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Publikationen von Knopf, Patrik
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Anzahl der Einträge: 19.
2024
Garcke, Harald 
, Hüttl, Paul , Kahle, Christian und Knopf, Patrik
(2024)
Sharp-Interface Limit of a Multi-phase Spectral Shape Optimization Problem for Elastic Structures.
Applied Mathematics & Optimization 89 (1).
2023
Giorgini, Andrea und Knopf, Patrik
(2023)
Two-Phase Flows with Bulk–Surface Interaction: Thermodynamically Consistent Navier–Stokes–Cahn–Hilliard Models with Dynamic Boundary Conditions.
Journal of Mathematical Fluid Mechanics 25 (3).
Garcke, Harald , Knopf, Patrik , Nürnberg, Robert und Zhao, Quan
(2023)
A Diffuse-Interface Approach for Solid-State Dewetting with Anisotropic Surface Energies.
Journal of Nonlinear Science 33 (2), Art. no. 34.
2022
Garcke, Harald , Knopf, Patrik , Mitra, Sourav und Schlömerkemper, Anja
(2022)
Strong well-posedness, stability and optimal control theory for a mathematical model for magneto-viscoelastic fluids.
Calculus of Variations and Partial Differential Equations 61 (5).
Knopf, Patrik und Signori, Andrea
(2022)
Existence of weak solutions to multiphase Cahn–Hilliard–Darcy and Cahn–Hilliard–Brinkman models for stratified tumor growth with chemotaxis and general source terms.
Communications in Partial Differential Equations 47 (2), S. 233-278.
Volltext nicht vorhanden.
und Signori, Andrea
(2022)
Existence of weak solutions to multiphase Cahn–Hilliard–Darcy and Cahn–Hilliard–Brinkman models for stratified tumor growth with chemotaxis and general source terms.
Communications in Partial Differential Equations 47 (2), S. 233-278.
Volltext nicht vorhanden.
Garcke, Harald , Knopf, Patrik und Yayla, Sema
(2022)
Long-time dynamics of the Cahn–Hilliard equation with kinetic rate dependent dynamic boundary conditions.
Nonlinear Analysis 215, S. 112619.
Volltext nicht vorhanden.
, Knopf, Patrik und Yayla, Sema
(2022)
Long-time dynamics of the Cahn–Hilliard equation with kinetic rate dependent dynamic boundary conditions.
Nonlinear Analysis 215, S. 112619.
Volltext nicht vorhanden.
Knopf, Patrik und Weber, Jörg
(2022)
On the two and one-half dimensional Vlasov–Poisson system with an external magnetic field: Global well-posedness and stability of confined steady states.
Nonlinear Analysis: Real World Applications 65, S. 103460.
Volltext nicht vorhanden.
und Weber, Jörg
(2022)
On the two and one-half dimensional Vlasov–Poisson system with an external magnetic field: Global well-posedness and stability of confined steady states.
Nonlinear Analysis: Real World Applications 65, S. 103460.
Volltext nicht vorhanden.
2021
Garcke, Harald, Hüttl, Paul und Knopf, Patrik
(2021)
Shape and topology optimization involving the eigenvalues of an elastic structure: A multi-phase-field approach.
Advances in Nonlinear Analysis 11 (1), S. 159-197.
Knopf, Patrik und Liu, Chun
(2021)
On second-order and fourth-order elliptic systems consisting of bulk and surface PDEs: Well-posedness, regularity theory and eigenvalue problems.
Interfaces and Free Boundaries 23 (4), S. 507-533.
Volltext nicht vorhanden.
Knopf, Patrik und Signori, Andrea
(2021)
On the nonlocal Cahn–Hilliard equation with nonlocal dynamic boundary condition and boundary penalization.
Journal of Differential Equations 280, S. 236-291.
Volltext nicht vorhanden.
und Signori, Andrea
(2021)
On the nonlocal Cahn–Hilliard equation with nonlocal dynamic boundary condition and boundary penalization.
Journal of Differential Equations 280, S. 236-291.
Volltext nicht vorhanden.
Knopf, Patrik , Lam, Kei Fong , Liu, Chun und Metzger, Stefan
(2021)
Phase-field dynamics with transfer of materials: The Cahn–Hilliard equation with reaction rate dependent dynamic boundary conditions.
ESAIM: Mathematical Modelling and Numerical Analysis 55 (1), S. 229-282.
Volltext nicht vorhanden.
, Lam, Kei Fong , Liu, Chun und Metzger, Stefan
(2021)
Phase-field dynamics with transfer of materials: The Cahn–Hilliard equation with reaction rate dependent dynamic boundary conditions.
ESAIM: Mathematical Modelling and Numerical Analysis 55 (1), S. 229-282.
Volltext nicht vorhanden.
2020
Matioc, Bogdan‑Vasile, Escher, Joachim , Knopf, Patrik und Lienstromberg, Christina
(2020)
Stratified periodic water waves with singular density gradients.
Annali di Matematica Pura ed Applicata 199, S. 1923-1959.
Knopf, Patrik und Lam, Kei Fong
(2020)
Convergence of a Robin boundary approximation for a Cahn–Hilliard system with dynamic boundary conditions.
Nonlinearity 33 (8), S. 4191-4235.
Volltext nicht vorhanden.
und Lam, Kei Fong
(2020)
Convergence of a Robin boundary approximation for a Cahn–Hilliard system with dynamic boundary conditions.
Nonlinearity 33 (8), S. 4191-4235.
Volltext nicht vorhanden.
Knopf, Patrik und Weber, Jörg
(2020)
Optimal Control of a Vlasov–Poisson Plasma by Fixed Magnetic Field Coils.
Applied Mathematics & Optimization 81 (3), S. 961-988.
Volltext nicht vorhanden.
und Weber, Jörg
(2020)
Optimal Control of a Vlasov–Poisson Plasma by Fixed Magnetic Field Coils.
Applied Mathematics & Optimization 81 (3), S. 961-988.
Volltext nicht vorhanden.
Ebenbeck, Matthias und Knopf, Patrik
(2020)
Optimal control theory and advanced optimality conditions for a diffuse interface model of tumor growth.
ESAIM: Control, Optimisation and Calculus of Variations 26, S. 71.
Volltext nicht vorhanden.
(2020)
Optimal control theory and advanced optimality conditions for a diffuse interface model of tumor growth.
ESAIM: Control, Optimisation and Calculus of Variations 26, S. 71.
Volltext nicht vorhanden.
Garcke, Harald und Knopf, Patrik
(2020)
Weak Solutions of the Cahn--Hilliard System with Dynamic Boundary Conditions: A Gradient Flow Approach.
SIAM Journal on Mathematical Analysis 52 (1), S. 340-369.
Volltext nicht vorhanden.
(2020)
Weak Solutions of the Cahn--Hilliard System with Dynamic Boundary Conditions: A Gradient Flow Approach.
SIAM Journal on Mathematical Analysis 52 (1), S. 340-369.
Volltext nicht vorhanden.
2019
Knopf, Patrik
(2019)
Confined steady states of a Vlasov‐Poisson plasma in an infinitely long cylinder.
Mathematical Methods in the Applied Sciences 42 (18), S. 6369-6384.
Volltext nicht vorhanden.
(2019)
Confined steady states of a Vlasov‐Poisson plasma in an infinitely long cylinder.
Mathematical Methods in the Applied Sciences 42 (18), S. 6369-6384.
Volltext nicht vorhanden.
Ebenbeck, Matthias und Knopf, Patrik
(2019)
Optimal medication for tumors modeled by a Cahn–Hilliard–Brinkman equation.
Calculus of Variations and Partial Differential Equations 58 (4).
Volltext nicht vorhanden.
(2019)
Optimal medication for tumors modeled by a Cahn–Hilliard–Brinkman equation.
Calculus of Variations and Partial Differential Equations 58 (4).
Volltext nicht vorhanden.
2018
Knopf, Patrik
(2018)
Optimal control of a Vlasov–Poisson plasma by an external magnetic field.
Calculus of Variations and Partial Differential Equations 57 (5).
Volltext nicht vorhanden.
(2018)
Optimal control of a Vlasov–Poisson plasma by an external magnetic field.
Calculus of Variations and Partial Differential Equations 57 (5).
Volltext nicht vorhanden.
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