Dr. Marvin Fritz

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

Publications

For a complete list of my work, including preprints and citations, see my profiles on arXiv, ResearchGate, and Google Scholar.

Preprints

  1. On feedback stabilisation for the Cahn-Hilliard equation and its numerical approximation
    with H. Egger, K. Kunisch, S. Rodrigues
    Submitted (2025)
    Links: Preprint
  1. Analysis and structure-preserving approximation of a Cahn-Hilliard-Forchheimer system with solution-dependent mass and volume source
    with A. Brunk
    Submitted (2025)
    Links: Preprint
  1. Analysis and discretization of the Ohta-Kawasaki equation with forcing and degenerate mobility
    with A. Brunk
    Submitted (2024)
    Links: Preprint
  1. Stabilization to trajectories of nonisothermal Cahn-Hilliard equations
    with B. Azmi and S. Rodrigues
    Submitted (2024)
    Links: Preprint

Peer-Reviewed Scientific Articles

  1. Well-posedness, long-time behavior, and discretization of some models of nonlinear acoustics in velocity-enthalpy formulation
    with H. Egger
    Mathematical Methods in the Applied Sciences (2025)
    Links: Preprint & Journal
  1. Analysis and computations of a stochastic Cahn-Hilliard model for tumor growth with chemotaxis and variable mobility
    with L. Scarpa
    Stochastics and Partial Differential Equations: Analysis and Computations (2025)
    Links: Preprint & Journal
  1. Structure-preserving approximation of the Cahn-Hilliard-Biot system
    with A. Brunk
    Numerical Methods for Partial Differential Equations (2025)
    Links: Preprint & Journal
  1. On the well-posedness of the Cahn-Hilliard-Biot model and its applications to tumor growth
    Discrete and Continuous Dynamical Systems - S (2024)
    Links: Preprint & Journal
  1. Well-posedness and simulation of weak solutions to the time-fractional Fokker-Planck equation with general forcing
    Discrete and Continuous Dynamical Systems - B (2024)
    Links: Preprint & Journal
  1. Analysis of a dilute polymer model with a time-fractional derivative
    with E. Süli and B. Wohlmuth
    SIAM Journal on Mathematical Analysis (2024)
    Links: Preprint & Journal
  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
    Mathematical Biosciences and Engineering (2023)
    Links: Preprint & Journal
  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

  1. 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
  2. The recent existence proofs of the Navier-Stokes equations
    Master's Thesis, Technical University of Munich (2017)
    Supervisor: Prof. Dr. Hans Wilhelm Alt

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