Parabolic Systems in Unbounded Domains. II. Equations with Time Delays

Abstract

This paper extends the results of an earlier article concerning the existence, uniqueness, comparison, and dynamics problems for a coupled system of parabolic equations in unbounded domains, including the whole space Rn. The present extension is for a system of functional parabolic-ordinary equations where the “reaction function” is allowed to depend on the unknown function with time delay, which may be discrete or continuous, finite or infinite. Applications are made to some model problems, with emphasis on the convergence fo the time-dependent solution to a steady-state solution and the decay property of the solution as |x|→∞.