[Past member] Postdoctoral Researcher (2022 – 2024)
Grant support researchers from Ukraine, Alexander von Humboldt Foundation
maria.filipkovska@fau.de
Room 03.334 | Friedrich-Alexander-Universität Erlangen-Nürnberg. FAU DCN-AvH Chair for Dynamics, Control, Machine Learning and Numerics – Alexander von Humboldt Professorship.
+49 9131 85-67143
I am a postdoctoral researcher at the Chair for Dynamics, Control and Numerics – Alexander von Humboldt Professorship. My research proposal is financed by a special grant to support researchers from Ukraine made available within the framework of the Alexander von Humboldt Professorship of Prof. Enrique Zuazua, that was bestowed by the Alexander von Humboldt Foundation and is funded by the German Federal Ministry of Education and Research.
Before, I collaborated as a visiting scientist supported by the Scholarship of the Collaborative Research Center TRR154, at the SFB TRR154 Transregio project: Mathematical modelling, simulation and optimization using the example of gas networks (May-June 2022) at FAU DCN-AvH.
I studied at the V.N. Karazin Kharkiv National University (Kharkiv, Ukraine) and got my Master degree (M.Sc. in Applied Mathematics) in 2012 and my Doctoral degree (PhD. in Physical and Mathematical Sciences) in 2016.
The areas of my research (research experience):
1. Differential-algebraic equations (DAEs are also called degenerate differential equations, descriptor systems and operator-differential equations): the theory, numerical methods and applications;
2. Nonlinear integrable PDEs (in particular, the Maxwell-Bloch equations) and the associated matrix Riemann-Hilbert problems: the theory and applications.
Generally, my research interests include mathematics and its applications in the natural sciences and engineering.
PhD Thesis: Global solvability of differential-algebraic equations and mathematical modelling of the dynamics of nonlinear radio engineering circuits (February 2016)
Events
• December 1, 2023. Lagrange and Lyapunov stability of degenerate differential equations. Julius-Maximilians-Universität Würzburg (Germany)
• September 4-9, 2023. Qualitative analysis of nonregular differential-algebraic equations and applications in the gas dynamics. XIII International Conference of the Georgian Mathematical Union, GMU2023. Batumi (Georgia)
• August 2022. Analysis off gas networks using mathematical models in the form of differential algebraic equations. IX Partial differential equations, optimal design and numerics. Benasque (Spain).
Publications
2024
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Cognitive Component of Development of the Innovative Diffusion of the Socio-Economic Systems
Conference on Integrated Computer Technologies in Mechanical Engineering – Synergetic Engineering, ICTM 2023 (Kharkiv, December 27, 2023 - December 29, 2023)
In: Mykola Nechyporuk, Volodymir Pavlikov, Dmytro Krytskyi (ed.): Integrated Computer Technologies in Mechanical Engineering - 2023. Synergetic Engineering, Volume 2, Cham: 2024
DOI: 10.1007/978-3-031-60549-9_2
BibTeX: Download - :
Combined numerical methods for solving time-varying semilinear differential-algebraic equations with the use of spectral projectors and recalculation
(2024)
DOI: 10.48550/arXiv.2212.00012
BibTeX: Download - :
Criterion of the global solvability of regular and singular differential-algebraic equations
In: Journal of Mathematical Sciences (2024)
ISSN: 1072-3374
DOI: 10.1007/s10958-024-07152-7
BibTeX: Download
2023
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Initial-boundary value problem for the Maxwell-Bloch equations with an arbitrary inhomogeneous broadening and periodic boundary function
In: Symmetry Integrability and Geometry-Methods and Applications 19 (2023), p. 1-39
ISSN: 1815-0659
DOI: 10.3842/SIGMA.2023.096
BibTeX: Download - :
Qualitative analysis of nonregular differential-algebraic equations and the dynamics of gas networks
In: Journal of Mathematical Physics Analysis Geometry 19 (2023), p. 719-765
ISSN: 1812-9471
DOI: 10.15407/mag19.04.719
BibTeX: Download
