arXiv subjects

Julia T. Kaiser

Publications and source records attributed to Julia T. Kaiser.

3 recordsLinked to original sources

arXiv2020

Riesz bases of port-Hamiltonian systems

The location of the spectrum and the Riesz basis property of well-posed homogeneous infinite-dimensional linear port-Hamiltonian systems on a 1D spatial domain are studied. It is shown that the Riesz basis property is equivalent to the fact that system operator generates a strongly continuous group. Moreover, in this situation the spectrum consists of eigenvalues only, located in a strip parallel to the imaginary axis and they can decomposed into finitely many sets having each a uniform gap.

math.FA↗

arXiv2019

On exact controllability of infinite-dimensional linear port-Hamiltonian systems

Infinite-dimensional linear port-Hamiltonian systems on a one-dimensional spatial domain with full boundary control and without internal damping are studied. This class of systems includes models of beams and waves as well as the transport equation and networks of nonhomogeneous transmission lines. The main result shows that well-posed port-Hamiltonian systems, with state space $L^2((0,1);\mathbb C^n)$ and input space $\mathbb C^n$, are exactly controllable.

math.OC↗

arXiv2018

Well-posedness of networks for 1-D hyperbolic partial differential equations

We consider the well-posedness of a class of hyperbolic partial differential equations on a one dimensional spatial domain. This class includes in particular infinite-dimensional networks of transport, wave and beam equations, or even combinations of these. Equivalent conditions for contraction semigroup generation are derived. In the first part we assume a finite interval and in the second part, we consider partial differential equations on the semi-axis.

math.FA↗