Prof. Dr. Katerina Nik

I am currently an Assistant Professor of Applied Mathematics and Computational Sciences (AMCS) in the Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division at KAUST. Prior to joining KAUST, I worked as a postdoctoral researcher at the Delft Institute of Applied Mathematics, TU Delft, and as a postdoctoral researcher at the Faculty of Mathematics, University of Vienna, Austria.

My research interests concern the modeling and analysis of partial differential equations. I am particularly interested in:

  • Nonlinear evolution equations and operator semigroups
  • Free boundary problems
  • Calculus of variations
  • Geometric measure theory
  • Well-posedness and qualitative properties of solutions
  • Nonlinear dispersive waves
  • Thin fluid film equations
  • Microelectromechanical systems (MEMS)
  • Biological growth processes, such as volumetric and surface growth
  • Brakke’s mean curvature flow.
CV

Publications

  • Jansen, J., Lienstromberg, C., Nik, K. Long-time behaviour and stability for quasilinear doubly degenerate parabolic equations of higher order.
    (2022) (under review)
  • Ehrnström, M., Nik, K., Walker, Ch. A direct construction of a full family of Whitham solitary waves
    (2022) (under review).
  • Davoli, E., Nik, K., Stefanelli, U. Existence results for a morphoelastic model. 
    (2022), to appear in ZAMM.
  • Laurençot, Ph., Nik, K., Walker, Ch. Energy Minimizers for an Asymptotic MEMS Model with Heterogeneous Dielectric Properties.
    Calc. Var. 61 (2022), no.1, 2–51.
  • Laurençot, Ph., Nik, K., Walker, Ch. Reinforced Limit of a MEMS Model with Heterogeneous Dielectric Properties.
    Appl. Math. Optim. (2021), no. 2, 1373–1393.
  • Nik, K. On a free boundary model for three-dimensional MEMS with a hinged top plate: Stationary case.
    Port. Math. 78 (2021), no.2, 211–232.
  • Laurençot, Ph., Nik, K., Walker, Ch. Convergence of Energy Minimizers of a MEMS Model in the Reinforced Limit.
    Acta Appl. Math. 173 (2021), no. 9, 1–23.
  • Nik, K. On a free boundary model for three-dimensional MEMS with a hinged top plate: Parabolic case.
    Commun. Pure Appl. Anal. 20 (2021), no. 10, 3395–3417.
  • Sweers, G., Vassi (maiden name) K. Positivity for a hinged plate with stress.
    SIAM J. Math. Anal. 50 (2018), no.1, 1163-1174

Teaching

University of Vienna

  • SS22 Introduction to mathematical methodology, Exercise class
  • WS21 PDEs, Exercise class
  • SS21 ODEs, Exercise class
  • SS21 Functional Analysis, Exercise class

University of Hanover

  • WS20 Mathematics for Special Pedagogues I, Lecture course
  • SS17 PDEs, Exercise class
  • WS19 Quantitative Theory of ODEs, Exercise class
  • WS16 Functional Analysis, Exercise class.
  • WS16 – WS19 Mathematics I for Life & Earth Sciences, Exercise class
  • WS16 Function Theory, Seminar
  • SS18 – SS19 Mathematics II for Life & Earth Sciences, Exercise class
  • WS14 & SS16 Numerical Methods for PDEs II, Exercise class
  • SS19 Function Theory, Exercise class
  • WS14 & WS15 Numerical Methods for PDEs I, Exercise class
  • SS18 Mathematics I for Physicists, Exercise class
  • WS15 Numerical Mathematics I, Exercise class
  • WS17 Semigroups and Evolution Equations, Exercise class
  • WS14 Multigrid & Domain Decomposition Methods, Exercise class

Contacts

Faculty of Mathematics, University of Vienna
Oskar-Morgenstern-Platz 1, 1090 Vienna
Office 9.11