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Prof. Dr. Günther Grün

Short Curriculum Vitae

1986 – 1991 Study of Mathematics (Minor: Physics) at University of Bonn
1991 Diploma in Mathematics
1994 PhD in Mathematics, University of Bonn
1996 Marie-Curie-Research-Fellowship at Universita di Tor Vergata, Rome
2001 Habilitation in Mathematics, University of Bonn
2002 / 2003 Visiting Full Professorship at Duisburg University („Lehrstuhlvertretung C4“)
2006 – Professor at University of Erlangen-Nürnberg

Um weitere Informationen über die Forschung von Herrn Prof Grün zu erhalten, besuchen Sie die Forschungsinteressen oder Projekte der Arbeitsgruppe Grün.

 

  • Section Applied Analysis as part of the Annual Meeting of Society of Applied Mathematics and Mechanics (GAMM) at FAU Erlangen-Nürnberg, March 10th-14th, 2014.
  • ITN-Springschool Optimization in pde, reaction-diffusion systems and phase-field models , Saint Raphael, Apr. 7th-12th, 2013, (with D. Hilhorst and G. Leugering).
  • ITN-Winterschool Mathematical models for wetting: analysis and numerics, Veilbronn, Feb. 13th-17th, 2012.
  • Mini-Symposium Modeling, Analysis, and Simulation of Transport Phenomena in Multi-Phase Flow as part of ICIAM2011, Vancouver, July 18th-22nd, 2011.
  • Workshop Phase-Field Models in Fluid Mechanics at Regensburg University, Feb. 14th-16th, 2011 (together with Helmut Abels and Harald Garcke).
  • Section Applied Analysis as part of the Annual Meeting of Society of Applied Mathematics and Mechanics (GAMM) at TU Karlsruhe, March, 22nd – 26th, 2010.
  • Mini-Symposium Nichtlineare partielle Differentialgleichungen und Anwendungen as part of the Annual Meeting of Deutsche Mathematiker-Vereinigung (DMV) at Erlangen University, September, 19th – 23nd, 2008.
  • Mini-Symposium Nonlinear evolution equations and free boundary problems as part of the Annual Meeting of Deutsche Mathematiker-Vereinigung (DMV) at Bonn University, September, 18th – 22nd, 2006.
  • Member of Scientific Committee of the Conference Wetting: Theory and Experiment at Technion, Haifa, Israel, July, 3th – 7th, 2005.
  • Mini-Symposium Dünne viskose Filme/Thin liquid films as part of the Annual Meeting of Society of Applied Mathematics and Mechanics (GAMM) at TU Dresden, March, 21st – 27th, 2004.
  • Mini-Symposium Higher order evolution equations in continuum mechanics as part of ICIAM2003 , Sydney, July, 4th – 11th, 2003.

  • Grenzflächen, komplexe Strukturen und singuläre Limiten in der Kontinuumsmechanik
    (Drittmittelfinanzierte Gruppenförderung – Gesamtprojekt)
    Laufzeit: 01-04-2018 - 30-09-2022
    Mittelgeber: DFG / Graduiertenkolleg (GRK)
  • Ausbreitung freier Ränder unter Einfluss von Rauschen: Analysis und Numerik stochastischer degeneriert parabolischer Gleichungen
    (Drittmittelfinanzierte Einzelförderung)
    Laufzeit: 01-04-2018 - 31-03-2020
    Mittelgeber: Deutsche Forschungsgemeinschaft (DFG), DFG-Einzelförderung / Sachbeihilfe (EIN-SBH)
    URL: https://www1.am.uni-erlangen.de/~gruen/
    The porous-medium equation and the thin-film equation are prominent
    examples of nonnegativity preserving degenerate parabolic equations
    which give rise to free boundary problems with the free boundary at time
    t > 0 defined as the boundary of the solution’s support at that
    time.
    As they are supposed to describe the spreading of gas in a
    porous-medium or the spreading of a viscous droplet on a horizontal
    surface, respectively, mathematical results on the propagation of free
    boundaries become relevant in applications. In contrast to, e.g., the
    heat equation, where solutions to initial value problems with compactly
    supported nonnegative initial data
    instantaneously become globally
    positive, finite propagation and waiting time phenomena are
    characteristic features of degenerate parabolic equations.
    In this
    project, stochastic partial differential equations shall be studied
    which arise from the aforementioned degenerate parabolic equations by
    adding multiplicative noise in form of source terms or of convective
    terms. The scope is to investigate the impact of noise on the
    propagation of free boundaries, including in particular necessary and
    sufficient conditions for the occurrence
    of waiting time phenomena
    and results on the size of waiting times. Technically, the project
    relies both on rigorous mathematical analysis and on numerical
    simulation.
  • Molekulare Kommunikationssysteme
    (FAU Funds)
    Laufzeit: 01-01-2017 - 31-12-2018
    URL: https://www.idc.tf.fau.de/efi-mcs/
    Neuentstehende Anwendungen in der Biologie, Nanotechnologie und Medizin machen die Vernetzung von Objekten und Maschinen mit Abmessungen im Nano- und Mikrometerbereich erforderlich. Traditionelle elektromagnetische Ansätze für den Entwurf entsprechender Kommunikationssysteme sind für solch kleine Größenordnungen nicht geeignet. In der Natur jedoch ist die Kommunikation zwischen Nano- und Mikro-Objekten, wie z.B. Bakterien und anderen Zellen, weit verbreitet. Dabei kommen oft Signalmoleküle als Informationsträger zum Einsatz, so dass ein natürliches molekulares Kommunikationssystem entsteht. Das Projekt bündelt die an der FAU vorhandene Expertise auf den Gebieten Elektrotechnik, Biologie, Materialwissenschaften, Mathematik und Nanomedizin, um – ausgehend von in der Natur vorkommenden Mechanismen und Prozessen – synthetische molekulare Kommunikationssysteme zu entwerfen und zu implementieren.
  • Diffuse interface models for transport processes at fluidic interfaces
    (Drittmittelfinanzierte Gruppenförderung – Teilprojekt)
    Titel des Gesamtprojektes: SPP 1506: Fluide Grenzflächen
    Laufzeit: 01-06-2013 - 31-10-2017
    Mittelgeber: DFG / Schwerpunktprogramm (SPP)
    In recent years, diffuse interface models turned out to be a promising
    approach to describe fundamental features of two-phase flow like droplet
    break-up or coalescence. In the second funding period, novel
    thermodynamical consistent phase-field models for species transport in
    two-phase flow shall be derived with an emphasis on soluble surfactants.
    Additional phenomena -- ranging from microscale effects like molecule
    orientation over thermal effects to electrostatic interactions -- shall
    be included as well. On this basis, new sharp-interface models shall
    be derived by formal asymptotic analysis.

    For selected diffuse-interface models, existence of solutions and
    stability of fluidic interfaces will be investigated by rigorous
    mathematical analysis. Stable numerical schemes shall be formulated and
    implemented in two and three space dimensions. By numerical
    simulations, partially guided by the "Leitmassnahme" Taylor-flow, the
    models shall be validated and further improved. By numerical analysis,
    convergence shall be established for the prototypical problem of
    species transport in two-phase flow with general mass densities.
  • Diffuse interface models for transport processes at fluidic interfaces
    (Drittmittelfinanzierte Gruppenförderung – Teilprojekt)
    Titel des Gesamtprojektes: SPP 1506: Fluide Grenzflächen
    Laufzeit: 01-04-2010 - 30-04-2013
    Mittelgeber: DFG / Schwerpunktprogramm (SPP)
    Topological transitions like droplet coalescence or droplet break-up are fundamental features of two-phase flows. In recent years, diffuse interface models turned out to be a promising approach to describe such phenomena. Species transport across fluidic interfaces and the effects exerted by soluble and insoluble surfactants are additional issues of still increasing technological importance. For those phenomena, novel thermodynamically consistent diffuse interface models shall be developed taking in particular general densities into account. Based on rigorous mathematical analysis, existence and qualitative behaviour of solutions will be investigated, this way enhancing the understanding of the fundamental model properties. Starting from energy and entropy inequalities, stable and convergent numerical schemes shall be formulated and implemented in two and three spatial dimensions. By numerical simulations, the models shall be validated and further improved.
  • Fronts and Interfaces in Science and Technology
    (Drittmittelfinanzierte Gruppenförderung – Teilprojekt)
    Titel des Gesamtprojektes: Fronts and Interfaces in Science and Technology
    Laufzeit: 01-02-2010 - 31-12-2013
    Mittelgeber: EU - 7. RP / People / Initial Training Networks (ITN)
    With this network, the universities of Bath, Eindhoven, Erlangen, Haifa
    (Technion), Madrid (Complutense), Paris (Orsay), Rome (La Sapienza),
    Zürich and the industrial partners EGIS and SIEMENS AG foster a joint
    training platform for PhD-students working on analysis and control of
    interfacial phenomena. Applications range from image processing over
    reaction-diffusion systems to complex multi-phase flow.
    FAU is
    involved in three projects, guided by Proff. Grün, Knabner, and
    Leugering. The first one is concerned with the effects electric fields
    have on two-phase flow with electrolyte solutions. The goal is to derive
    thermodynamically consistent diffuse-interface models for general mass
    densities and ion distributions and to prove existence and regularity
    of solutions.
    The second one is a tandem project with Prof. Peletier
    (TU Eindhoven) devoted to contaminant flow in porous media. There is
    experimental evidence that attachment to colloids strongly enhances
    contaminant transport. Derivation and analysis of appropriate
    multi-scale models are in the focus of this project.
    Prof.
    Leugering's project -- jointly with Prof. Coron (University Pierre et
    Marie Curie, Paris) -- is devoted to optimal control and stabilization
    of flow of gas, water, and traffic in networked pipe- and road-systems.
    It focusses on reachability and stabilizability properties under
    constraints both in states and controls and on the derivation of
    appropriate sensitivities for a numerical treatment of optimal controls
    for systems of realistic size.

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