Ricerc@Sapienza

This paper is concerned with the optimal control of the parabolic p-Laplace equation with lower order reaction terms. The autonomous equation is shown to be exponentially stable with respect to the square integral norm. On the basis of this result, the task of reference tracking using a distributed control input is investigated and, in particular, the optimal control problem associated to the minimization of a power functional is addressed.

We introduce several notions of generalised principal eigenvalue for a linear elliptic operator on a general unbounded domain, under boundary condition of the oblique derivative type. We employ these notions in the stability analysis of semilinear problems. Some of the properties we derive are new even in the Dirichlet or in the whole space cases. As an application, we show the validity of the hair-trigger effect for the Fisher-KPP equation on general, uniformly smooth domains.