Institut für Angewandte Mathematik

Institut für Angewandte Mathematik (Math D)
Priv.-Doz. Andrii Khrabustovskyi

Postal Address	Technische Universität Graz Institut für Angewandte Mathematik Steyrergasse 30 8010 Graz Austria
Phone	+43 (316) 873 - 8629
Telefax	+43-(0)316-873 8621
Room	ST 03 156
Electronic Mail	khrabustovskyi@math.tugraz.at
Office hour	by arrangement
TUGRAZonline	link

News
September 8-13 2019: I am invited to The Sixth Najman Conference on Spectral Theory and Differential Equations, Sveti Martin na Muri, Croatia August 25-30, 2019: I am invited to be a plenary speaker on WAVES 2019, TU Vienna July 22-26, 2019: Together with Carsten Trunk and Olaf Post we organize a special session "Spectral Theory and Differential Operators" on IWOTA 2019 at University of Lisbon, Portugal. February 25 - March 1, 2019: Together with Jussi Behrndt we organized the conference "Differential operators on graphs and waveguides"
Teaching in TU Graz
Summer semester 2019, TU Graz: Partial differential equations and boundary value problems (lectures, exercise classes, description) Winter semester 2018/2019, TU Graz: Advanced functional analysis (lectures, exercise classes, description) Summer semester 2018, TU Graz: Elective subjects mathematics (Asymptotic Analysis) (lectures)
Topics of Interest
Asymptotic analysis and homogenization of PDEs Spectral theory Periodic PDEs Quantum graphs, waveguides Schrödinger operators Metamaterials
Curriculum vitae
CV in PDF format: click here
Publications
Preprints
Construction of self-adjoint differential operators with prescribed spectral properties Jussi Behrndt, Andrii Khrabustovskyi arXiv:1911.04781 [math.SP] preprint Towards more general constitutive relations for metamaterials: A checklist for consistent formulations Fatima Z. Goffi, Karim Mnasri, Michael Plum, Carsten Rockstuhl, Andrii Khrabustovskyi CRC 1173 Preprint 2019/24, Karlsruhe Institute of Technology, December 2019 preprint
Refereed publications
The inverse problem of two-state quantum systems with non-adiabatic static linear coupling Andrii Khrabustovskyi, Imen Rassas, Eric Soccorsi Communications in Contemporary Mathematics (2020), doi: 10.1142/S0219199720500029 preprint, article δ′-interaction as a limit of a thin Neumann waveguide with transversal window, Giuseppe Cardone, Andrii Khrabustovskyi Journal of Mathematical Analysis and Applications 473(2) (2019), 1320-1342 preprint, article Retrieving effective material parameters of metamaterials characterized by nonlocal constitutive relations Karim Mnasri, Andrii Khrabustovskyi, Michael Plum, Carsten Rockstuhl Physical Review B 99 (3) (2019), 035442 preprint, article Spectral estimates for Dirichlet Laplacian on tubes with exploding twisting velocity Diana Barseghyan, Andrii Khrabustovskyi Operators and Matrices 13 (1) (2019), 311-322 preprint, article Operator estimates for the crushed ice problem Andrii Khrabustovskyi, Olaf Post Asymptotic Analysis 110(3-4) (2018),137-161 preprint, article Gap control by singular Schrödinger operators in a periodically structured metamaterial Pavel Exner, Andrii Khrabustovskyi Journal of Mathematical Physics, Analysis, Geometry 14(3) (2018), 270-285 preprint, article Surface Plasmon Polaritons Sustained at the Interface of a Nonlocal Metamaterial Joshua Feis, Karim Mnasri, Andrii Khrabustovskyi, Christian Stohrer, Michael Plum, Carsten Rockstuhl Physical Review B 98 (11) (2018), 115409 preprint, article Beyond local effective material properties for metamaterials Karim Mnasri, Andrii Khrabustovskyi, Christian Stohrer, Michael Plum, Carsten Rockstuhl Physical Review B, 97 (2018), 075439 preprint. part 1, preprint. part 2, article Spectrum of a singularly perturbed periodic thin waveguide Giuseppe Cardone, Andrii Khrabustovskyi Journal of Mathematical Analysis and Applications 454(2) (2017), 673-694 preprint, article Example of a periodic Neumann waveguide with a gap in its spectrum Giuseppe Cardone, Andrii Khrabustovskyi In: J. Dittrich, H. Kovarik, A. Laptev (Eds.), Functional Analysis and Operator Theory for Quantum Physics. The Pavel Exner Anniversary Volume, Europ. Math. Soc. Publ. House, 2017, pp.177-187 preprint, article Spectral properties of elliptic operator with double-contrast coefficients near a hyperplane Andrii Khrabustovskyi, Michael Plum Asymptotic Analysis, 98 (1-2) (2016), 91-130. preprint, article Spectral analysis of a class of Schrödinger operators exhibiting a parameter-dependent spectral transition Diana Barseghyan, Pavel Exner, Andrii Khrabustovskyi, Milos Tater Journal of Physics A: Mathematical and Theoretical, 49 (16) (2016), 165302 preprint, article On the spectrum of narrow Neumann waveguide with periodically distributed δ′ traps Pavel Exner, Andrii Khrabustovskyi Journal of Physics A: Mathematical and Theoretical, 48 (31) (2015), 315301 preprint, article Neumann spectral problem in a domain with very corrugated boundary Giuseppe Cardone, Andrii Khrabustovskyi Journal of Differential Equations, 259(6) (2015), 2333-2367 preprint, article Gaps in the spectrum of a periodic quantum graph with periodically distributed δ′-type interactions Diana Barseghyan, Andrii Khrabustovskyi Journal of Physics A: Mathematical and Theoretical, 48(25) (2015), 255201 preprint, article Opening up and control of spectral gaps of the Laplacian in periodic domains Andrii Khrabustovskyi Journal of Mathematical Physics, 55(12) (2014), 121502 preprint, article Gaps in the spectrum of the Neumann Laplacian generated by a system of periodically distributed traps Andrii Khrabustovskyi, Evgeni Khruslov Mathematical Methods in the Applied Sciences, 38(1) (2015), 11-26 preprint, article Homogenization of spectral problem on Riemannian manifold consisting of two domains connected by many tubes Andrii Khrabustovskyi Proceedings of the Royal Society of Edinburgh, Section: A Mathematics, 143(6) (2013), 1255-1289 preprint, article Periodic elliptic operators with asymptotically preassigned spectrum Andrii Khrabustovskyi Asymptotic Analysis, 82(1-2) (2013), 1-37 preprint, article Periodic Riemannian manifold with preassigned gaps in spectrum of Laplace-Beltrami operator Andrii Khrabustovskyi Journal of Differential Equations, 252(3) (2012), 2339–2369 preprint, article Homogenization of eigenvalue problem for Laplace-Beltrami operator on Riemannian manifold with complicated "bubble-like" microstructure Mathematical Methods in the Applied Sciences, 32(16) (2009), 2123–2137 article On spectrum of Riemannian manifolds with attached thin handles Andrii Khrabustovskyi Journal of Mathematical Physics, Analysis, Geometry, 5(2) (2009), 145-169 article (free access) Asymptotic behaviour of spectrum of Laplace-Beltrami operator on Riemannian manifolds with complex microstructure Andrii Khrabustovskyi Applicable Analysis, 87(12) (2008), 1357-1372 article Positivity and time behavior of a linear reaction-diffusion system, non-local in space and time Andrii Khrabustovskyi, Holger Stephan Mathematical Methods in the Applied Sciences, 31(15) (2008), 1809-1834 preprint, article Klein-Gordon equation as a result of wave equation averaging on the Riemannian manifold of complex microstructure Andrii Khrabustovskyi Journal of Mathematical Physics, Analysis, Geometry, 3 (2) (2007), 213-233 article (free access)
Conference proceedings
Asymptotically predefined spectral gaps for the Neumann Laplacian in periodic domain Andrii Khrabustovskyi Mathematical Results in Quantum Mechanics: Proceedings of the QMath12 Conference, World Scientific, 2014 article