P. Knopf

发表

Optimal control theory and advanced optimality conditions for a diffuse interface model of tumor growth

Matthias Ebenbeck, P. Knopf, 2019, ESAIM: Control, Optimisation and Calculus of Variations.

Optimal medication for tumors modeled by a Cahn–Hilliard–Brinkman equation

Matthias Ebenbeck, P. Knopf, 2018, Calculus of Variations and Partial Differential Equations.

Phase-field dynamics with transfer of materials: The Cahn-Hillard equation with reaction rate dependent dynamic boundary conditions pdf

Stefan Metzger, Chun Liu, Kei Fong Lam, 2020, ESAIM: Mathematical Modelling and Numerical Analysis.

A diffuse-interface approach for solid-state dewetting with anisotropic surface energies

R. Nürnberg, H. Garcke, P. Knopf, 2022, ArXiv.

Confined steady states of a Vlasov‐Poisson plasma in an infinitely long cylinder

P. Knopf, 2018, Mathematical Methods in the Applied Sciences.

Existence of weak solutions to multiphase Cahn–Hilliard–Darcy and Cahn–Hilliard–Brinkman models for stratified tumor growth with chemotaxis and general source terms

A. Signori, P. Knopf, 2021, Communications in Partial Differential Equations.

Phase-field methods for spectral shape and topology optimization

Tim Laux, H. Garcke, P. Knopf, 2021, ESAIM: Control, Optimisation and Calculus of Variations.

A phase-field version of the Faber--Krahn theorem

Tim Laux, P. Knopf, Paul Huttl, 2022, 2207.10946.

A Diffuse-Interface Approach for Solid-State Dewetting with Anisotropic Surface Energies

R. Nürnberg, H. Garcke, P. Knopf, 2022, Journal of Nonlinear Science.

Phase-field dynamics with transfer of materials: The Cahn-Hillard equation with reaction rate dependent dynamic boundary conditions pdf

Stefan Metzger, Kei Fong Lam, Patrik Knopf, 2020, ESAIM: Mathematical Modelling and Numerical Analysis.

Weak Solutions of the Cahn-Hilliard System with Dynamic Boundary Conditions: A Gradient Flow Approach

Harald Garcke, Patrik Knopf, H. Garcke, 2018, SIAM J. Math. Anal..

Optimal control of a Vlasov-Poisson plasma by an external magnetic field - The basics for variational calculus

P. Knopf, 2017, 1708.02464.

Sharp-Interface Limit of a Multi-phase Spectral Shape Optimization Problem for Elastic Structures

H. Garcke, P. Knopf, Christian Kahle, 2023, Applied Mathematics & Optimization.

Phase-field methods for spectral shape and topology optimization

Tim Laux, H. Garcke, P. Knopf, 2021, ESAIM: Control, Optimisation and Calculus of Variations.

Optimal control of a Vlasov–Poisson plasma by an external magnetic field

P. Knopf, 2018, Calculus of Variations and Partial Differential Equations.

Convergence of a Robin boundary approximation for a Cahn–Hilliard system with dynamic boundary conditions

Kei Fong Lam, Patrik Knopf, P. Knopf, 2019, Nonlinearity.

Stratified periodic water waves with singular density gradients

J. Escher, P. Knopf, Christina Lienstromberg, 2019, Annali di Matematica Pura ed Applicata (1923 -).

Strong well-posedness, stability and optimal control theory for a mathematical model for magneto-viscoelastic fluids

Harald Garcke, Sourav Mitra, Patrik Knopf, 2021, Calculus of Variations and Partial Differential Equations.

Two-Phase Flows with Bulk–Surface Interaction: Thermodynamically Consistent Navier–Stokes–Cahn–Hilliard Models with Dynamic Boundary Conditions

P. Knopf, A. Giorgini, 2022, Journal of Mathematical Fluid Mechanics.

The anisotropic Cahn–Hilliard equation: Regularity theory and strict separation properties

H. Garcke, P. Knopf, J. Wittmann, 2023, Discrete and Continuous Dynamical Systems - S.

Controlling a Vlasov-Poisson plasma by a Particle-In-Cell method based on a Monte Carlo framework

P. Knopf, S. Scheurer, Jörg Weber, 2023, 2304.02083.

Long-time dynamics of the Cahn–Hilliard equation with kinetic rate dependent dynamic boundary conditions

H. Garcke, P. Knopf, Sema Yayla, 2021, Nonlinear Analysis.

On second-order and fourth-order elliptic systems consisting of bulk and surface PDEs: Well-posedness, regularity theory and eigenvalue problems

Chun Liu, P. Knopf, 2020, Interfaces and Free Boundaries.

On the nonlocal Cahn–Hilliard equation with nonlocal dynamic boundary condition and boundary penalization

A. Signori, P. Knopf, 2020, Journal of Differential Equations.

Optimal Control of a Vlasov–Poisson Plasma by Fixed Magnetic Field Coils

P. Knopf, Jörg Weber, 2017, Applied Mathematics & Optimization.

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, 2021, Nonlinear Analysis: Real World Applications.

Shape and topology optimization involving the eigenvalues of an elastic structure: A multi-phase-field approach

Harald Garcke, Patrik Knopf, Paul Huttl, 2020, Advances in Nonlinear Analysis.

Well-posedness of a bulk-surface convective Cahn--Hilliard system with dynamic boundary conditions

P. Knopf, Jonas Stange, 2024, 2401.08400.

Two-phase flows through porous media described by a Cahn--Hilliard--Brinkman model with dynamic boundary conditions

P. Colli, P. Knopf, G. Schimperna, 2023, 2312.15274.

A phase-field version of the Faber--Krahn theorem

Tim Laux, P. Knopf, Paul Huttl, 2022, 2207.10946.