Aaron Brunk

Analysis of PDEs, Numerical Analysis, Mathematical Modeling.

Most of my preprints can be found on arXiv.org and ResearchGate. My articles can also be tracked on Google Scholar and ORCID.

Preprints:

  1. Structure-preserving approximation for the non-isothermal Cahn-Hilliard-Navier-Stokes system
    with Dennis Schumann
    Links: Preprint
  2. Variational approximation for a non-isothermal coupled phase-field system: Structure-preservation & Nonlinear stability
    with Oliver Habrich, Timileyin David Oyedeji, Yangyiwei Yang, Bai-Xiang Xu
    Links: Preprint
  3. Fundamentals of the Oldroyd-B model revisited: Tensorial vs. vectorial theory
    with Joydip Chaudhuri, Burkhard Dünweg and Mária Lukácová-Medvidová
    Links: Preprint
  4. A second-order structure-preserving discretization for the Cahn-Hilliard/Allen-Cahn system with cross-kinetic coupling
    with Herbert Egger, Oliver Habrich
    Links: Preprint

Peer-Reviewed Articles:

  1. On existence, uniqueness and stability of solutions to Cahn-Hilliard/Allen-Cahn systems with cross-kinetic coupling
    with Herbert Egger, Timileyin David Oyedeji, Yangyiwei Yang and Bai-Xiang Xu
    Nonlinear Analysis: Real World Applications (2023)
    Links: Preprint & Journal

  2. A second-order fully-balanced structure-preserving variational discretization scheme for the Cahn-Hilliard Navier-Stokes system
    with Herbert Egger, Oliver Habrich and Mária Lukácová-Medvidová
    Mathematical Models and Methods in Applied Sciences (M3AS) (2023)
    Links: Preprint & Journal

  3. On uniqueness and stable estimation of multiple parameters in the Cahn-Hilliard equation
    with Herbert Egger, Oliver Habrich
    Inverse Probleme (2023)
    Links: Preprint & Journal

  4. Stability and discretization error analysis for the Cahn-Hilliard system via relative energy estimates
    with Herbert Egger, Oliver Habrich and Mária Lukácová-Medvidová
    ESAIM: Mathematical Modelling and Numerical Analysis (2023)
    Links: Preprint & Journal

  5. Existence and weak-strong uniqueness for global weak solutions for the viscoelastic phase separation model in three space dimensions
    Discrete and Continuous Dynamical Systems (2023)
    Links: Preprint & Journal

  6. Relative energy and weak-strong uniqueness of the two-phase viscoelastic phase separation model
    with Mária Lukácová-Medvidová
    Zeitschrift für Angewandte Mathematik und Mechanik (2022)
    Links: Preprint & Journal

  7. Global existence of weak solutions to viscoelastic phase separation: Part II Degenerate Case
    with Mária Lukácová-Medvidová
    Nonlinearity (2022)
    Links: Preprint & Journal

  8. Global existence of weak solutions to viscoelastic phase separation: Part I Regular Case
    with Mária Lukácová-Medvidová
    Nonlinearity (2022)
    Links: Preprint & Journal

  9. Existence, regularity and weak-strong uniqueness for three-dimensional Peterlin viscoelastic model
    with Yong Lu and Mária Lukácová-Medvidová
    Communications in Mathematical Sciences (2022)
    Links: Preprint & Journal

  10. Systematic derivation of hydrodynamic equations for viscoelastic phase separation
    with Burkhard Dünweg, Herbert Egger, Oliver Habrich, Mária Lukácová-Medvidová and Dominic Spiller
    Journal of Physics: Condensed Matter (2021)
    Links: Preprint & Journal

  11. Analysis of a viscoelastic phase separation model
    with Burkhard Dünweg, Herbert Egger, Oliver Habrich, Mária Lukácová-Medvidová and Dominic Spiller
    Journal of Physics: Condensed Matter (2021)
    Links: Preprint & Journal

  12. Modelling cell-cell collision and adhesion with the filament based lamellipodium model
    with Diane Peurichard, Nikolas Sfakianakis and Christian Schmeiser
    Biomath (2018)
    Links: Preprint & Journal

  13. Stability, Convergence, and Sensitivity Analysis of the FBLM and the Corresponding FEM
    with Nikolas Sfakianakis
    Bulletin of Mathematical Biology (2018)
    Links: Preprint & Journal

  14. Chemotaxis and Haptotaxis on Cellular Level
    with Niklas Kolbe and Nikolas Sfakianakis
    HYP 16: Theory, Numerics and Applications of Hyperbolic Problem I (2018)
    Links: Preprint & Journal

Theses:

  • Viscoelastic phase separation: Well-posedness and numerical analysis
    PhD Dissertation, Johannes Gutenberg University Mainz (2022)
  • Numerische Behandlung von zeitgebrochenen Diffusionsgleichungen
    Master’s Thesis, Johannes Gutenberg University Mainz (2017)
  • Mathematische Modellierung von Phosphorylierungssystemen
    Bachelor’s Thesis, Johannes Gutenberg University Mainz (2015)