On a Class of Boundary Control Problems

TL;DR

This paper introduces a unified abstract framework for boundary control problems in Hilbert spaces, applicable to various PDE systems including hyperbolic, parabolic, and visco-elastic equations, emphasizing flexible boundary data spaces.

Contribution

It develops an abstract boundary data space approach that simplifies boundary control formulations without strict geometric restrictions, and applies it to visco-elasticity models.

Findings

Unified boundary control framework for diverse PDEs

Abstract boundary data spaces facilitate control formulation

Application to visco-elasticity demonstrates practical relevance

Abstract

We discuss a class of linear control problems in a Hilbert space setting, which covers diverse systems such as hyperbolic and parabolic equations with boundary control and boundary observation even including memory terms. We introduce abstract boundary data spaces in which the control and observation equations can be formulated without strong geometric constraints on the underlying domain. The results are applied to a boundary control problem for the equations of visco-elasticity.