Alim Sukhtayev, Assistant Professor

Department of Mathematics
Miami University

Email: sukhtaa@miamioh.edu
Office: 226 BAC
Phone: (513) 529-2189


Teaching 

I am a member of the organizing committee of the Forty-Seventh Annual Conference: Differential Equations and Dynamical Systems and their Applications  to be held at Miami University, September 20-21, 2019.

The conference is partially supported by the U.S. National Science Foundation (DMS-1919555) and by the Department of Mathematics of Miami University through Buckingham and Bohn Scholarships.

Research Interests 

My research is partially supported by the U.S. National Science Foundation (DMS-1910820).

 

Curriculum Vitae


Publications

  1. Exponential dichotomies for elliptic PDE on radial domains, submitted (with M. Beck, G. Cox, C. Jones, Y. Latushkin) arXiv:1907.10372

  2. A dynamical approach to semilinear elliptic equations, submitted (with M. Beck, G. Cox, C. Jones, Y. Latushkin) arXiv:1907.09986

  3. A Sturm-Liouville theorem for quadratic operator pencils, to appear in Journal of Differential Equations (with K. Zumbrun) arXiv:1907.05679

  4. The Maslov and Morse Indices for Sturm-Liouville Systems on the Half-Line, to appear in Discr. Cont. Dynam. Systems Ser. A (with P. Howard) arXiv:1903.07583

  5. Spectral stability of hydraulic shock profiles, to appear in Physica D: Nonlinear Phenomena (with Z. Yang, K. Zumbrun) arXiv:1810.01490

  6. Renormalized oscillation theory for linear Hamiltonian systems on [0,1] via the Maslov index, submitted (with P. Howard) arXiv:1808.08264

  7. Instability of pulses in gradient reaction--diffusion systems: A symplectic approach, Philosophical Transactions of the Royal Society A 376 (2018), no. 2117
    (with M. Beck, G. Cox, C. Jones, Y. Latushkin, K. McQuighan) arXiv:1705.03861

  8. Diffusive stability of spatially periodic patterns with a conservation law, submitted arXiv:1610.05395

  9. Diffusive stability of spatially periodic solutions of the Brusselator model, Communications in Mathematical Physics 358 (2018), no. 1, 1-43 (with K. Zumbrun, S. Jung, R. Venkatraman) arXiv:1608.08476

  10. The Maslov and Morse indices for Schr\"odinger operators on $\mathbb{R}$, Indiana University Mathematics Journal 67 (2018), no. 5, 1765-1815 (with P. Howard, Y. Latushkin) arXiv:1608.05692

  11. The Morse and Maslov Indices for Schr\"odinger Operators, Journal d'Analyse Mathematique 135 (2018), no. 1, 345-387 (with Y. Latushkin, S. Sukhtaiev) arXiv:1411.1656

  12. The Maslov and Morse indices for Lagrangian pairs on $\mathbb{R}^{2n}$, J. Math. Anal. Appl. 451 (2017), no. 2, 794-821 (with P. Howard, Y. Latushkin) arXiv:1608.00632

  13. Hadamard-type formulas via the Maslov form, J. Evol. Equ. 17 (2017), no. 1, 443-472 (with Y. Latushkin) arXiv:1601.07509

  14. The Maslov and Morse indices for Schr\"odinger Operators on $[0,1]$, Journal of Differential Equations 260 (2016), no. 5, 4499-4549 (with P. Howard) arXiv:1603.02648

  15. The Morse and Maslov indices for multidimensional Schr\"odinger operators with matrix-valued potentials, Trans. Amer. Math. Soc. 368 (2016), no. 11, 8145-8207
    (with G. Cox, C. Jones, Y. Latushkin) arXiv:1408.1103

  16. Vakhitov-Kolokolov and energy vanishing conditions for linear instability of solitary waves in models of classical self-interacting spinor fields, Nonlinearity 28 (2015), 577--592
    (with G. Berkolaiko, A. Comech) arXiv:1306.5150

  17. The Evans function and the Weyl-Titchmarsh function, in Special issue on stability of travelling waves, Disc. Cont. Dynam. Syst. Ser. S 5 (2012), no. 5, 939 - 970 (with Y. Latushkin)

  18. The algebraic multiplicity of eigenvalues and the Evans function revisited, in Memorial M. Birman's volume, Mat. Model. Nat. Phenom., 5 (2010) 269 - 292 (with Y. Latushkin)

  19. Spectral decomposition of normal operators in Hilbert quaternion bimodules, Scientific Notes of Taurida National University, 19(58) (2006), no. 1, 3-20 (with I. Karpenko, D. Tyshkevich)

  20. On an approach to differentiation of functions of a quaternion variable, Scientific Notes of Taurida National University}, 17(56) (2004), no. 1, 30-37 (with I. Karpenko, D. Tyshkevich)

  21. Thesis: "The Evans function, the Weyl-Titchmarsh function, and the Birman-Schwinger operators", July 2012

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