Pinning stationary planar fronts in diffusion-convection-reaction systems

This paper considers various strategies for controlling a stationary planar front solution, in a rectangular domain with a diffusion-reaction distributed system, by pinning the solution to one or few points and using actuators with the simplest possible spatial dependence. We review previous results obtained for one-dimensional diffusion-reaction (with or without convection) systems, for which we applied two approaches: an approximate model reduction to a form that follows the front position while approximating the front velocity, and linear stability analysis. We apply the same two approaches for the planar fronts. The approximate model reduction allows us to analyze qualitatively various control strategies and to predict the critical width below which the control mode of the one-dimensional system is sufficient. These results are corroborated by linear analysis of a truncated model with the spectral methods representation, using concepts of finite and infinite zeros of linear multidimensional systems.