Duality for Evolutionary Equations with Applications to Null Controllability

Abstract

We study evolutionary equations in exponentially weighted ${\mathrm{L}}^2$-spaces as introduced by Picard in 2009. First, for a given evolutionary equation, we explicitly describe the $\hat{I}½$-adjoint system, which turns out to describe a system backwards in time. We prove well-posedness for the $\hat{I}½$-adjoint system. We then apply the thus obtained duality to introduce and study notions of null-controllability for evolutionary equations.

19 pages; v2: referee's comments addressed, references added, title adapted, affiliations updated