Boundary control of fronts in a Burgers-type equation with modular adhesion and periodic amplification

We consider a singularly perturbed periodic problem for a Burgers-type equation with modular advection and periodic linear amplification. We obtain conditions for the existence, uniqueness, and asymptotic stability in the sense of Lyapunov of a periodic solution with an interior transition layer and construct its asymptotic approximation. The asymptotics of the solution is used to determine boundary conditions ensuring the implementation of a prescribed mode of the front motion, i.e., the boundary control problem. We also formulate the notion of an asymptotic solution of the boundary control problem and obtain sufficient conditions for the existence of the required periodic mode of the front motion.