Patrik Knopf
Zitiert von
Zitiert von
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
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 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
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, 1–28, 2018
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
Phase-field dynamics with transfer of materials: The Cahn--Hillard equation with reaction rate dependent dynamic boundary conditions
P Knopf, KF Lam, C Liu, S Metzger
arXiv preprint arXiv:2003.12983, 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
arXiv preprint arXiv:2004.00093, 2020
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
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
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
arXiv preprint arXiv:2005.13497, 2020
Stratified periodic water waves with singular density gradients
J Escher, P Knopf, C Lienstromberg, BV Matioc
Annali di Matematica Pura ed Applicata 199, 1923–1959, 2019
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