Projects and Publications
Projects
Funding source: DFG / Graduiertenkolleg (GRK)
Project leader:
Funding source: Deutsche Forschungsgemeinschaft (DFG), DFG-Einzelförderung / Sachbeihilfe (EIN-SBH)
Project leader:
The porous-medium equation and the thin-film equation are prominent examples of nonnegativity preserving degenerate parabolic equations which give rise to free boundary problems with the free boundary at time t > 0 defined as the boundary of the solution’s support at that time.
As they are supposed to describe the spreading of gas in a porous-medium or the spreading of a viscous droplet on a horizontal surface, respectively, mathematical results on the propagation of free boundaries become r…
Project leader:
Neuentstehende Anwendungen in der Biologie, Nanotechnologie und Medizin machen die Vernetzung von Objekten und Maschinen mit Abmessungen im Nano- und Mikrometerbereich erforderlich. Traditionelle elektromagnetische Ansätze für den Entwurf entsprechender Kommunikationssysteme sind für solch kleine Größenordnungen nicht geeignet. In der Natur jedoch ist die Kommunikation zwischen Nano- und Mikro-Objekten, wie z.B. Bakterien und anderen Zellen, weit verbreitet. Dabei kommen oft Signalmoleküle als I…
Funding source: DFG / Schwerpunktprogramm (SPP)
Project leader:
In recent years, diffuse interface models turned out to be a promising approach to describe fundamental features of two-phase flow like droplet break-up or coalescence. In the second funding period, novel thermodynamical consistent phase-field models for species transport in two-phase flow shall be derived with an emphasis on soluble surfactants. Additional phenomena -- ranging from microscale effects like molecule orientation over thermal effects to electrostatic interactions -- shall be…
Funding source: DFG / Schwerpunktprogramm (SPP)
Project leader:
Topological transitions like droplet coalescence or droplet break-up are fundamental features of two-phase flows. In recent years, diffuse interface models turned out to be a promising approach to describe such phenomena. Species transport across fluidic interfaces and the effects exerted by soluble and insoluble surfactants are additional issues of still increasing technological importance. For those phenomena, novel thermodynamically consistent diffuse interface models shall be developed taking…
Funding source: EU - 7. RP / People / Initial Training Networks (ITN)
Project leader:
With this network, the universities of Bath, Eindhoven, Erlangen, Haifa (Technion), Madrid (Complutense), Paris (Orsay), Rome (La Sapienza), Zürich and the industrial partners EGIS and SIEMENS AG foster a joint training platform for PhD-students working on analysis and control of interfacial phenomena. Applications range from image processing over reaction-diffusion systems to complex multi-phase flow.
FAU is involved in three projects, guided by Proff. Grün, Knabner, and Leugering. T…
Publications
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Zero-contact angle solutions to stochastic thin-film equations
In: Journal of Evolution Equations 22 (2022)
ISSN: 1424-3199
DOI: 10.1007/s00028-022-00818-2
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Existence of nonnegative solutions to stochastic thin-film equations in two space dimensions
In: Interfaces and Free Boundaries 24 (2022), p. 307-387
ISSN: 1463-9971
DOI: 10.4171/IFB/476
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Non-negative Martingale Solutions to the Stochastic Thin-Film Equation with Nonlinear Gradient Noise
In: Archive for Rational Mechanics and Analysis (2021)
ISSN: 0003-9527
DOI: 10.1007/s00205-021-01682-z
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ON STOCHASTIC POROUS-MEDIUM EQUATIONS WITH CRITICAL-GROWTH CONSERVATIVE MULTIPLICATIVE NOISE
In: Discrete and Continuous Dynamical Systems 41 (2021), p. 2829-2871
ISSN: 1078-0947
DOI: 10.3934/dcds.2020388
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On the Field-Induced Transport of Magnetic Nanoparticles in Incompressible Flow: Existence of Global Solutions
In: Journal of Mathematical Fluid Mechanics 23 (2021), Article No.: 10
ISSN: 1422-6928
DOI: 10.1007/s00021-020-00523-5
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On the field-induced transport of magnetic nanoparticles in incompressible flow: Modeling and numerics
In: Mathematical Models & Methods in Applied Sciences (2019)
ISSN: 0218-2025
DOI: 10.1142/S0218202519500477
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Existence of positive solutions to stochastic thin-film equations
In: SIAM Journal on Mathematical Analysis 50 (2018), p. 411-455
ISSN: 0036-1410
DOI: 10.1137/16m1098796
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Nonnegativity preserving convergent schemes for the stochastic porous-medium equation
In: Mathematics of Computation (2018), p. 1021-1059
ISSN: 0025-5718
DOI: 10.1090/mcom/3372
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Micro-macro-models for two-phase flow of dilute polymeric solutions: macroscopic limit, analysis, numerics
In: Advances in Mathematical Fluid Mechanics, Springer, 2017, p. 291-303 (Transport processes at fluidic interfaces)
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Diffuse interface models for incompressible two-phase flows with different densities
In: Advances in Mathematical Fluid Mechanics, springer, 2017, p. 203-229 (Transport processes at fluidic interface)
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On fully decoupled, convergent schemes for diffuse interface models for two-phase flow with general mass densities
In: Communications in Computational Physics 19 (2016), p. 1473-1502
ISSN: 1815-2406
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On micro-macro-models for two-phase flow with dilute polymeric solutions -- modeling and analysis
In: Mathematical Models & Methods in Applied Sciences 26 (2016), p. 823-866
ISSN: 0218-2025
DOI: 10.1142/S0218202516500196
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Finite speed of propagation and waiting times for the stochastic porous medium equation -- a unifying approach
In: SIAM Journal on Mathematical Analysis 47 (2015), p. 825-854
ISSN: 0036-1410
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Two-phase flow with mass density contrast: stable schemes for a thermodynamic consistent and frame-indifferent diffuse interface model
In: Journal of Computational Physics 257 (2014), p. 708-725
ISSN: 0021-9991
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On convergent schemes for diffuse interface models for two-phase flow of incompressible fluids with general mass densities
In: SIAM Journal on Numerical Analysis 51 (2013), p. 3036-3061
ISSN: 0036-1429
DOI: 10.1137/130908208
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On uniqueness results for an elliptic-parabolic system of pde arising in dynamic electrowetting
In: ZAMM - Zeitschrift für angewandte Mathematik und Mechanik 93 (2013), p. 777-788
ISSN: 0044-2267
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Thermodynamically consistent diffuse interface models for incompressible two-phase flows with different densities
In: Mathematical Models & Methods in Applied Sciences 22 (2012), p. 1150013-1150052
ISSN: 0218-2025
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On modeling and simulation of electrokinetic phenomena in two-phase flow with general mass densities
In: SIAM Journal on Applied Mathematics 72 (2012), p. 1899-1925
ISSN: 0036-1399
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Numerical simulation of static and dynamic electrowetting
In: Journal of Adhesion Science and Technology 26 (2012), p. 1805-1824
ISSN: 0169-4243
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On a phase-field model for electrowetting and other electrokinetic phenomena
In: SIAM Journal on Mathematical Analysis 43 (2011), p. 527-563
ISSN: 0036-1410
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A phase-field model for electrowetting
In: Interfaces and Free Boundaries 11 (2009), p. 259-290
ISSN: 1463-9963
DOI: 10.4171/IFB/211
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A phase-field model for electrowetting and related phenomena
In: Proceedings in Applied Mathematics and Mechanics 7 (2007), p. 1151205-1151207
ISSN: 1617-7061
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Lower bounds on waiting time for degenerate parabolic equations and systems
In: Interfaces and Free Boundaries 8 (2006), p. 111-129
ISSN: 1463-9971
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Thin-film flow influenced by thermal noise
In: Journal of Statistical Physics 122 (2006), p. 1261-1291
ISSN: 0022-4715
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The thin-film equation: recent advances and some new perspectives
In: Journal of Physics: Condensed Matter 17 (2005), p. 291-307
ISSN: 0953-8984
DOI: 10.1088/0953-8984/17/9/002
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Droplet spreading under weak slippage: existence for the Cauchy problem
In: Communications in Partial Differential Equations (2004), p. 1697-1744
ISSN: 0360-5302
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Droplet spreading under weak slippage: the waiting time phenomenon
In: Annales de l'Institut Henri Poincaré - Analyse Non Linéaire 21 (2004), p. 255-269
ISSN: 0294-1449
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Some remarks on modelling and simulation of thin-film flow
In: Proceedings in Applied Mathematics and Mechanics 4 (2004), p. 47-50
ISSN: 1617-7061
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Complex dewetting scenarios captured by thin-film models
In: Nature Materials 2 (2003), p. 59-63
ISSN: 1476-1122
DOI: 10.1038/nmat788
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Droplet spreading under weak slippage: a basic result on finite speed of propagation
In: SIAM Journal on Mathematical Analysis 34 (2003), p. 992-1006
ISSN: 0036-1410
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On the convergence of entropy consistent schemes for lubrication type equations in multiple space dimensions
In: Mathematics of Computation 72 (2003), p. 1251-1279
ISSN: 0025-5718
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Correlated dewetting patterns in thin polystyrene films
In: Journal of Physics: Condensed Matter 15 (2003), p. 421-426
ISSN: 0953-8984
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Satellite hole formation during dewetting; experiment and simulation
In: Journal of Physics: Condensed Matter 15 (2003), p. 3355-3366
ISSN: 0953-8984
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Waiting time phenomena for degenerate parabolic equations -- a unifying approach
In: S. Hildebrandt, H. Karcher (ed.): Geometric analysis and nonlinear partial differential equations, Heidelberg: Springer-Verlag, 2003, p. 637-648
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Droplet spreading under weak slippage: the optimal asymptotic propagation rate in the multi-dimensional case
In: Interfaces and Free Boundaries 4 (2002), p. 309-323
ISSN: 1463-9971
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Numerical methods for fourth order nonlinear diffusion problems
In: Applications of Mathematics 47 (2002), p. 517-543
ISSN: 0862-7940
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On space-time adaptive convergent finite element schemes for a general class of lubrication-type equations
In: H.A. Mang, F.G. Rammerstorfer, J. Eberhardsteiner (ed.): Proceedings of the 5th World Congress on Computational Mechanics, Vienna Technical University, 2002
ISBN: 3-9501554-0-6
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A finite volume scheme for surfactant driven thin film flow
In: R. Herbin, D. Krönger (ed.): Proceedings of the Third International Symposium on Finite Volumes for Complex Applications, Hermes Penton Science, 2002, p. 567-574
ISBN: 1-9039-9634-1
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On Bernis' interpolation inequalities in multiple space dimensions
In: Zeitschrift für Analysis und ihre Anwendungen 20 (2001), p. 987-998
ISSN: 0232-2064
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Dewetting films: Bifurcations and concentrations
In: Nonlinearity 14 (2001), p. 1569-1592
ISSN: 0951-7715
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A waiting time phenomenon for thin film equations
In: Annali della Scuola Normale Superiore di Pisa-Classe di Scienze XXX (2001), p. 437-463
ISSN: 0391-173X
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Simulation of singularities and instabilities in thin film flow
In: European Journal of Applied Mathematics 12 (2001), p. 293-320
ISSN: 0956-7925
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Nonnegativity preserving convergent schemes for the thin film equation
In: Numerische Mathematik 87 (2000), p. 113-152
ISSN: 0029-599X
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Entropy consistent finite volume schemes for the thin film equation
In: R. Vilsmeier, F. Benkhaldoun, D. Hänel (ed.): Finite volume schemes for complex applications II, Hermes Science Publications, Paris, 1999
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The thin viscous flow equation in higher space dimensions
In: Advances in Differential Equations 3 (1998), p. 417-440
ISSN: 1079-9389
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On a fourth order degenerate parabolic equation: gobal entropy estimates and qualitative behavior of solutions
In: SIAM Journal on Mathematical Analysis 29 (1998), p. 321-342
ISSN: 0036-1410
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Degenerate parabolic equations of fourth order and a plasticity model with nonlocal hardening
In: Zeitschrift für Analysis und ihre Anwendungen 14 (1995), p. 541-573
ISSN: 0232-2064
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