Hannes Uecker, Forschung

Einen “anschaulichen” Forschungsüberblick zu Teilen der Angewandten Analysis und Mathematischen Modellierung finden Sie hier. Im Zentrum meiner Forschung stehen: Analysis nichtlinearer partieller Differentialgleichungen, Mathematische Modellierung und Numerische Simulation. Zuletzt bildet pde2path einen Schwerpunkt.

Zur Übersicht möchte ich meine Arbeiten in sechs Gebiete einteilen, mit den neueren Interessen zuerst, und gegenseitigen Überschneidungen.

1.
Bifurkation und Musterbildung in PDE Systemen über beschränkten Gebieten, inklusive numerischer Methoden (pde2path), Klassische und erweiterte Modelle aus Physik, Chemie und Biologie. [7, 10, 11,12,13, 14, 16, 18,20, 23,28,40,42, 41, 50,60, 63, 61, 69]
2.
pde2path Entwicklung. [74,17, 28, 29], siehe auch diverse Tutorials
3.
Musterbildung in Optimalsteuerung mit PDE Nebenbedingungen. [9, 15,20, 23]
4.
Nichtlineare Optik (und andere Probleme, in denen die Nichtlineare Schrödinger Gleichung oder andere Wellengleichungen eine wichtige Rolle spielen) [21,22, 24, 25,26, 38,45, 49, 55,56,66,71, 59]
5.
Flüssigkeitsströmungen, insbesondere mit freiem Rand über geneigte Ebenen [ 43, 47, 57, 46, 53,51, 64, 67]
6.
Musterbildende Systeme über unbeschränktem Gebiet, in denen vielfach Ginzburg–Landau Gleichungen und verwandte Amplitudengleichungen eine wichtige Rolle spielen) [27, 77,31, 52,65,62, 72, 70,73]

Publikationsliste, Stand 14. März 2024. Hinweis: Die verlinkten Preprints können leicht von den publizierten Versionen abweichen.
Bücher
PIC PIC
Numerical continuation and bifurcation in Nonlinear PDEs, SIAM, 2021, SIAM
Nonlinear PDEs: A Dynamical Systems Approach, AMS, Graduate Studies in Mathematics 182, 2017, mit Guido Schneider. AMS

Preprints

1.
Phase transition and minimal interfaces on manifolds with conical singularities, 2024, (mit D. Grieser, S. Held and B. Vertman), preprint
2.
Time-dependent localized patterns in a predator–prey model, 2024, (mit F. Al Saadi, E. Knobloch and M. Nelson), preprint
3.
Numerical continuation and bifurcation for differential geometric PDEs, 2024, (mit A. Meiners), preprint

Veröffentlichungen in Zeitschriften und Buchkapitel

2021–...

4.
Nonlinear dynamics of modulated waves on graphene like quantum graphs, Mathematische Nachrichten 295 (11), 2147-2170, 2022, (mit S. Gilg and G. Schneider), preprint
5.
Origin of Jumping Oscillons in an Excitable Reaction-Diffusion System, PRE, E 104 (6), L062201 2021, (mit E. Knobloch and A. Yochelis), preprint
6.
Numerical continuation and bifurcation in Nonlinear PDEs - Algorithms, Applications, and Experiments, Jahresbericht der DMV, 2021.
7.
Localized and extended patterns in the cubic-quintic Swift-Hohenberg equation on a disk, Phys. Rev. E, 104:014208, 2021, (mit N. Verschueren und E.Knobloch) preprint
8.
Optimal spatial patterns in feeding, fishing, and pollution, DCDS-S, 2021, preprint
9.
Optimal Stock–Enhancement of a Spatially Distributed Renewable Resource, Journal of Economic Dynamics & Control, 123, 104060, 2021 (mit Th. Upmann, L. Hammann, B. Blasius)

2016–2020

10.
Bending and pinching of three-phase stripes: From secondary instabilities to morphological deformations in organic photovoltaics, Phys. Rev. E, 102, 062213, 2020 (mit A. Shapira, N. Gavish und A. Yochelis)
11.
Stripes on finite domains: Why the zigzag instability is only a partial story, Chaos, 30, 073104, 2020 (mit A. Shapira und A. Yochelis) preprint
12.
The role of spatial self-organization in the design of agroforestry system, PLOS ONE, 15:7, e0236325, 2020 (mit O. Tzuk und E. Meron) preprint
13.
Snaking branches of planar BCC fronts in the 3D Brusselator, Physica D, 406, 132383, 2020, (mit D. Wetzel) preprint
14.
Defect–like structures and localized patterns in the cubic–quintic–septic Swift–Hohenberg equation, PRE, 100:1, 012204, 2019, mit E. Knobloch und D. Wetzel) preprint
15.
Optimal fishery with Coastal Catch, Natural Resource Modelling, e12235, 2019 (mit D. Grass und Th. Upmann) preprint
16.
Continuation for thin film hydrodynamics and related scalar problems, in Comput. Methods Appl. Sci., 50, Springer, Cham, 2019 (mit S. Engelnkemper, S. V. Gurevich, D. Wetzel and U. Thiele), preprint.
17.
Hopf bifurcation and time periodic orbits with pde2path - algorithms and applications, Comm. in Comp. Phys., 2019, preprint, pde2path homepage.
(This replaces the old version (2016), where the algorithms, applications, and implementations were reviewed in a single document. Now the paper focusses on the algorithms and applications, while the implementation is reviewed in a Tutorial on Hopf bifurcation; see also pde2path tutorials.
18.
Mean field approach to first and second order phase transitions in ionic liquids, PRE, 95:060201, 2017, preprint, (mit S. Bier, N. Gavish and A. Yochelis)
19.
Desertification by Front Propagation?, Journal of Theoretical Biology 418 (2017), 27–35, (mit Y. Zelnik, U. Feudel und E. Meron) preprint
20.
Optimal management and spatial patterns in a distributed shallow lake model, 1:1-21, 2017, (mit D. Grass), preprint
21.
Low regularity justification results for envelope approximations of nonlinear wave packets in periodic media, Asymptotic Analysis, 99 (1-2), pp. 53-65, 2016 (mit K. Matthies), preprint
22.
Sine-Gordon solitons in networks: Scattering and transmission at vertices, Europ. Phys. Letters 115: 50002, 2016 (mit Z. Sobirov, D. Babajanov, K. Nakamura and D. Matrasulov), preprint
23.
Optimal control and spatial patterns in a semi arid vegetation system, Natural Resource Modeling, 29:2, 229–258, 2016, preprint
24.
Bifurcation of Nonlinear Bloch Waves from the Spectrum in the Gross-Pitaevskii Equation, Journal of Nonlinear Science, 26:3, 581–618, 2016, (mit T. Dohnal), preprint

2011–2015

25.
Exact solutions of the Cauchy problem for the linearized KdV equation on metric star graphs, Uzbek Mathematical J, 2015:3, 143-154, (mit Z. Sobirov und M. Akhmedov), preprint
26.
Soliton transport in tubular networks: transmission at vertices in the shrinking limit, PRE 91, 023209, 2015, (mit D. Grieser, Z. Sobirov, D. Babajanov and D. Matrasulov), preprint
27.
Individual-based model for quorum sensing with background flow, Bull. Math. Biology, (mit J. Müller und B. Hense), 2014, preprint
28.
Numerical results for snaking of patterns over patterns in some 2D Selkov–Schnakenberg Reaction–Diffusion systems, SIADS, 13-1:94–128, 2014 (mit D. Wetzel) preprint,
29.
pde2path – a Matlab package for continuation and bifurcation in 2D elliptic systems, NMTMA (Numerical Mathematics: Theory, Methods and Applications), 7:58–106, 2014 (mit D. Wetzel und J. Rademacher) preprint, pde2path homepage
30.
Approximating the dynamics of communicating cells in a diffusive medium by ODEs -Â Homogenization with Localization, J. Math. Biology, 2012, (mit J. Müller) preprint
31.
Diffusive stability and diffusive mixing of periodic wave trains in reaction diffusion systems. JDE, 252, 3541–3574, 2012. (mit B. Sandstede, A. Scheel and G. Schneider) preprint
32.
Self-similar decay to the marginally stable ground state in a model for film flow over inclined wavy bottoms, EJDE, 2012:61, 1–51, 2012, (mit T. Häcker und G. Schneider) preprint
33.
Traveling interface modulations in the NH3+O2 reaction on a Rh(110) surface, Physical Chemistry Chemical Physics, 14, 5260–5264, 2012, (mit M. Rafti, F. Lovis, V. Krupennikova and R. Imbihl) preprint
34.
Corrigendum to 41, Proc. Royal Soc. Edinburgh, 141A, 819-824, 2011 (mit R. Kaiser), preprint
35.
Interfacing Fortran routines from Matlab in a simple and efficient way - with applications to ordinary and partial differential equations Summer School Modern Computational Science, Oldenburg 2011, Universitätsverlag Oldenburg, 2011, preprint,
36.
Local existence and uniqueness of solutions of the weak electrolyte model describing electro-convection in nematic liquid crystals. ZAMM, 91:3, 247-256, 2011 (mit W.-P. Düll und G. Schneider) preprint
37.
Erratum to (published version of) 45, Physica D, 240, 357-362, 2011 (mit T. Dohnal)preprint
38.
Interaction of modulated pulses in nonlinear oscillator chains, J. Diff. Eq. Appl., 17:3, 279-298, 2011 (mit G. Schneider und M. Wand) preprint

2006-2010

39.
Amplitude equations – an invitation to multiple scale analysis Summer School Modern Computational Science, Oldenburg 2010, Universitätsverlag Oldenburg, 2010, preprint,
40.
Statistics for surface modes of nanoparticles with shape fluctuations, Commun. in Comp. Physics, 8, 1224, 2010, (mit F. Rüting), preprint,
41.
Well-posedness of some initial-boundary-value problems for dynamo-generated poloidal magnetic fields, Proc. Royal Soc. Edinburgh, 139A, 1209-1235, 2009 (mit R. Kaiser) preprint
42.
Perturbation theory for plasmonic eigenvalues, Phys. Rev. B, 80:245405, 2009, (mit D. Grieser, S. Biehs, O. Huth, F. Rüting, and M. Holthaus) preprint
43.
An integral boundary layer equation for film flow over inclined wavy bottoms, Phys. of Fluids, 21, 092105, 2009. (mit T. Häcker) preprint
44.
A short ad hoc introduction to spectral methods for parabolic PDE and the Navier–Stokes equations, in Summer School Modern Computational Science, Oldenburg 2009, Universitätsverlag Oldenburg, 2009 preprint, software
45.
Coupled Mode Equations and Gap Solitons for the 2D Gross-Pitaevsky equation with a non-separable periodic potential, Physica D, 238: 860-879, 2009. (mit T. Dohnal) (updated version)
46.
Linear Resonance in viscous films on inclined planes. IJ Mutiphase Flow 34: 580–589, 2008. (mit A. Wierschem, V. Bontozoglou, C. Heining, und N. Aksel)
47.
A Hopf-bifurcation theorem for the vorticity formulation of the Navier-Stokes equations in ℝ3, Comm. PDE 33:5, 772–783, 2008. (mit A. Melcher and G. Schneider) preprint
48.
A remark about the justification of the nonlinear SchrÃdinger equation in quadratic spatially periodic media, ZAMP, 59:1-4, 2008 (mit C. Blank, M. Chirilus-Bruckner, C. Chong, V. Lescarret and G. Schneider) preprint
49.
Separation of internal and interaction dynamics for NLS-described wave packets with different carrier waves, Math. Anal. Appl. 347, 304Â314 (2008), (mit M. Chirilus-Bruckner, C. Chong, and G. Schneider) preprint
50.
Mass transport of alkali metal with pulses in a surface reaction, Phys. Rev. E, 78:055203(R), 2008, (mit M. Hinz, R. Imbihl, Y. Keverekidis und Q. Liang) preprint
51.
Long time persistence of KdV solitons as transient dynamics in a model of inclined film flow, Proc. Roy. Soc. Edinb., 137A: 133–146, 2007. (mit R.L. Pego and G. Schneider) preprint
52.
Exponential averaging and traveling waves in rapidly varying periodic media, Mathematische Nachrichten, 280:4, 408-422, 2007 (mit K. Matthies and G. Schneider) preprint
53.
Self–similar decay of localized perturbations of the Nusselt solution for the Navier–Stokes equations on an inclined plane, Arch.Rat.Mech.Anal. 184:3, 401–447, 2007 preprint
54.
The amplitude equations for the first instability of electro-convection in nematic liquid crystals in case of two unbounded space directions, Nonlinearity 20:1361-1386, 2007. (mit G. Schneider) preprint
55.
On the interaction of modulating pulses with different carrier waves, Mathematical Methods Applied Sciences, 30:15, 1965–1978, 2007. (mit M. Chirilus-Bruckner und G. Schneider) preprint
56.
The mathematics of light pulses in dispersive media, Jahresberichte der DMV, 109:3, 139-161, 2007 (mit G. Schneider) preprint
57.
A spatially periodic Kuramoto-Sivashinsky equation as a model problem for inclined film flow over wavy bottom. EJDE 118, 1-18, 2007, (mit A. Wierschem) preprint
58.
Simulation of the life cycle of adsorbate islands on the Pt(100) surface during the NO+NH3 reaction. Chem. Phys. Letters, 421:4–6, 577–583. 2006. (mit M. Rafti, J. L. Vicente and R. Imbihl) preprint
59.
Justification of the Nonlinear Schrödinger equation in spatially periodic media, ZAMP, 57:6, 905–939, 2006 (mit K. Busch, G. Schneider and L. Tkeshelashvili) preprint

2001-2005

60.
Pattern formation for NO+NH3 on Pt(100) – 2-dimensional numerical results, Phys. Rev.E, 71, 016207, 2005. preprint
61.
Standing waves, clustering, and phase waves in 1d-simulations of kinetic relaxation oscillations in NO+NH3 on Pt(100) coupled by diffusion. Physica D 190:249–265, 2004. preprint
62.
Stable transport of information near essentially unstable localized structures. Discrete Contin.Dyn.Syst.B 4:2, 349–390, 2004. (mit Th. Gallay und G. Schneider) preprint
63.
Relaxed plasma vacuum states in cylinders. Q.J. Mech. Appl. Math., 57:1, 1–17, 2004. (mit R. Kaiser) preprint
64.
Self–similar decay of localized perturbations in the Integral Boundary Layer equation. Journal Diff. Eq., 207:2, 407–422, 2004.preprint
65.
Validity of the Ginzburg-Landau approximation in pattern forming systems with time periodic forcing. Dynamics and Bifurcations of Patterns in Dissipative Systems, World Scientific, 39–57, 2004. (mit N. Breindl und G. Schneider) preprint
66.
Existence and stability of modulating pulse solutions in Maxwell’s equations describing nonlinear optics. ZAMP 54, 677-712, 2003. (mit G. Schneider) preprint
67.
Approximation of the Integral Boundary Layer equation by the Kuramoto–Sivashinsky equation. SIAM J. Appl. Math. 63:4, 1359–1377, 2003. preprint
68.
Almost global existence and transient self similar decay for Poiseuille flow at criticality over exponentially long times. Physica D 185:3–4, 209–226, 2003. (mit G. Schneider) preprint
69.
Adiabatic reduction and hysteresis of the LFI–model of NO+NH3 on Pt(100). Chem. Phys. Let., 382, 232–244, 2003. (mit R. Imbihl, M. Rafti, I.M. Iruzun, J.L. Vicente und E.E. Mola) preprint
70.
Stability and diffusive dynamics on unbounded domains. In Ergodic Theory, Analysis and Efficient Simulation of Dynamical Systems, ed. B. Fiedler, Springer, 563-584, 2001. (mit A. Mielke und G. Schneider)preprint
71.
Nonlinear coupled mode dynamics in hyperbolic and parabolic periodically structured spatially extended systems. Asymptot. Anal. 28:2, 163-180, 2001. (mit G. Schneider) preprint
72.
Stable modulating multi-pulse solutions for dissipative systems with resonant spatially periodic forcing. J. Nonlin. Sci.,11:2, 89-121, 2001. preprint
73.
Diffusive stability of rolls in the two-dimensional real and complex Swift–Hohenberg equation. Comm. PDE 24:11&12, 2109-2146, 1999.preprint

Tagungsbeiträge

74.
pde2path – V2 : multi-parameter continuation and periodic domains, 2014, in H. Ecker, A. Steindl, S. Jakubek, eds, ENOC 2014 - Proceedings of 8th European Nonlinear Dynamics Conference, ISBN: 978-3-200-03433-4. (mit T. Dohnal, J. Rademacher und D. Wetzel), preprint, pde2path homepage
75.
Modeling of film flows over inclined wavy bottoms, PAMM 8:10721-10722, 2009 (mit T. Häcker)
76.
Resonance in viscous film flow over topography PAMM 7:4100025–4100026, 2008 (mit C. Heining, A. Wierschem, V. Bontozoglou und N. Aksel)
77.
Mathematical theory for the Ginzburg-Landau approximation in pattern forming systems with time-periodic forcing – with applications to electro-convection in nematic liquid crystals. Proceedings of Equa∂iff–11: 507–517, 2005. (mit N. Breindl and G. Schneider) preprint
78.
Local in time nonlinear stability of pulses in an unstable medium. XIVth International Congress on Mathematical Physics, Lisboa 2003, 296–303, World Scientific, 2005. (mit R.L. Pego und G. Schneider)
79.
Rolls and modulating pulses in Swift–Hohenberg type of equations, in International Conference on Differential Equations, Equadiff 99, World Scientific, 408-413, 2000.

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