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Dr. Patrik Knopf Research Assistant(Akademischer Rat a.Z.)
Faculty for Mathematics Office: M114 Phone: +49 (0)941 943 2953 |
This is the homepage of Patrik Knopf.
You can browse through this site here:
Sharp-interface limit of a multi-phase spectral shape optimization problem for elastic structures
with Harald Garcke, Paul Hüttl and Christian Kahle (April 2023)
Preprint: arXiv:2304.02477
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 (April 2023)
Preprint: arXiv:2304.02083
A phase-field version of the Faber-Krahn theorem
with Paul Hüttl and Tim Laux (July 2022)
Preprint: arXiv:2207.10946
The anisotropic Cahn--Hilliard equation: regularity theory and strict separation properties
with Harald Garcke and Julia Wittmann (May 2023)
This paper is dedicated to the 65th birthday of Professor Pierluigi Colli (Università di Pavia)
Discrete and Continuous Dynamical Systems - Series S, 2023
Preprint: arXiv:2305.18255
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
Preprint: arXiv:2208.09695
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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