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My academic research is in the field of partial differential equations, and is divided into two topics:
  • Fokker-Planck equations with nonlocal perturbations: Equations of this type arise in the kinetic formulation of quantum mechanical systems (e.g., the Wigner-Fokker-Planck equation). The Fokker-Planck operator is linear, and the perturbation is the convolution with a massless distribution, satisfying weak regularity assumptions. I did a complete spectral analysis of the perturbed operator in weighted Lebesgue spaces, and gave a detailed analysis of the generated semigroup of operators. The main result is that there exists a unique normalized steady state, and every other solution converges with an explicitly known exponential rate towards this steady state.
  • Nonlinear control of an Euler-Bernoulli beam: The systems considered here describe nonlinear feedback control in order to stabilize vibrations of eleastic beams. Applications comprise robotic and hydraulic arms, antennae, and high-rise buildings. Asymtotic stability of these systems has been shown by my coauthors and me by using tools of nonlinear functional analysis, confirming the functionality of the controller.

    Fig.: An elastic beam with a damper and a spring (from [4]).
Publications:

  1. D. Stürzer, A. Arnold, A. Kugi. Stability of a Closed-Loop Control System – Applied to a Gantry Crane with Heavy Chains. Proceedings of the Junior Scientist Conference, (2010).
  2. D. Stürzer, A. Arnold. Spectral analysis and long-time behaviour of a Fokker-Planck equation with a nonlocal perturbation. Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 25, 1 (2014), 53–89.
  3. F. Achleitner, A. Arnold, D. Stürzer. Large-time behavior in nonsymmetric Fokker-Planck equations. Rivista di Matematica della Università di Parma 6, 1 (2015).
  4. M. Miletic, D. Stürzer, A. Arnold. An Euler-Bernoulli beam with nonlinear damping and a nonlinear spring at the tip. Discrete and Continuous Dynamical System - B 20, 9 (2015).
  5. M. Miletic, D. Stürzer, A. Arnold, A. Kugi. Stability of an Euler-Bernoulli beam with a nonlinear dynamic feedback system. IEEE Transactions on Automatic Control  61, 10 (2016).
  6. D. Stürzer, A. Arnold, and A. Kugi.  Closed-loop stability analysis of a gantry crane with heavy chain. To appear in International Journal of Control (2017).