Feedback spreading controls for semilinear parabolic systems

Distributed biophysical processes usually involve spreads in space, e.g., pollution, desertification in vegetation dynamics, etc. In this paper, based on the fact that spreadability of a distributed system reduces to a monotonicity problem, we show how feedback spreading control laws can be determined in semilinear parabolic systems. In case of affine dependence upon the control the use of a technique which combines saddle points and contraction mapping theorem yields a minimum “energy” feedback spreading control law. A mathematical example is examined in order to illustrate the derived results.