Homepage of Patrik Knopf

Dr. Patrik Knopf  

Research Assistant
(Akademischer Rat a.Z.)

Faculty for Mathematics
University of Regensburg
Universitätsstraße 31
93040 Regensburg

Email: patrik.knopf∂ur.de

Office: M114

Phone: +49 (0)941 943 2953

This is the homepage of Patrik Knopf.

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Recent preprints:

Papers in peer-reviewed journals:

  1. Well-posedness of a bulk-surface convective Cahn--Hilliard system with dynamic boundary conditions
    with Jonas Stange
    Accepted in: NoDEA. Nonlinear Differential Equations and Applications
    Preprint: arXiv:2401.08400

  2. Controlling a Vlasov-Poisson plasma by a Particle-In-Cell method based on a Monte Carlo framework
    with Jan Bartsch, Stefania Scheurer and Jörg Weber
    Accepted in: SIAM Journal on Control and Optimization
    Preprint: arXiv:2304.02083

  3. A phase-field version of the Faber-Krahn theorem
    with Paul Hüttl and Tim Laux
    Interfaces and Free Boundaries (Online first)
    Preprint: arXiv:2207.10946

  4. Sharp-interface limit of a multi-phase spectral shape optimization problem for elastic structures
    with Harald Garcke, Paul Hüttl and Christian Kahle
    Applied Mathematics & Optimization 89(1):24, 2024 (Open Access)
    Preprint: arXiv:2304.02477

  5. The anisotropic Cahn--Hilliard equation: regularity theory and strict separation properties
    with Harald Garcke and Julia Wittmann
    This paper is dedicated to the 65th birthday of Professor Pierluigi Colli (Università di Pavia)
    Discrete and Continuous Dynamical Systems - Series S, 16(12): 3622-3660, 2023
    Preprint: arXiv:2305.18255

  6. Two-Phase Flows with Bulk-Surface Interaction: Thermodynamically Consistent Navier-Stokes-Cahn-Hilliard Models with Dynamic Boundary Conditions
    with Andrea Giorgini
    Journal of Mathematical Fluid Mechanics 25, no.3, 65, 2023 (Open Access)
    Preprint: arXiv:2208.09695

  7. A diffuse-interface approach for solid-state dewetting with anisotropic surface energies
    with Harald Garcke, Robert Nürnberg and Quan Zhao
    Journal of Nonlinear Science 33(34), 2023 (Open Access)
    Preprint: arXiv:2210.01698

  8. Phase-Field Methods for Spectral Shape and Topology Optimization
    with Harald Garcke, Paul Hüttl, Christian Kahle and Tim Laux
    ESAIM: Control, Optimisation and Calculus of Variations 29:10, 2023
    Preprint: arXiv:2107.03159

  9. Strong well-posedness, stability and optimal control theory for a mathematical model for magneto-viscoelastic fluids
    with Harald Garcke, Sourav Mitra and Anja Schlömerkemper
    Calculus of Variations and Partial Differential Equations 61, 179, 2022 (Open Access)
    Preprint: arXiv:2108.03094

  10. Existence of weak solutions to multiphase Cahn-Hilliard-Darcy and Cahn-Hilliard-Brinkman models for stratified tumor growth with chemotaxis and general source terms
    with Andrea Signori
    Communications in Partial Differential Equations 47(2): 233-278, 2022
    Preprint: arXiv:2105.09068

  11. On the two and one-half dimensional Vlasov-Poisson system with an external magnetic field: global well-posedness and stability of confined steady states
    with Jörg Weber
    Nonlinear Analysis: Real World Applications 65: 103460, 2022 (Open Access)
    Preprint: arXiv:2104.14179

  12. Long-time dynamics of the Cahn--Hilliard equation with kinetic rate dependent dynamic boundary conditions
    with Harald Garcke and Sema Yayla
    Nonlinear Analysis 125: 112619, 2022
    Preprint: arXiv:2103.15612

  13. Shape and topology optimization involving the eigenvalues of an elastic structure: A multi-phase-field approach
    with Harald Garcke and Paul Hüttl
    Advances in Nonlinear Analysis 11(1): 159-197, 2022 (Open Access)
    Preprint: arXiv:2005.13497

  14. On second-order and fourth-order elliptic systems consisting of bulk and surface PDEs: Well-posedness, regularity theory and eigenvalue problems
    with Chun Liu
    Interfaces and Free Boundaries 23(4): 507-533, 2021
    Preprint: arXiv:2008.00895

  15. On the nonlocal Cahn--Hilliard equation with nonlocal dynamic boundary condition and boundary penalization
    with Andrea Signori
    Journal of Differential Equations 280(4): 236-291, 2021
    Preprint: arXiv:2004.00093

  16. Phase-field dynamics with transfer of materials: The Cahn--Hilliard equation with reaction rate dependent dynamic boundary conditions
    with Kei Fong Lam, Chun Liu, and Stefan Metzger
    ESAIM: Mathematical Modelling and Numerical Analysis 55(1): 229-282, 2021
    Preprint: arXiv:2003.12983

  17. Stratified periodic water waves with singular density gradients
    with Joachim Escher, Christina Lienstromberg, and Bogdan-Vasile Matioc
    Annali di Matematica Pura ed Applicata 199(5): 1923-1959, 2020 (Open Access)
    Preprint: arXiv:1911.13046

  18. Optimal control theory and advanced optimality conditions for a diffuse interface model of tumor growth
    with Matthias Ebenbeck
    ESAIM: Control, Optimisation and Calculus of Variations 26(71): 38, 2020
    Preprint: arXiv:1903.00333

  19. Convergence of a Robin boundary approximation for a Cahn--Hilliard system with dynamic boundary conditions
    with Kei Fong Lam
    Nonlinearity 33(8): 4191-4235, 2020
    Preprint: arXiv:1908.06124

  20. Optimal control of a Vlasov-Poisson plasma by fixed magnetic field coils
    with Jörg Weber
    Applied Mathematics & Optimization 81(3): 961-988, 2020
    Preprint: arXiv:1710.09619

  21. Weak solutions of the Cahn-Hilliard system with dynamic boundary conditions: A gradient flow approach
    with Harald Garcke
    SIAM Journal on Mathematical Analysis 52(1): 340-369, 2020
    Preprint: arXiv:1810.09817

  22. Optimal medication for tumors modeled by a Cahn-Hilliard-Brinkman equation
    with Matthias Ebenbeck
    Calculus of Variations and Partial Differential Equations 58(4): 131, 2019
    Preprint: arXiv:1811.07783

  23. Confined steady states of a Vlasov-Poisson plasma in an infinitely long cylinder
    Mathematical Methods in the Applied Sciences 42(18): 6369-6384, 2019
    Preprint: arXiv:1805.04009

  24. Optimal control of a Vlasov-Poisson plasma by an external magnetic field
    Calculus of Variations and Partial Differential Equations 57(5): 134, 2018
    Preprint: arXiv:1808.00547

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