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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
502020
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
462021
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
332020
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
332019
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
232020
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
212021
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
Communications in Partial Differential Equations 47 (2), 233-278, 2022
172022
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, 2021
172021
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
162018
Stratified periodic water waves with singular density gradients
J Escher, P Knopf, C Lienstromberg, BV Matioc
Annali di Matematica Pura ed Applicata (1923-) 199, 1923-1959, 2020
142020
Optimal Control of a Vlasov–Poisson Plasma by Fixed Magnetic Field Coils
P Knopf, J Weber
Applied Mathematics & Optimization 81 (3), 961–988, 2020
142020
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
Interfaces and Free Boundaries 23 (4), 507-533, 2020
122020
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
122019
Two-Phase Flows with Bulk–Surface Interaction: Thermodynamically Consistent Navier–Stokes–Cahn–Hilliard Models with Dynamic Boundary Conditions
A Giorgini, P Knopf
Journal of Mathematical Fluid Mechanics 25 (3), 65, 2023
102023
Long-time dynamics of the Cahn–Hilliard equation with kinetic rate dependent dynamic boundary conditions
H Garcke, P Knopf, S Yayla
Nonlinear Analysis 215, 112619, 2022
102022
Strong well-posedness, stability and optimal control theory for a mathematical model for magneto-viscoelastic fluids
H Garcke, P Knopf, S Mitra, A Schlömerkemper
Calculus of Variations and Partial Differential Equations 61 (5), 179, 2022
92022
Phase-field methods for spectral shape and topology optimization
H Garcke, P Hüttl, C Kahle, P Knopf, T Laux
ESAIM: Control, Optimisation and Calculus of Variations 29, 10, 2023
82023
A diffuse-interface approach for solid-state dewetting with anisotropic surface energies
H Garcke, P Knopf, R Nürnberg, Q Zhao
Journal of Nonlinear Science 33 (2), 34, 2023
42023
A phase-field version of the Faber--Krahn theorem
P Hüttl, P Knopf, T Laux
arXiv preprint arXiv:2207.10946, 2022
32022
Two-phase flows through porous media described by a Cahn--Hilliard--Brinkman model with dynamic boundary conditions
P Colli, P Knopf, G Schimperna, A Signori
arXiv preprint arXiv:2312.15274, 2023
22023
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