Dr. Marvin Fritz

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

Publications

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

Preprints

  1. Well-posedness and simulation of weak solutions to the time-fractional Fokker-Planck equation with general forcing
    Submitted (2023)


  1. A phase-field model for non-small cell lung cancer under the effects of immunotherapy
    with C. Kuttler, J.T. Oden, P. Schlicke, C. Schumann, A. Wagner and B. Wohlmuth
    Submitted (2023)
    Links: Preprint


Peer-Reviewed Scientific Articles

  1. Tumor evolution models of phase-field type with nonlocal effects and angiogenesis
    Bulletin of Mathematical Biology (2023)
    Links: Preprint & Journal


  1. Equivalence between a time-fractional and an integer-order gradient flow: The memory effect reflected in the energy
    with U. Khristenko and B. 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 T. Köppl, J.T. Oden, A. Wagner, B. Wohlmuth and C. 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 M.L. Rajendran and B. Wohlmuth
    Computers & Mathematics with Applications (2022)
    Links: Preprint & Journal


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


  1. Modeling and simulation of vascular tumors embedded in evolving capillary networks
    with P.K. Jha, T. Köppl, J.T. Oden, A. Wagner and B. 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 P.K. Jha, T. Köppl, J.T. Oden, B. 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 E.A.B.F. Lima, V. Nikolić, J.T. Oden and B. 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 E.A.B.F. Lima, J.T. Oden and B. 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 V. Nikolić and B. 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)
Supervisor: Prof. Dr. Barbara Wohlmuth
Links: MediaTUM

The recent existence proofs of the Navier-Stokes equations
Master’s Thesis, Technical University of Munich (2017)
Supervisor: Prof. Dr. Hans Wilhelm Alt

On the stability of relative equilibria in vortex dynamics
Bachelor’s Thesis, Technical University of Munich (2015)
Supervisor: Prof. Dr. Jürgen Scheurle