Patrik Knopf
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Weak Solutions of the Cahn--Hilliard System with Dynamic Boundary Conditions: A Gradient Flow Approach
H Garcke, P Knopf
SIAM Journal on Mathematical Analysis 52 (1), 340–369, 2020
Optimal medication for tumors modeled by a Cahn–Hilliard–Brinkman equation
M Ebenbeck, P Knopf
Calculus of Variations and Partial Differential Equations 58 (4), 131, 2019
Optimal control theory and advanced optimality conditions for a diffuse interface model of tumor growth
M Ebenbeck, P Knopf
ESAIM: Control, Optimisation and Calculus of Variations 26, 71, 2020
Phase-field dynamics with transfer of materials: The Cahn--Hilliard equation with reaction rate dependent dynamic boundary conditions
P Knopf, KF Lam, C Liu, S Metzger
ESAIM: Mathematical Modelling and Numerical Analysis 55 (1), 229-282, 2021
Convergence of a Robin boundary approximation for a Cahn–Hilliard system with dynamic boundary conditions
P Knopf, KF Lam
Nonlinearity 33 (8), 4191–4235, 2020
Optimal control of a Vlasov–Poisson plasma by an external magnetic field
P Knopf
Calculus of Variations and Partial Differential Equations 57 (5), 134, 2018
Optimal Control of a Vlasov–Poisson Plasma by Fixed Magnetic Field Coils
P Knopf, J Weber
Applied Mathematics & Optimization 81 (3), 961–988, 2020
Confined steady states of a Vlasov-Poisson plasma in an infinitely long cylinder
P Knopf
Mathematical Methods in the Applied Sciences 42 (18), 6369–6384, 2019
On the nonlocal Cahn–Hilliard equation with nonlocal dynamic boundary condition and boundary penalization
P Knopf, A Signori
Journal of Differential Equations 280, 236-291, 2021
Stratified periodic water waves with singular density gradients
J Escher, P Knopf, C Lienstromberg, BV Matioc
Annali di Matematica Pura ed Applicata (1923-) 199 (5), 1923-1959, 2020
On second-order and fourth-order elliptic systems consisting of bulk and surface PDEs: Well-posedness, regularity theory and eigenvalue problems
P Knopf, C Liu
arXiv preprint arXiv:2008.00895, 2020
Shape and topology optimization involving the eigenvalues of an elastic structure: A multi-phase-field approach
H Garcke, P Hüttl, P Knopf
Advances in Nonlinear Analysis 11 (1), 159-197, 2022
Phase-field methods for spectral shape and topology optimization
H Garcke, P Hüttl, C Kahle, P Knopf
arXiv preprint arXiv:2107.03159, 2021
Optimal control of a Vlasov-Poisson plasma by an external magnetic field-The basics for variational calculus
P Knopf
arXiv preprint arXiv:1708.02464, 2017
Strong well-posedness, stability and optimal control theory for a mathematical model for magneto-viscoelastic fluids
H Garcke, P Knopf, S Mitra, A Schlömerkemper
arXiv preprint arXiv:2108.03094, 2021
Existence of weak solutions to multiphase Cahn-Hilliard-Darcy and Cahn-Hilliard-Brinkman models for stratified tumor growth with chemotaxis and general source terms
P Knopf, A Signori
arXiv preprint arXiv:2105.09068, 2021
On the two and one-half dimensional Vlasov-Poisson system with an external magnetic field: global well-posedness and stability of confined steady states
P Knopf, J Weber
arXiv preprint arXiv:2104.14179, 2021
Long-time dynamics of the Cahn--Hilliard equation with kinetic rate dependent dynamic boundary conditions
H Garcke, P Knopf, S Yayla
arXiv preprint arXiv:2103.15612, 2021
Optimal control of a Vlasov-Poisson plasma by an external magnetic field-Analysis of a tracking type optimal control problem
P Knopf
arXiv preprint arXiv:1708.02753, 2017
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