C0 - semigroups and beyond

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WG1 - C0 - semigroups and beyond

Overview

The theory of C0-semigroups, time-continuous linear dynamical systems, is a useful tool to study evolution equations. There is a one-to-one correspondence between these objects and well-posed abstract Cauchy problems on Banach spaces. In many situations, however, the notion of C0-semigroups is not satisfactory, and depending on the framework there are a couple of competing approaches. This Working Group will generalize the theory of semigroups by relaxing the classical theory and studying some novel continuity concepts. These are, for example, important to obtain the well-posedness on Lor continuous function spaces on infinite networks.

Especially important for applications will be the study of systems driven by two competing processes: (Additive) perturbation theory asks for conditions on a linear operator B such that the sum A + B (defined in an appropriate sense) generates a C0-semigroup, whenever A does. In this case, a formula (or an approximation) relating the perturbed and the unperturbed semigroups is also desired.

Tasks

  1. Generalize the theory of C0-semigroups by modifying analytic or algebraic features.
  2. Study examples which are appropriate for the theory (in collaboration with W2 and W3).
  3. Obtain stability results for the semigroup in terms of spectral properties of the generating operator.
  4. Develop perturbation results for the semigroups discussed above.
  5. In collaboration with WG5 develop appropriate numerical methods for applications.
  6. Use perturbation results for questions regarding control of the system.

Members

Leader

Abdelaziz RHANDI Italy

University of Salerno
Via Giovanni Paolo II, 132
Fisciano (Salerno)
Italy
Vice Leader

Balint FARKAS Germany

University of Wuppertal
Gaussstrasse 20
Wuppertal
Germany
No additional info

Working Group Participants

Jean-Bernard BRU

András BÁTKAI

Austria
Pädagogische Hochschule Vorarlberg
Liechtensteiner Straße 33-37
Feldkirch
Austria

Jussi BEHRNDT

Austria

Ivica NAKIĆ

Croatia
University of Zagreb
Bijenička cesta 30
Zagreb
Croatia

Dijana ILIŠEVIĆ

Croatia
University of Zagreb
Bijenicka 30
Zagreb
Croatia

David KREJCIRIK

Czech Republic
Czech Technical University in Prague
Trojanova 13
Prague
Czech Republic

Lassi PAUNONEN

Finland
Faculty of Information Technology and Communication Sciences, Tampere University
Korkeakoulunkatu 10 553
Tampere
Finland

Birgit JACOB

Germany

Christian SEIFERT

Germany
Technische Universität Hamburg
Am Schwarzenberg-Campus 3, 21073, Hamburg
Hamburg
Germany

Jochen GLÜCK

Germany
Universität Passau Faculty of Computer Science and Mathematics
Innstraße 33
Passau
Germany

Agnes Radl

Germany
TU Berlin
Straße des 17. Juni 136, 10623 Berlin
Berlin
Germany

Markus Haase

Germany
Mathematisches Seminar, Kiel University
Ludewig-Meyn-Str. 4, 24118 Kiel, Germany
Kiel
Germany

Tanja Eisner

Germany
University of Leipzig
Augustusplatz 10
Leipzig
Germany

Britta Dorn

Germany
University of Tübingen
Sand, 13
Tübingen
Germany

Alexander Dobrick

Germany
Christian-Albrechts-Universität zu Kiel
Ludewig-Meyn-Straße 4
Kiel
Germany

Petra CSOMÓS

Hungary
Eötvös Loránd University, Institute of Mathematics
Pázmány Péter sétány 1/C
Budapest
Hungary

Stefano DE LUCA

Italy

Roberta DI PACE

Italy

Lorenzo LAMBERTI

Italy

Marianna PORFIDO

Italy

Raffaele CARLONE

Italy

Federica GREGORIO

Italy
Università degli Studi di Salerno
Via Giovanni Paolo II, 132
Fisciano
Italy

Abdelaziz RHANDI

Italy
University of Salerno
Via Giovanni Paolo II, 132
Fisciano (Salerno)
Italy

Alessia Elisabetta Kogoj

Italy
Università di Urbino Carlo Bo
Piazza della Repubblica 13
Urbino (PU)
Italy

Alessandra Lunardi

Italy
Parma
Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Università di Parma
Parma
Italy

Said HADD

Morocco

Lahcen MANIAR

Morocco



Morocco

Martin LUKAREVSKI

North Macedonia
University "Goce Delcev" - Stip
"Krste Misirkov" 10-A
Stip
North Macedonia

Ivana Vojnović

Serbia
Department of Mathematics and Informatics, Faculty of Sciences, University of Novi Sad
Dositej Obradović Square 4, 21000, Novi Sad, Serbia
Novi Sad
Serbia

Marjeta KRAMAR FIJAVŽ

Slovenia
University of Ljubljana
Kongresni trg 12
Ljubljana
Slovenia
Research interests: functional analysis, operator semigroups, evolution equations, dynamical networks

Michael KAPLIN

Slovenia

Christian BUDDE

South African Republic
North-West University
School of Mathematics and Applied Mathematics, Building G3, Room 125, 11 Hoffman Street
2531 Potchefstroom, South Africa
South African Republic

Matthias Langer

United Kingdom
Department of Mathematics and Statistics, University of Strathclyde
26 Richmond Street Glasgow G1 1XH
Glasgow
United Kingdom

David SEIFERT

United Kingdom
Newcastle University
Herschel Building
Newcastle upon Tyne
United Kingdom
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