Approximate Controllability of the generalized Burgers-Huxley equation in one dimension

Abstract: The generalized Burgers-Huxley (GBH) equation is a prototype model that describes the interplay among reaction, convection, and diffusion. In this article, we explore the controllability of this model by means of an interior control supported in an arbitrary non-empty open subset of the domain. We establish that the GBH equation is not globally approximately controllable in a given time. However, it is possible to steer the system from any steady state to an arbitrarily small neighborhood of another steady state in some suitable time by means of a localized interior control, provided that both steady states lie in the same connected component of the set of steady states.