• Nonlinear (multi-scale) partial differential systems (arising in fluid dynamics and evolving microstructures): Weak solvability, regularity, boundedness, etc.
  • Degenerating parabolic equations: Existence of weak solutions by regularization
  • Mathematical modeling of biological processes (biofilms, chemotaxis, etc.) in evolving microstructures: Homogenization in a level-set framework
  • Numerical analysis of nonlinear (multi-scale) PDE systems: (Upwind, mixed) finite element methods



  • Multiscale modeling with evolving microstructure: An approach to
    emergence in the rhizosphere via effective soil functions

    (Third Party Funds Group – Sub project)

    Overall project: DFG Priority Programme 2089 “Rhizosphere Spatiotemporal Organisation – a Key to Rhizosphere Functions”
    Term: 01-02-2019 - 31-01-2022
    Funding source: DFG / Schwerpunktprogramm (SPP)

    The self-organization of the aggregates in the rhizosphere by various
    attracting forces influenced by geochemistry, and microbiology shall
    be studied by a novel, comprehensive model. This model should
    account for processes on the microscale (single roots, pore scale),
    and then be upscaled to the root system scale (macroscale) by
    mathematical homogenization. This goal exceeds the functional range
    of existing models for aggregation and needs the introduction of an
    explicit phase of mucilage, and attachment properties of root hairs in
    the rhizosheath. The project aims at the development of a mechanistic modeling approach that allows for dynamic structural reorganization of the rhizosphere at the single root scale and couples this evolving microscale model to the root system scale including the inference of soil functions. This means that we do not assume a static rhizosphere but develop a tool that is capable to dynamically track this zone on the basis of the underlying spatiotemporal aggregegate formation and geochemical patterns. The collaboration with experimental groups – analyzing CT images in various moisture and growth conditions - the Central Experiment will allow to derive the properties of the mucilage phase, the pore structure and thus the
    influence of root hairs on aggregation mechanisms.

  • German-Norwegian collaborative research support scheme

    (Third Party Funds Single)

    Term: 01-01-2016 - 31-12-2017
    Funding source: Deutscher Akademischer Austauschdienst (DAAD)

    Homogenisierung reaktiven Transports in variablen Mikrostrukturen

Friedrich-Alexander-Universität Erlangen-Nürnberg