Miriam Bombieri | Searcharxiv

arXiv2015

Perturbation of Analytic Semigroups and Applications to Partial Differential Equations

In a recent paper we presented a general perturbation result for generators of $C_0$-semigroups. The aim of the present paper is to replace, in case the unperturbed semigroup is analytic, the various conditions appearing in this result by simpler assumptions on the domain and range of the operators involved. The power of our result to treat classes of PDE's systematically is illustrated by considering a generic example, a degenerate differential operator with generalized Wentzell boundary conditions and a reaction diffusion equation subject to Neumann boundary conditions with distributed unbounded delay.

math.FA↗

arXiv2013

A semigroup characterization of well-posed linear control systems

We study the well-posedness of a linear control system $Σ(A,B,C,D)$ with unbounded control and observation operators. To this end we associate to our system an operator matrix $\mathcal{A}$ on a product space $\mathcal{X}^p$ and call it $p$-well-posed if $\mathcal{A}$ generates a strongly continuous semigroup on $\mathcal{X}^p$. Our approach is based on the Laplace transform and Fourier multipliers.

math.FA↗