Dr. Marvin Fritz

Analysis of PDEs, Numerical Analysis, Mathematical Modeling & Computational Science

Publications

Additional links to my preprints can be found on arXiv.org and ResearchGate. My published work can also be tracked on Scopus, Google Scholar, and ORCID.

Preprints

  1. Tumor evolution models of phase-field type with nonlocal effects and angiogenesis
    Submitted
    Links: TBA


Peer-Reviewed Scientific Articles

  1. Equivalence between a time-fractional and an integer-order gradient flow: The memory effect reflected in the energy
    with Ustim Khristenko and Barbara Wohlmuth
    Advances in Nonlinear Analysis (2023)
    Links: Preprint & Journal


  1. A 1D-0D-3D coupled model for simulating blood flow and transport processes in breast tissue
    with Tobias Köppl, J. Tinsley Oden, Andreas Wagner, Barbara Wohlmuth and Chengyue Wu
    International Journal for Numerical Methods in Biomedical Engineering (2022)
    Links: Preprint & Journal


  1. Time-fractional Cahn-Hilliard equation: Well-posedness, degeneracy, and numerical solutions
    with Mabel L. Rajendran and Barbara Wohlmuth
    Computers & Mathematics with Applications (2022)
    Links: Preprint & Journal


  1. On a subdiffusive tumour growth model with fractional time derivative
    with Christina Kuttler, Mabel L. Rajendran, Laura Scarabosio and Barbara Wohlmuth
    IMA Journal of Applied Mathematics (2021)
    Links: Preprint & Journal


  1. Modeling and simulation of vascular tumors embedded in evolving capillary networks
    with Prashant K. Jha, Tobias Köppl, J. Tinsley Oden, Andreas Wagner and Barbara Wohlmuth
    Computer Methods in Applied Mechanics and Engineering (2021)
    Links: Preprint & Journal


  1. Analysis of a new multispecies tumor growth model coupling 3D phase-fields with a 1D vascular network
    with Prashant K. Jha, Tobias Köppl, J. Tinsley Oden, Andreas Wagner, Barbara Wohlmuth
    Nonlinear Analysis: Real World Applications (2020)
    Links: Preprint & Journal


  1. Local and nonlocal phase-field models of tumor growth and invasion due to ECM degradation
    with Ernesto Lima, Vanja Nikolić, J. Tinsley Oden and Barbara Wohlmuth
    Mathematical Models and Methods in Applied Sciences (2019)
    Links: Preprint & Journal


  1. On the unsteady Darcy-Forchheimer-Brinkman equation in local and nonlocal tumor growth models
    with Ernesto Lima, J. Tinsley Oden and Barbara Wohlmuth
    Mathematical Models and Methods in Applied Sciences (2019)
    Links: Preprint & Journal


  1. Well-posedness and numerical treatment of the Blackstock equation in nonlinear acoustics
    with Vanja Nikolić and Barbara Wohlmuth
    Mathematical Models and Methods in Applied Sciences (2018)
    Links: Preprint & Journal

Theses

Well-posedness of nonlocal and mixed-dimensional phase-field models applied to tumor growth
PhD Dissertation, Technical University of Munich (2022)
Links: MediaTUM

The recent existence proofs of the Navier-Stokes equations
Master’s Thesis, Technical University of Munich (2017)

On the stability of relative equilibria in vortex dynamics
Bachelor’s Thesis, Technical University of Munich (2015)