Institut für Angewandte Mathematik (Math D)
Dr. 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
RoomST 03 156
Electronic Mail khrabustovskyi@math.tugraz.at
Office hour by arrangement

Teaching

Summer semester 2018: Elective subjects mathematics (Asymptotic Analysis)

Topics of Interest
  • Asymptotic analysis and homogenization of PDEs
  • Spectral theory
  • Periodic PDEs
  • Quantum graphs, waveguides
  • Schrödinger operators
  • Metamaterials
Curriculum Vitae

PDF

Publications
Submitted papers
  1. δ′-interaction as a limit of a thin Neumann waveguide with transversal window,
    Giuseppe Cardone, Andrii Khrabustovskyi
    arXiv:1808.05402 [math.SP]
    preprint
  2. Surface Plasmon Polaritons Sustained at the Interface of a Nonlocal Metamaterial
    Joshua Feis, Karim Mnasri, Andrii Khrabustovskyi, Christian Stohrer, Michael Plum, Carsten Rockstuhl
    arXiv:1804.06054 [physics.optics]
    preprint
Refereed publications
  1. Spectral estimates for Dirichlet Laplacian on tubes with exploding twisting velocity
    Diana Barseghyan, Andrii Khrabustovskyi
    Operators and Matrices (2018), accepted
    preprint
  2. Gap control by singular Schrödinger operators in a periodically structured metamaterial
    Pavel Exner, Andrii Khrabustovskyi
    Journal of Mathematical Physics, Analysis, Geometry (2018), accepted
    preprint
  3. Operator estimates for the crushed ice problem
    Andrii Khrabustovskyi, Olaf Post
    Asymptotic Analysis (2018), accepted
    preprint
  4. 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
  5. 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
  6. 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
  7. 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
  8. 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
  9. 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
  10. 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
  11. 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
  12. 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
  13. 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
  14. 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
  15. Periodic elliptic operators with asymptotically preassigned spectrum
    Andrii Khrabustovskyi
    Asymptotic Analysis, 82(1-2) (2013), 1-37
    preprint, article
  16. 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
  17. 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
  18. 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)
  19. Asymptotic behaviour of spectrum of Laplace-Beltrami operator on Riemannian manifolds with complex microstructure
    Andrii Khrabustovskyi
    Applicable Analysis, 87(12) (2008), 1357-1372
    article
  20. 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
  21. 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
  1. 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