Using Lyapunov's direct method for wave suppression in reactive systems

This paper proposes a new approach for stabilizing a homogeneous solution in reaction–convection–diffusion system with oscillatory kinetics, in which moving or stationary patterns emerge in the absence of control. Specifically, we aim to suppress patterns by using a spatially weighted finite-dimensional feedback control that assures stability of the solution according to Lyapunov's direct method. A practical design procedure, based on spectral representation of the system and dissipative nature of parabolic PDEs, is presented.