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Dr. Georg Heinze

Georg Heinze
Address:
Weierstrass Institute for Applied Analysis and Stochastics
Mohrenstraße 39
10117 Berlin, Germany
Phone: +49(0) 30 20372 474
Email: georg.heinze(at)wias-berlin.de
ORCID: ORCID logo 0000-0002-4576-4683  
Google Scholar: Georg Heinze  

I am a member of the research group Partial Differential Equations at the Weierstrass Institute of Applied Analysis and Stochastics.
Furthermore, I am a member of the GAMM Juniors and the GAMM Activity Group "Analysis of Partial Differential Equations".

Scientific interests

My research focuses on the mathematical analysis of evolution equations from a partial differential equations and calculus of variations point of view. I am particularly interested in (generalized) gradient flows and their corresponding gradient systems as well as limits of such systems. Such limits can be used to study problems on multiple scales and derive macroscopic models from microscopic descriptions in a rigorous way.
One of my research topics concerns gradient flows on graphs as well as the recovery of (systems of) PDEs as limits of such graph problems. During my PhD I studied graph problems related to a system of aggregation PDEs for multiple interacting species and concave mobilities as well as their approximation properties.


Publications

Peer-reviewed articles

  1. A. Esposito, G. Heinze, A. Schlichting.
    Graph-to-local limit for the nonlocal interaction equation.
    To appear in Journal de Mathématiques Pures et Appliquées 2024+. [arXiv] 
  2. G. Heinze, J.-F. Pietschmann, M. Schmidtchen.
    Nonlocal cross-interaction systems on graphs: Energy landscape and dynamics.
    Kinetic and Related Models 2023. [Link]  [arXiv] 
  3. G. Heinze, J.-F. Pietschmann, M. Schmidtchen.
    Nonlocal cross-interaction systems on graphs: Nonquadratic Finslerian structure and nonlinear mobilities.
    SIAM Journal on Mathematical Analysis 2023. [Link]  [arXiv] 

Conference proceedings

  1. A. Esposito, G. Heinze, J.-F. Pietschmann, A. Schlichting.
    Graph-to-local limit for a multi-species nonlocal cross-interaction system.
    Proceedings in Applied Mathematics and Mechanics 2024. [Link]  [arXiv] 

Dissertation thesis

  • G. Heinze.
    Graph-based nonlocal gradient systems and their local limits.
    PhD thesis 2024. [Link]
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