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Research Training Group 2339 (RTG 2339) Interfaces, Complex Structures, and Singular Limits





"Optimal control of anisotropic Allen-Cahn equations"
Luise Blank and Johannes Meisinger
Preprint arXiv: 2105.13310

"Long-time dynamics of the Cahn--Hilliard equation with kinetic rate dependent dynamic boundary conditions"
Harald Garcke, Patrick Knopf and Sema Yayla
Preprint arXiv:2103.15612

"Two-phase Stokes flow by capillarity in the plane: The case of different viscosities"
Bogdan-Vasile Matioc and Georg Prokert
Preprint arXiv:2102.12814

"Optimal control of a quasilinear parabolic equation and its time discretization"
Luise Blank and Johannes Meisinger
Preprint arXiv: 2102.02616

"The multiphase Muskat problem with equal viscosities in two dimensions"
Jonas Bierler and Bogdan-Vasile Matioc
Preprint arXiv: 2101.07728, accepted for publication in Interfaces and Free Boundaries.


"Existence of Nonnegative Solutions to Stochastic Thin-Film Equations in Two Space Dimensions"
S. Metzger und G. Grün

"Non-negative Martingale Solutions to the Stochastic Thin-Film Equation with Nonlinear Gradient Noise"
K. Dareiotis, B. Gess, M.V. Gnann, G. Grün
arXiv:2012.04356, to appear in Arch. Rat. Mech. Anal.

PhD theses

"Temporal Multiscale Methods for a Model of Atherosclerosis"
Florian Sonner, FAU Erlangen (February 2021)

"Sharp Interface Limits for Diffuse Interface Models with Contact Angle"
Maximilian Moser, University of Regensburg (January 2021)

"Boundary Value Problems for Evolutions of Willmore Type"
Julia Menzel, University of Regensburg (January, 2021)



"Numerical approximation of boundary value problems for curvature flow and elastic flow in Riemannian manifolds"
Harald Garcke, Robert Nürnberg
arXiv:2012.02707 Preprint (2020)

"The Muskat problem with surface tension and equal viscosities in subcritical Lp-Sobolev spaces"
Anca-Voichita Matioc and Bogdan-Vasile Matioc
Preprint arXiv:2010.12261, accepted for publication in Journal of Elliptic and Parabolic Equations.

„Coarse-graining of a Fokker-Planck equation with excluded volume effects preserving gradient flow structures“
M.Bruna, M.Burger, J.Carrillo,
European Journal of Applied Mathematics (2021), to appear.

„Network-structured kinetic models of social interactions“,
Preprint on arXiV (2020), and submitted.

„Delayed blow-up for chemotaxis models with local sensing“,
M.Burger, P.Laurencot, A.Trescases
Preprint on arXiV (2020), and submitted.

“Variational regularisation for inverse problems with imperfect forward operators and general noise models“,
L. Bungert, M. Burger, Y. Korolev, C. Schönlieb,
Preprint on arXiV (2020), and submitted

„Structural analysis of an L-infinity variational problem and relation to distance functions“,
L.Bungert, Y.Korolev, M.Burger,
Pure and Applied Analysis (2020), to appear.

„Nonlinear spectral decompositions by gradient flows of one-homogeneous functionals“
L.Bungert, M.Burger, A.Chambolle, M.Novaga,
Analysis and PDE (2020), to appear

"On a linearized Mullins-Sekerka/Stokes system for two-phase flows"
Helmut Abels, Andreas Marquardt
Preprint https://arxiv.org/abs/2006.01654, accepted for publication in Discrete Contin. Dyn. Syst. Ser. S

"Sparse optimal control of a phase field tumour model with mechanical effects"
Harald Garcke, Kei Fong Lam, Andrea Signori
Preprint: https://arxiv.org/abs/2010.03767

"Singular limit for reactive diffusive transport through an array of thin channels in case of critical diffusivity"
Markus Gahn, Maria Neuss-Radu
Preprint: https://arxiv.org/abs/2003.13310

"On second-order and fourth-order elliptic systems consisting of bulk and surface PDEs: Well-posedness, regularity theory and eigenvalue problems"
Patrik Knopf, Chun Liu
Preprint: https://arxiv.org/abs/2008.00895

"On the nonlocal Cahn--Hilliard equation with nonlocal dynamic boundary condition and boundary penalization"
Patrik Knopf, Andrea Signori
Preprint: https://arxiv.org/abs/2004.00093

"Existence of Global Weak Solutions to an Inhomogeneous Doi Model for Active Liquid Crystals",
Oliver Sieber
Preprint arXiv:2006.16832

"Local Well-Posedness of a Quasi-Incomressible Two-Phase Flow."
Helmut Abels, Josef Weber
Preprint: https://arxiv.org/abs/2006.14251

"Shape and Topology Optimization involving the eigenvalues of an elastic structure: A multi-phase-field approach",
Harald Garcke, Paul Hüttl, Patrik Knopf
Preprint arXiv:2005.13497

"Two-phase Stokes flow by capillarity in full 2D space: an approach via hydrodynamic potentials",
Bogdan-Vasile Matioc, Georg Prokert
Preprint arXiv:2003.14010

accepted for publication in Proc. Roy. Soc. Edinburgh Sect. A

"Phase-field dynamics with transfer of materials: The Cahn--Hillard equation with reaction rate dependent dynamic boundary conditions",
Patrick Knopf, Kei Fong Lam, Chun Liu, Stefan Metzger
Preprint arXiv:2003.12983

"Sharp Interface Limit of a Stokes/Cahn-Hilliard System, Part II: Approximate Solutions"
Helmut Abels, Adreas Marquardt
Preprint http://arxiv.org/abs/2003.14267

"Cahn-Hilliard-Brinkman systems for tumour growth",
Matthias Ebenbeck, Harald Garcke, Robert Nürnberg
Preprint arXiv:2003.08314

"Well-posedness of the Muskat problem in subcritical Lp-Sobolev spaces",
Helmut Abels, Bogdan-Vasile Matioc
Preprint arXiv:2003.07656

accepted for publication in European J. Appl. Math.

"Sharp Interface Limit of a Stokes/Cahn-Hilliard System,Part I:Convergence Result",
Helmut Abels, Andreas Marquardt
Preprint arXiv:2003.03139


"Weak and stationary solutions to a Cahn-Hilliard-Brinkman model with singular potentials and source term"
Matthias Ebenbeck and Kei Fong Lam
Advances in nonlinear Analysis, DOI: https://doi.org/10.1515/anona-2020-0100

„Segregation and gap formation in nonlinear cross-diffusion models“,
M.Burger, J.Carrillo, J.Pietschmann, M.Schmidtchen,
Interfaces and Free Boundaries 22 (2020), 175-203.

„A PDE model for bleb formation and interaction with linker proteins“,
P.Werner, M.Burger, J.Pietschmann,
Transactions of Mathematics and its Applications 4 (2020), tnaa001.

Stable discretizations of elastic flow in Riemannian manifolds
Harald Garcke, John W. Barrett and Robert Nürnberg
SIAM J. Numer. Anal. 57 (4), 1987-2018 (2019), doi/pdf/10.1137/18M1227111

Numerical approximation of curve evolutions in Riemannian manifolds
Harald Garcke, John W. Barrett and Robert Nürnberg
IMA Journal of Numerical Analysis 40 (3), 1601-1651, drz012, https://doi.org/10.1093/imanum/drz012

Parametric finite element approximations of curvature-driven interface evolutions
Harald Garcke, John W. Barrett and Robert Nürnberg
Handbook of Numerical Analysis 21, 275-423

On the surface diffusion flow with triple junctions in higher space dimensions
Harald Garcke, Michael Gößwein
Geometric Flows 5 (1), 1-39 (2020) (with) DOI:

On a degenerate parabolic system describing the mean curvature flow of rotationally symmetric closed surfaces
Harald Garcke, Bogdan-Vasile Matioc
J. Evol. Equ. (2020)

"Long-time dynamics for a Cahn–Hilliard tumor growth model with chemotaxis"
Garcke, H., Yayla, S.
Z. Angew. Math. Phys. 71, 123 (2020). https://doi.org/10.1007/s00033-020-01351-3

"On a phase field model of Cahn-Hilliard type for tumour growth with mechanical effects"
Harald Garcke, Kei Fong Lam and Andrea Signori
Nonlinear Analysis: Real World Applications 57 (2020), 1031922019, doi.org/10.1016/j.nonrwa.2020.103192

"Long time existence of solutions to an elastic flow of networks"
Harald Garcke, Julia Menzel, Alessandra Pluda
Communications in Partial Differential Equations (2020), DOI: 10.1080/03605302.2020.1771364

"Learning patient-specific parameters for a diffuse interface glioblastoma model from neuroimaging data"
Harald Garcke, Abramo Agosti, Pasquale Ciarletta, Michael Hinze
Math. Meth. Appl. Sci. 43 (15), 8945-8979 (2020), DOI: 10.1002/mma.6588 arxiv

"Correctors and error estimates for reaction–diffusion processes through thin heterogeneous layers in case of homogenized equations with interface diffusion"
Gahn M., Jäger W., Neuss-Radu M.
Journal of Computational and Applied Mathematics 383 (2021), Art.Nr.: 113126, ISSN: 0377-0427
DOI: 10.1016/j.cam.2020.113126

"Effective transmission conditions for reaction-diffusion processes in domains separated by thin channels"
Bhattacharya A., Gahn M., Neuss-Radu M.
Applicable Analysis (2020), ISSN: 0003-6811
DOI: 10.1080/00036811.2020.1789599

"Modeling of the early stage of atherosclerosis with emphasis on the regulation of the endothelial permeability"
Silva T., Jäger W., Neuss-Radu M., Sequeira A.
Journal of Theoretical Biology 496 (2020), Art.Nr.: 110229, ISSN: 0022-5193
DOI: 10.1016/j.jtbi.2020.110229

"A Mathematical Model of HIF-1 Regulated Cellular Energy Metabolism"
Bocharov G., Jäger W., Knoch J., Neuss-Radu M., Thiel M.
Vietnam Journal of Mathematics (2020), ISSN: 0866-7179
DOI: 0.1007/s10013-020-00426-y
URL: https://link.springer.com/article/10.1007/s10013-020-00426-y

"Convergence of a Robin boundary approximation for a Cahn--Hilliard system with dynamic boundary conditions"
Patrik Knopf, Kei Fong Lam
Nonlinearity 33(8), 4191--4235, 2020, Preprint: https://arxiv.org/abs/1908.06124

"Weak solutions of the Cahn-Hilliard system with dynamic boundary conditions: A gradient flow approach "
Patrik Knopf and Harald Garcke

SIAM Journal on Mathematical Analysis 52(1), 340--369, 2020

"Structure preserving discretisations of gradient flows for axisymmetric two-phase biomembranes"
Harald Garcke, Robert Nürnberg
IMA Journal of Numerical Analysis 00, 1-42 (2020), doi.org/10.1093/imanum/draa027

"Stratified periodic water waves with singular density gradients ",
Joachim Escher, Patrik Knopf, Christina Lienstromberg, Bogdan-Vasile Matioc
Annali di Matematica Pura ed Applicata
Volume 199, Issue 5, Pages 1923-1959, 2020
"Voronoi implicit interface method for geometry evolution of two minerals with applications in reactive porous media"
Peter Frolkovič, Nikola Gajdošová, Stephan Gärttner, Nadja Ray
Proceedings of the Conference Algoritmy 2020, pp. 121 - 130

''Efficiency and Accuracy of Micro‐Macro Models for Mineral Dissolution''
Stephan Gärttner, Peter Frolkovič,  Peter Knabner, Nadja Ray
Water Resources Research, 10.1029/2020WR027585, 56, 8, (2020)
"Existence of Weak Solutions for a Sharp Interface Model for Phase Separation on Biological Membranes"
Helmut Abels, Johannes Kampmann
Discrete Contin. Dyn. Syst. Ser. S. doi: 10.3934/dcdss.2020325
"Well posedness and stability results for some periodic Muskat problems"
Bogdan-Vasile Matioc
"On the principle of linearized stability in interpolationspaces for quasilinear evolution equations",
Bogdan-Vasile Matioc and Christoph Walker
Monatshefte für Mathematik, Volume 191, 2020, Pages 615–634
Preprint arXiv: 1804.10523

"Weak Solutions for a Diffuse Interface Model for Two-Phase Flows of Incompressible Fluids with Different Densities and Nonlocal Free Energies"
Helmut Abels, Yutaka Terasawa
Math Meth Appl Sci. Vol. 43, Issue 6, pp. 3200-3219, 2020 https://doi.org/10.1002/mma.6111

"On convergent schemes for a two-phase Oldroyd-B type model with variable polymer density"
Oliver Sieber
Journal of Numerical Mathematics
Volume 28, Issue 2, Pages 99-129, 2020

PhD theses

"Nonlinear Spectral Analysis with Variational Methods"
Leon Bungert, FAU Erlangen (September 7, 2020)

Matthias Ebenbeck, University of Regensburg (June 22, 2020)



„Mean-field models for segregation dynamics“,
M.Burger, J.Pietschmann, H.Ranetbauer, C.Schmeiser, M.Wolfram,
European Journal of Applied Mathematics (2020), to appear.

Finite element methods for fourth order axisymmetric geometric evolution equations
Harald Garcke, John W. Barrett and Robert Nürnberg
Journal of Computational Physics 376, 733--766 (2019), doi.org/10.1016/j.jcp.2018.10.006

"Stable approximations for axisymmetric Willmore flow for closed and open surfaces",
Harald Garcke, John W. Barrett and Robert Nürnberg
Preprint arXiv:1911.01132

"Non-linear stability of double bubbles under surface diffusion",
Harald Garcke, Michael Gößwein
Preprint arXiv:1910.01041

"Stability analysis for stationary solutions of the Mullins-Sekerka flow with boundary contact"
Harald Garcke, Maximilian Rauchecker
Preprint arXiv:1907.00833
to appear Math.Nachr.

"Convective transport in nanofluids: regularity of solutions and error estimates for finite element approximations"
Eberhard Bänsch and Pedro Morin
Preprint arXiv:1912.04205

"Convective transport in nanofluids: the stationary problem"
Eberhard Bänsch, Sara Faghih--Naini and Pedro Morin
Preprint arXiv:1911.04958

"On the field-induced transport of magnetic nanoparticles in incompressible flow: existence of global solutions"
Günther Grün and Patrick Weiß
J. Math. Fluid Mech., in press

"On the field-induced transport of magnetic nanoparticles in incompressible flow: modeling and numerics"
Günther Grün and Patrick Weiß
Mathematical Models and Methods in Applied Sciences, in press

"One-dimensionality of the minimizers for a diffuse interface generalized antiferromagnetic model in general dimension ",
Sara Daneri, Alicja Kerschbaum, Eris Runa
Preprint arXiv:1907.06419

"Parametric finite element approximations of curvature driven interface evolutions",
John W. Barett, Harald Garcke, Robert Nürnberg
Preprint arXiv:1903.09462

"Optimal control theory and advanced optimality conditions for a diffuse interface model of tumor growth",
Matthias Ebenbeck, Patrik Knopf
Preprint arXiv:1903.00333, DOI: https://doi.org/10.1051/cocv/2019059

"Well-Posedness and qualitative behaviour of the Mullins-Sekerka problem with ninety-degree angle boundary contact ",
Helmut Abels, Maximilian Rauchecker, Mathias Wilke
Preprint arXiv:1902.03611


„On a Reaction-Cross-Diffusion System Modelling the Growth of Glioblastoma,
M.Burger, P.Friele, J.F.Pietschmann,
SIAM J. Appl. Math. 80 (2019), 160-182.

„On Fokker-Planck equations with in- and outflow of mass“,
M.Burger, I.Humpert, J.Pietschmann,
Kinetic and Related Methods 13 (2019), 249-277

„Strong solutions and weak-strong stability in a system of cross-diffusion equations“,
J.Berendsen, M.Burger, V.Ehrlacher, J.Pietschmann,
J. Evolution Equations (2019), https://doi.org/10.1007/s00028-019-00534-4

„A mesoscopic model of biological transport networks“,
M.Burger, J.Haskovec, P.Markowich, H.Ranetbauer,
Comm. Math. Sci. 17 (2019), 1213-1234

„Asymptotic Profiles of Nonlinear Homogeneous Evolution Equations of Gradient Flow Type,
L.Bungert, M.Burger,
J. Evolution Equations 1-32 (2019)

Variational discretization of axisymmetric curvature flows“ 
Harald Garcke, John W. Barrett and Robert Nürnberg
Numerische Mathematik 141 (3), 791-837, doi.org/10.1007/s00211-018-1013-z

Optimal control of time-discrete two-phase flow driven by a diffuse-interface model
Harald Garcke, Michael Hinze and Christian Kahle
ESAIM: COCV 25 (13) (2019), DOI: 10.1051/cocv/2018006

Existence of weak solutions for a diffuse interface model for two-phase flow with surfactants
Harald Garcke, Helmut Abels and Josef Weber
Comm. Pure Appl. Anal. 18 (1), 195-225

"Analysis of a Cahn-Hilliard-Brinkman model for tumour growth with chemotaxis" ,
Matthias Ebenbeck and Harald Garcke
Journal of Differential Equations
Volume 266, Issue 9, 15 April 2019, 5998-6036

"On a Cahn-Hilliard-Brinkman model for tumor growth and its singular limits" ,
Matthias Ebenbeck and Harald Garcke
SIAM Journal on Mathematical Analysis
Volume 51, Issue 3, 2019, Pages 1868–1912

"Optimal medication for tumors modeled by a Cahn-Hilliard-Brinkman equation" ,
Matthias Ebenbeck and Patrik Knopf
Calculus of Variations and Partial Differential Equations
Volume 58, number 4, 2019

"Willmore flow of planar networks"
Harald Garcke, Julia Menzel and Alessandra Pluda
Journal of Differential Equations 266 (4), 2019-2051 (2019)
doi: https://doi.org/10.1016/j.jde.2018.08.019



"Numerical investigation of a fully coupled micro-macro model for mineral dissolution and precipitation",
Jens Oberlander and Nadja Ray

"Standard planar double bubbles are stable under surface diffusion flow"
to appear in Communications in Analysis and Geometry
Harald Garcke, Helmut Abels, Nasrin Arab


 „Cahn--Hilliard inpainting with the double obstacle potential
Harald Garcke, Kei Fong Lam and Vanessa Styles
SIAM J. Imaging Sciences 11 (3), 2064--2089 (2018), doi.org/10.1137/18M1165633

A multiphase Cahn-Hilliard-Darcy model for tumour growth with necrosis
Harald Garcke, Kei Fong Lam, Robert Nürnberg and Emanuel Sitka
Mathematical Models and Methods in Applied Sciences 28 (3), 525-577 (2018), DOI: 10.1142/S0218202518500148

A phase field approach to shape optimization in Navier-Stokes flow with integral state constraint
Harald Garcke, Michael Hinze and Christian Kahle and Kei Fong Lam
Adv. Comput. Math. 44 (5), 1345-1383 (2018), https://doi.org/10.1007/s10444-018-9586-8

Gradient flow dynamics of two-phase biomembranes: Sharp interface variational formulation and finite element approximation
Harald Garcke, John W. Barrett and Robert Nürnberg
SMAI J. Comput. Math. 4, 151-195 (2018), doi: 10.5802/smai-jcm.32

"Mathematical modelling and analysis of nanoparticle gradients induced by magnetic fields" ,
Dominik Himmelsbach, Maria Neuss-Radu, Nicolas Neuß
Journal of Mathematical Analysis and Applications
Volume 461, Issue 2, 15 May 2018, Pages 1544-1560

"Effective interface conditions for processes through thin heterogeneous layers with nonlinear transmission at the bulk-layer interface" ,
Markus Gahn and Maria Neuss-Radu and Peter Knabner
Networks & Heterogeneous Media
2018, 13(4): 609-640

Refereed book contributions

On a Cahn-Hilliard-Darcy system for tumour growth with solution dependent source terms 
Harald Garcke, Kei Fong Lam
Rocca, Elisabetta, Stefanelli, Ulisse, Truskinovsky, Lev, Visintin, Augusto (Eds.)
Trends in applications of mathematics to mechanics 243-264, Springer INdAM Ser. 27, Springer Cham (2018)

Diffuse interface approaches in atmosphere and ocean - modeling and numerical implementation 
Harald Garcke, Michael Hinze, Christian Kahle
Eden, Carsten, Iske, Armin (Eds.): Mathematics of Planet Earth 1, Energy Transfers in Atmosphere and Ocean, 287-307 (2019), Springer Nature Switzerland