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"Estimating relative diffusion from 3D micro-CT images using CNNs"
Stephan Gärttner, Florian Frank, Fabian Woller, Andreas Meier and Nadja Ray
Preprint arXiv:2208.03337

"The nonlocal mean curvature flow of periodic graphs"
Bogdan-Vasile Matioc and Christoph Walker
Preprint arXiv:2207.07474

"Weak-strong uniqueness for a class of degenerate parabolic cross-diffusion systems"
Philippe Laurencot and Bogdan-Vasile Matioc
Preprint arXiv:2207.00361

"Qualitative Properties for a System Coupling Scaled Mean Curvature Flow and Diffusion"
Helmut Abels, Felicitas Bürger, Harald Garcke
Preprint arXiv:2205.02493

"Viscoelastic Cahn--Hilliard models for tumour growth"
Harald Garcke, Balázs Kovács, Dennis Trautwein
Preprint arXiv:2204.04147

"Short Time Existence for Coupling of Scaled Mean Curvature Flow and Diffusion"
Helmut Abels, Felicitas Bürger, Harald Garcke
Preprint arXiv:2204.07626

"A new reformulation of the Muskat problem with surface tension"
Anca-Voichita Matioc and Bogdan-Vasile Matioc
Preprint arXiv:2203.13567

"The multiphase Muskat problem with general viscosities in two dimensions"
Jonas Bierler and Bogdan-Vasile Matioc
Preprint arXiv:2202.12004

"Sharp Interface Limit for a Navier-Stokes/Allen-Cahn System with Different Viscosities"
Helmut Abels and Mingwen Fei
Preprint arXiv:2201.09343

"Bounded weak solutions to a class of degenerate cross-diffusion systems"
Philippe Laurencot and Bogdan-Vasile Matioc
Preprint arXiv:2201.06479

"Convergence of a Nonlocal to a Local Diffuse Interface Model for Two-Phase Flow with Unmatched Densities"
Helmut Abels and Yutaka Terasawa
Preprint arXiv:2201.06101


"Two-phase Stokes flow by capillarity in the plane: The case of different viscosities"
Bogdan-Vasile Matioc and Georg Prokert
NoDEA Nonlinear Differential Equations Appl., 29(5), Art. 54, 34 pp., 2022

"Bounded weak solutions to the thin film Muskat problem via an infinite family of Liapunov functionals"
Philippe Laurencot and Bogdan-Vasile Matioc,
Trans. Amer. Math. Soc., 375(8), 5963–5986, 2022

"The multiphase Muskat problem with equal viscosities in two dimensions"
Jonas Bierler and Bogdan-Vasile Matioc
Interfaces Free Bound., 24(2), 163-196, 2022

"Well-posedness of the Muskat problem in subcritical Lp-Sobolev spaces",
Helmut Abels, Bogdan-Vasile Matioc
European J. Appl. Math., 33(2). 224-266, 2022.

"Convergence of the Allen-Cahn equation with a nonlinear Robin Boundary Condition to Mean Curvature Flow with Contact Angle close to 90°."
H. Abels, M. Moser
SIAM J. Math. Anal., 2022

"(Non-)convergence of solutions of the convective Allen–Cahn equation"
H. Abels
Partial Differ. Equ. Appl. 3, 1 (2022)

"Numerical study of single droplet drying in an acoustic levitator before the critical point of time."
M. Doß, E. Bänsch
Chemical Engineering Science Volume 248, Part A, February 2, 2022, 117149. DOI:10.1016/j.ces.2021.117149



"On a fluid-structure interaction problem for plaque growth: cylindrical domain"
H. Abels, Y. Liu
Preprint arXiv:2112.12538, 2021

"Convergence rates for the Allen-Cahn equation with boundary contact energy: The non-perturbative regime"
S. Hensel, M. Moser
Preprint arXiv: 2112.11173, 2021

"Overhang penalization in additive manufacturing via phase field structural topology optimization with anisotropic energies."
Harald Garcke, Kei Fong Lam, Robert Nürnberg and Andrea Signori
Preprint arXiv:2111.14070, 2021

"On a fluid-structure interaction problem for plaque growth."
H. Abels, Y. Liu
Preprint arXiv:2110.00042, 2021

"Homogenization of a nonlinear drift-diffusion system for multiple charged species in a porous medium."
A. Bhattacharya, M. Gahn, M. Neuss-Radu
Preprint arXiv:2110.09257, 2021

"Convergence for thin vibrating rods to a linear beam equation."
H. Abels, T. Ameismeier
Preprint arXiv:2110.01064, 2021

"Large time existence for thin vibrating rods."
H. Abels, T. Ameismeier
Preprint arXiv:2109.11618, 2021

"Efficiency of micro-macro models for surface active two-mineral systems."
S. Gärttner, P. Frolkovič, P. Knabner, N.Ray
Friedrich-Alexander-Universität Erlangen-Nürnberg, 2021,
accepted for publication in SIAM J. Multiscale and Simulation

"Comparison study of phase-field and level-set method for three-phase systems including two minerals."
M. Kelm, S. Gärttner, C. Bringedal, B. Flemisch, P. Knabner, N. Ray
Friedrich-Alexander-Universität Erlangen-Nürnberg}, 2021,

"Estimating permeability of 3D micro-CT images by physics-informed CNNs based on DNS."
S. Gärttner, F. O. Alpak, A. Meier, N. Ray, F. Frank
Preprint: arXiv, 2021, https://arxiv.org/abs/2109.01818

"Numerical analysis for a Cahn-Hilliard system modelling tumour growth with chemotaxis and active transport."
H. Garcke, D. Trautwein
Preprint arXiv:2108.01507, 2021

"The porous medium equation as a singular limit of the thin film Muskat problem"
Philipp Laurencot and Bogdan-Vasile Matioc
Preprint arXiv:2108.09032, to appear in Asymptot. Anal.

"A diffuse interface model for cell blebbing including membrane-cortex coupling with linker dynamics."
M. Burger, F. Frank, H. Garcke, P. Werner
Preprint arXiv:2107.06334, 2021

"Phase-Field Methods for Spectral Shape and Topology Optimization."
H. Garcke, P. Hüttl, C. Kahle, P. Knopf
Preprint arXiv:2107.03159, 2021

"Convergence of the scalar- and vector-valued Allen-Cahn equation to Mean Curvature Flow with 90°-Contact Angle in Higher Dimensions."
M. Moser
Preprint arXiv:2105.07100, 2021

"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

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

"Stripped patterns for generalized antiferromagnetic functionals with power law kernels of exponent smaller than d+2."
A. Kerschbaum
Preprint arXiv:2101.02992


"Two-phase Stokes flow by capillarity in full 2D space: an approach via hydrodynamic potentials",
Bogdan-Vasile Matioc, Georg Prokert
Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 151:1815-1845, 2021

"Singular limit for reactive diffusive transport through an array of thin channels in case of critical diffusivity, Multiscale Model.",
M. Gahn, M. Neuss-Radu
Simul. 19, 1573–1600, 2021

"Convective transport in nanofluids: regularity of solutions and error estimates for finite element approximations"
Eberhard Bänsch and Pedro Morin
J. Math. Fluid Mech. 23, 42 (2021)

"Homogenization of a reaction-diffusion-advection problem in an evolving micro-domain and including nonlinear boundary conditions.",
M. Gahn, M. Neuss-Radu, I.S. Pop
J. Differ. Equations 289:95–127, 2021

"On the field-induced transport of magnetic nanoparticles in incompressible flow: existence of global solutions"
Günther Grün and Patrick Weiß
J. Math. Fluid Mech., 23(10), 1-54, 2021. DOI:10.1007/s00021-020-00523-5

"Cahn-Hilliard-Brinkman systems for tumour growth",
Matthias Ebenbeck, Harald Garcke, Robert Nürnberg
Discrete Contin. Dyn. Syst. Ser. S, 2021. DOI:10.3934/dcdss.202134

"Weak and stationary solutions to a Cahn-Hilliard-Brinkman model with singular potentials and source term"
Matthias Ebenbeck and Kei Fong Lam
Adv. Nonlinear Anal. 10(1), 24-65, 2021. DOI:10.1515/anona-2020-0100

" A stochastic porous medium equation with divergence form noise."
N. Dirr, H. Grillmeier, G. Grün
Discrete and Continuous Dynamical Systems, 41, 2829-2871, 2021. DOI:10.3934/dcds.2020388

" Nonlinear spectral decompositions by gradient flows of one-homogeneous functionals."
L. Bungert, M. Burger, A. Chambolle, M. Novaga
Analysis and PDE, 14(3), 823-860, 2021, DOI:10.2140/apde.2021.14.823

" Nonlinear Power Method for Computing Eigenvectors of Proximal Operators and Neural Networks "
L. Bungert, E. Hait-Fraenkel, N. Papadakis, G. Gilboa
SIAM Journal on Imaging Sciences, In press. DOI:10.1137/20M1384154

"On a degenerate parabolic system describing the meancurvature flow of rotationally symmetric closed surfaces ",
Bogdan-Vasile Matioc, Harald Garcke
Journal of Evolution Equations, Volume 21, Issue 1, 2021, Pages 201-224 ,
Preprint arXiv:1905.09675

"Existence of Nonnegative Solutions to Stochastic Thin-Film Equations in Two Space Dimensions" accepted for publication in Interfaces and Free Boundaries
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

"Analysis and Numerics of Two-Phase Flows of Active Liquid Crystals with Willmore-type Interfacial Energy: A Micro-Macro Approach."
Oliver Sieber, FAU Erlangen (December 2021)

"On the field-induced transport of magnetic nanoparticles in incompressible flow"
Patrick Weiß, FAU Erlangen (November 2021)

"Interaction of Mean Curvature Flow and a Diffusion Equation"
Felicitas Bürger, University of Regensburg (October 2021)

"Sharp and diffuse interface models for the evolution of surfaces that are immersed in fluids and coupled through surfactants"
Philipp Werner, FAU Erlangen (May 2021)

"Thin Vibrating Rods: Gamma-Convergence, Large Time Existence and First Order Asymptotics"
Tobias Ameismeier, University of Regensburg (April 2021)

"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)



"Existence of global weak solutions to an inhomogeneous Doi model for active liquid crystals.",
O. Sieber
Preprint arXiv:2006.16832, 2020

"Long-time Dynamics for a Cahn-Hilliard Tumor Growth Model with Chemotaxis",
Harald Garcke, Sema Yayla
Preprint arXiv:2005.02803

"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

"Long-time Dynamics for a Cahn-Hilliard Tumor Growth Model with Chemotaxis",
Harald Garcke, Sema Yayla
Preprint arXiv:2005.02803

"The infinity Laplacian eigenvalue problem: reformulation and a numerical scheme.",
F. Bozorgnia, L. Bungert, D. Tenbrinck
Preprint arXiv:2004.08127, 2020

"Existence and Uniqueness of the Motion by Curvature of regular networks"
M. Gößwein, J. Menzel, A. Pluda
Preprint arXiv:2003.09962

"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 I:Convergence Result",
Helmut Abels, Andreas Marquardt
Preprint arXiv:2003.03139


"Modeling of the early stage of atherosclerosis with emphasis on the regulation of the endothelial permeability"
T. Silva, W. Jäger, M. Neuss-Radu, A. Sequeira
J. Theor. Biol. 496, 2020, DOI: 10.1016/j.jtbi.2020.110229

"A PDE model for bleb formation and interaction with linker proteins ",
Philipp Werner, Martin Burger, Jan-Frederik Pietschmann
Trans. Math. Appl.,4, 2020. DOI:10.1093/imatrm/tnaa001

"On convergent schemes for a two-phase Oldroyd-B type model with variable polymer density"
Oliver Sieber
Journal of Numerical Mathematics, 28(2), 99-129, 2020. DOI:10.1515/jnma-2019-0019

"Convective transport in nanofluids: the stationary problem"
Eberhard Bänsch, Sara Faghih--Naini and Pedro Morin
J. Math. Anal. Appl. 489, no. 1, 124151 (2020)

"Optimal control theory and advanced optimality conditions for a diffuse interface model of tumor growth",
Matthias Ebenbeck, Patrik Knopf
ESIAM: COCV, 26, 71, 2020. DOI:10.1051/cocv/2019059

"Effective transmission conditions for reaction-diffusion processes in domains separated by thin channels",
Apratim Bhattacharya, Markus Gahn, Maria Neuss-Radu
Appl. Anal., 1-15, 2020. DOI:10.1080/00036811.2020.1789599

"Second Order Pressure Estimates for the Crank-Nicolson Discretization of the Incompressible Navier-Stokes Equations.",
F. Sonner, T. Richter
SIAM Journal on Numerical Analysis. S.375-409.58, 2020. DOI:10.1137/18M1234813

"Long time existence of solutions to an elastic flow of networks.",
H. Garcke, J. Menzel, A. Pluda
Comm. Partial Differential Equations, 45(10), 1253-1305, 2020, DOI:10.1080/03605302.2020.1771364

"A Mathematical Model of HIF-1 Regulated Cellular Energy Metabolism.",
G. Bocharov, W. Jäger, J. Knoch, M. Neuss-Radu, M. Thiel
Vietnam Journal of Mathematics, 49(1), 119-141,2020, DOI:10.1007/s10013-020-00426-y

"Voronoi implicit interface method for geometry evolution of two minerals with applications in reactive porous media.",
P. Frolkovič, N. Gajdosovà, S. Gärttner, N. Ray
Proceedings of the Conference Algoritmy, 121-130, 2020

"Efficiency and accuracy of micro-macro models for mineral dissolution.",
S. Gärttner, P. Frolkovič, P. Knabner, N. Ray
Water Resources Research 56(8), 2020, DOI: 10.1029/2020WR027585

"Localization of Passive 3-D Coils as an Inverse Problem: Theoretical Analysis and a Numerical Method.",
M. Doß, L. Bungert, D. Cichon, H. Brauer, R. Psiuk
IEEE Transactions on Magnetics, 56(4), 1-10, 2020

"Variational regularisation for inverse problems with imperfect forward operators and general noise models.",
L. Bungert, M. Burger, Y. Korolev, C.-B. Schönlieb
Inverse Problems, 36(12), 125014, 2020, DOI: 10.1088/1361-6420/abc531

"Robust Image Reconstruction with Misaligned Structural Information.",
L. Bungert, M.J. Ehrhardt
IEEE Access, 8, 222944-222955, 2020, DOI: 10.1109/ACCESS.2020.3043638

"Structural analysis of an L-ininity variational problem and relations to distance functions.",
L. Bungert, Y. Korolev, M. Burger
Pure and Applied Analysis. 2(3), 703-738, 2020, DOI: 10.2140/paa.2020.2.703

"Asymptotic profiles of nonlinear homogenous evolution equations of gradient flow type.",
L. Bungert, M. Burger
Journal of Evolution Equations, 20(3), 1061-1092, 2020, DOI: 10.1007/s00028-019-00545-1

"Stratified periodic waterwaves with singular density gradients ",
Joachim Escher, Patrik Knopf, Christina Lienstromberg, Bogdan-Vasile Matioc
Annali di Matematica Pura ed Applicata, Volume 199, Issue 5, 2020, Pages 1923–1959
Preprint arXiv:1911.13046

"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

"Well-posedness and stability results for some periodic Muskat problems",
Bogdan-Vasile Matioc
Journal of Mathematical Fluid Mechanics, Volume 22, Issue 2, 2020, Paper No. 31, 45 Pages, Preprint arXiv:1804.10403

"A mixed finite element method for elliptic operators with Wentzell boundary condition",
E. Bänsch, M. Gahn
IMA J. Num. Analysis, 40, no. 1, 87--108 (2020)

PhD theses

"Nonlinear spectral analysis with variational methods."
Leon Bungert, FAU Erlangen (September 2020)

"Cahn-Hilliard-Brinkman models for tumour growth: Modelling, analysis and optimal control."
Matthias Ebenbeck, University of Regensburg (July 2020)

"Free-boundary problems and noise: Analysis and numerics of stochastic porous-medium equations and of stochastic parabolic p-Laplace equations."
Hubertus Grillmeier, FAU Erlangen (January 2020)



"On a phase field model of Cahn-Hilliard type for tumour growth with mechanical effects",
Harald Garcke, Kei Fong Lam, Andrea Signori
Preprint arXiv:1912.01945

"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

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

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

"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 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, 29(12), 2321-2357, 2019. DOI:10.1142/s0218202519500477

"A thermodynamically consistent model for convective transport in nanofluids: existence of weak solutions and fem computations."
E. Bänsch
JMMA, 447, no. 1, 41-59 (2019)

"Numerical investigation of a fully coupled micro-macro model for mineral dissolution and precipitation."
N. Ray, J. Oberlander, P. Frolkovič
Computational Geosciences, 23, 1173-1192, 2019, DOI: 10.1007/s10596-019-09876-x

"Convergence of the Allen-Cahn Equation to the Mean Curvature Flow with 90°-Contact Angle in 2D."
H. Abels, M. Moser,
Interfaces and Free Boundaries, 21(3), 313-365, 2019

"Application of a Cellular Automaton Method to Model the Structure Formation in Soils Under Saturated Conditions: A Mechanistic Approach."
A. Rupp, T. Guhra, A. Meier, A. Prechtel, T. Ritschel, N. Ray, K.U. Totsche,
Frontiers in Environmental Science, 7, 170, 2019, DOI: 10.3389/fenvs.2019.00170

"Solution paths of variational regularization methods for inverse problems."
L. Bungert, M. Burger,
Inverse Problems, 35(10), 105012, 2019, DOI: 10.1088/1361-6420/ab1d71

"Computing nonlinear eigenfunctions via gradient flow extencion."
L. Bungert, M. Burger,
International Conference on Scale Space and Variational Methods in Computer Vision, 291-302, 2019. DOI: 10.1007/978-3-030-22368-7_23.

"Nonnegativity preserving schemes for stochastic porous medium equations"
H. Grillmeier, G. Grün, Math. Comp, 88(317), 1021–1059, 2019. DOI:10.1090/mcom/3372

"Willmore flow of planar networks"
H. Garcke, J. Menzel, and A. Pluda
J. Differential Equations
266(4), 2019–2051, 2019. DOI:10.1016/j.jde.2018.08.019

"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



"Weak solutions of the Cahn-Hilliard system with dynamic boundary conditions: A gradient flow approach " ,
Patrik Knopf and Harald Garcke
Preprint arXiv:1810.09817

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


"Well-Posedness of a Navier–Stokes/Mean Curvature Flow system"
H. Abels, M. Moser
AMS Contemporary Mathematics
710, (Mathematical Analysis in Fluid Mechanics: Selected Recent Results), 1–24, 2018. DOI:10.1090/conm/710

"Numerical study of droplet evaporation in an acoustic levitator." ,
E. Bänsch, M. Götz
Journal of Mathematical Analysis and Applications
Physics of Fluids, 30, 037103 (2018)

"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