Hannes Uecker, Research

My research centers around the analysis of nonlinear PDE over unbounded domains. Another focus are Mathematical Modeling and numerical simulation. For an overview, my research can be arranged into 4 overlapping areas:

  1. Fluid flow, in particular film flow with a free boundary over inclined planes [38, 39, 35, 22, 24, 17, 28, 18, 14]
  2. Nonlinear Optics and related systems (NLS related problems) [42, 37, 30, 27, 26, 20, 16, 9]
  3. Dynamics of pattern formation ((dissipative) problems in which the Ginzburg–Landau equation and variants play important roles) [44, 41, 43, 33, 36, 23, 1, 47]
  4. Miscellaneous PDE systems from physics, chemistry and biology, e.g., Reaction–diffusion systems from surface catalysis, and plasmonic nano–particles, [40, 32, 34, 31, 21, 12, 13, 11]

From the analytic point of view the focus are existence and stability problems and approximation by amplitude or modulation equations. Concerning stability the main issue are continuous spectra up to the imaginary axis, which for parabolic problems yields at most diffusive stability, characterized by polynomial decay rates of spatially algebraically localized perturbations. The amplitude equations are important for model reduction and unification. A recent development is the consideration of problems which are not translationally invariant, e.g., spatially periodic problems or slowly varying coefficients.

Publications 12. August 2011

Hint: the linked preprints may differ slightly from the published versions.

PICPreprints

  1. Diffusive stability and diffusive mixing of periodic wave trains in reaction diffusion systems. Preprint, 2011. (mit B. Sandstede, A. Scheel and G. Schneider) preprint
  2. Traveling Interface Modulations in a catalytic NH_3+O_2 reaction on the Rh(110) surface. Preprint 2011. (mit M. Rafti, F. Lovis, V. Krupennikova and R. Imbihl) preprint
  3. Self-similar decay to the marginally stable ground state in a model for film flow over inclined wavy bottoms, Preprint, 2010, (mit T. Häcker und G. Schneider), preprint
  4. Approximating the dynamics of active cells in a diffusive medium by ODEs Homogenization with Localization, Preprint, 2011, (mit J. Müller) preprint

    Peer revieved Journals and Book chapters

  5. Corrigendum to 12, Proc. Royal Soc. Edinburgh, 141A, 819-824, 2011 (mit R. Kaiser), preprint
  6. 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,
  7. 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
  8. Erratum to (published version of) 16, Physica D, 240, 357-362, 2011 (mit T. Dohnal)preprint
  9. 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

  10. Amplitude equations – an invitation to multiple scale analysis Summer School Modern Computational Science, Oldenburg 2010, Universitätsverlag Oldenburg, 2010, preprint,
  11. Statistics for surface modes of nanoparticles with shape fluctuations, Commun. in Comp. Physics, 8, 1224, 2010, (mit F. Rüting)
  12. 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
  13. Perturbation theory for plasmonic eigenvalues, Phys. Rev. B, 80:245405, 2009, (mit D. Grieser, S. Biehs, O. Huth, F. Rüting, and M. Holthaus) preprint
  14. An integral boundary layer equation for film flow over inclined wavy bottoms, Phys. of Fluids, 21, 092105, 2009. (mit T. Häcker) preprint
  15. 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
  16. 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)
  17. 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)
  18. 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
  19. A remark about the justification of the nonlinear Schrödinger 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
  20. Separation of internal and interaction dynamics for NLS-described wave packets with different carrier waves, Math. Anal. Appl. 347, 304314 (2008), (mit M. Chirilus-Bruckner, C. Chong, and G. Schneider) preprint
  21. 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
  22. 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
  23. Exponential averaging and traveling waves in rapidly varying periodic media, Mathematische Nachrichten, 280:4, 408-422, 2007 (mit K. Matthies and G. Schneider) preprint
  24. 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
  25. 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
  26. 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
  27. The mathematics of light pulses in dispersive media, Jahresberichte der DMV, 109:3, 139-161, 2007 (mit G. Schneider) preprint
  28. 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
  29. 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
  30. 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

  31. Pattern formation for NO+NH3 on Pt(100) – 2-dimensional numerical results, Phys. Rev.E, 71, 016207, 2005. preprint
  32. 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
  33. 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
  34. Relaxed plasma vacuum states in cylinders. Q.J. Mech. Appl. Math., 57:1, 1–17, 2004. (mit R. Kaiser) preprint
  35. Self–similar decay of localized perturbations in the Integral Boundary Layer equation. Journal Diff. Eq., 207:2, 407–422, 2004.preprint
  36. 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
  37. Existence and stability of modulating pulse solutions in Maxwell’s equations describing nonlinear optics. ZAMP 54, 677-712, 2003. (mit G. Schneider) preprint
  38. Approximation of the Integral Boundary Layer equation by the Kuramoto–Sivashinsky equation. SIAM J. Appl. Math. 63:4, 1359–1377, 2003. preprint
  39. 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
  40. 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
  41. 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
  42. Nonlinear coupled mode dynamics in hyperbolic and parabolic periodically structured spatially extended systems. Asymptot. Anal. 28:2, 163-180, 2001. (mit G. Schneider) preprint
  43. Stable modulating multi-pulse solutions for dissipative systems with resonant spatially periodic forcing. J. Nonlin. Sci.,11:2, 89-121, 2001. preprint
  44. Diffusive stability of rolls in the two-dimensional real and complex Swift–Hohenberg equation. Comm. PDE 24:11&12, 2109-2146, 1999.preprint

    Proceedings

  45. Modeling of film flows over inclined wavy bottoms, PAMM 8:10721-10722, 2009 (mit T. Häcker)
  46. Resonance in viscous film flow over topography PAMM 7:4100025–4100026, 2008 (mit C. Heining, A. Wierschem, V. Bontozoglou und N. Aksel)
  47. 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
  48. 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)
  49. Rolls and modulating pulses in Swift–Hohenberg type of equations, in International Conference on Differential Equations, Equadiff 99, World Scientific, 408-413, 2000.

Thesen

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