Problems And Positivity
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Periodic-parabolic Boundary Value Problems and Positivity
Author | : Peter Hess |
Publisher | : Longman |
Total Pages | : 164 |
Release | : 1991 |
Genre | : Mathematics |
ISBN | : |
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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.
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