Well-posedness of infinite-dimensional non-autonomous passive boundary control systems

Birgit Jacob; Hafida Laasri

doi:10.3934/eect.2020072

Article Contents

2021, Volume 10, Issue 2: 385-409. Doi: 10.3934/eect.2020072

This issue Previous Article Stability and dynamics for a nonlinear one-dimensional full compressible non-Newtonian fluids Next Article Approximation theorems for controllability problem governed by fractional differential equation

Well-posedness of infinite-dimensional non-autonomous passive boundary control systems

Birgit Jacob and
Hafida Laasri

University of Wuppertal, Work group Functional Analysis, 42097 Wuppertal, Germany

The second author gratefully acknowledges support from Deutsche Forschungsgemeinschaft (Grant LA 4197/1-1)

Received: May 31, 2019

Revised: March 31, 2020

Early access: June 2020

Published: June 2021

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Abstract

We study a class of non-autonomous linear boundary control and observation systems that are governed by non-autonomous multiplicative perturbations. This class is motivated by fundamental partial differential equations, such as controlled wave equations and Timoshenko beams. Our main results give sufficient condition for well-posedness, existence and uniqueness of classical and mild solutions.

Keywords:

infinite-dimensional non-autonomous control system,
evolution family,
port-Hamiltonian system,
well-posedness.

Mathematics Subject Classification: 93C25, 47D06, 93C20.

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