Page 470 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 470
CA18232: VARIATIONAL METHODS AND EQUATIONS ON GRAPHS (MS-40)
Telegraph systems on networks and port-Hamiltonians
Jacek Banasiak, jacek.banasiak@up.ac.za
University of Pretoria, South Africa
Coauthor: Adam Błoch
In this talk we consider a system of linear hyperbolic differential equations on a network cou-
pled through general transmission conditions of Kirchhoff’s type at the nodes. We discuss the
reduction of such a problem to a system of 1-dimensional hyperbolic problems, also called port-
Hamiltonian, for the associated Riemann invariants and provide a semigroup theoretic proof of
its well-posedness in any Lp.
In the second part of the talk we consider a reverse question, that is, we derive conditions
under which such a port-Hamiltonian with general linear Kirchhoff’s boundary conditions can
be written as a system of 2 × 2 hyperbolic equations on a metric graph Γ. This is achieved by
interpreting the matrix of the boundary conditions as a potential map of vertex connections of
Γ and then showing that, under the derived assumptions, that matrix can be used to determine
the adjacency matrix of Γ.
Gibbs Evolution Families
András Bátkai, andras.batkai@ph-vorarlberg.ac.at
Pädagogische Hochschule Vorarlberg, Austria
We extend results of Zagrebnov and coauthors on Gibbs semigroups to the nonautonomous
case.
Sufficient conditions will be given to evolution equations in the parabolic case so that the
generated evolution family belogs to appropriate operator ideals. Applications to Schrödinger
operators and the trace class ideal will be also given.
The results were achieved in part in a joint work with Bálint Farkas (Wuppertal). Support
by the COST Action CA18232 - Mathematical models for interacting dynamics on networks is
acknowledged.
On transmission conditions in modeling equations on graphs
Adam Bobrowski, a.bobrowski@pollub.pl
Lublin University of Technology, Poland
I will discuss the role of transmission conditions in modeling equations on graph-like spaces,
by considering two recent examples. The first of these is a theorem on thin layer approximation,
the other is a simple kinetic model with interface.
468
Telegraph systems on networks and port-Hamiltonians
Jacek Banasiak, jacek.banasiak@up.ac.za
University of Pretoria, South Africa
Coauthor: Adam Błoch
In this talk we consider a system of linear hyperbolic differential equations on a network cou-
pled through general transmission conditions of Kirchhoff’s type at the nodes. We discuss the
reduction of such a problem to a system of 1-dimensional hyperbolic problems, also called port-
Hamiltonian, for the associated Riemann invariants and provide a semigroup theoretic proof of
its well-posedness in any Lp.
In the second part of the talk we consider a reverse question, that is, we derive conditions
under which such a port-Hamiltonian with general linear Kirchhoff’s boundary conditions can
be written as a system of 2 × 2 hyperbolic equations on a metric graph Γ. This is achieved by
interpreting the matrix of the boundary conditions as a potential map of vertex connections of
Γ and then showing that, under the derived assumptions, that matrix can be used to determine
the adjacency matrix of Γ.
Gibbs Evolution Families
András Bátkai, andras.batkai@ph-vorarlberg.ac.at
Pädagogische Hochschule Vorarlberg, Austria
We extend results of Zagrebnov and coauthors on Gibbs semigroups to the nonautonomous
case.
Sufficient conditions will be given to evolution equations in the parabolic case so that the
generated evolution family belogs to appropriate operator ideals. Applications to Schrödinger
operators and the trace class ideal will be also given.
The results were achieved in part in a joint work with Bálint Farkas (Wuppertal). Support
by the COST Action CA18232 - Mathematical models for interacting dynamics on networks is
acknowledged.
On transmission conditions in modeling equations on graphs
Adam Bobrowski, a.bobrowski@pollub.pl
Lublin University of Technology, Poland
I will discuss the role of transmission conditions in modeling equations on graph-like spaces,
by considering two recent examples. The first of these is a theorem on thin layer approximation,
the other is a simple kinetic model with interface.
468
