Anna R. Ghazaryan

Research Interests:

Applied Dynamical Systems
Nonlinear PDEs:
  •  Traveling waves
  •  Nonlinear stability of traveling waves
  •  Singularly perturbed systems.

NCSU 2007. From left: John Franke, Vahagn Manukian, David Long, Ming Jiang, Dmitry Zenkov, and G.


Past and Current Research Funding:

Publications

  1. H. Cai, A. Ghazaryan, V. Manukian. Fisher-KPP dynamics in diffusive Rosenzweig-MacArthur and Holling-Tanner models. Math.Model. Nat. Phenom. 14:4 (2019). Special issue: Singular perturbations and multiscale systems.
  2. A. Ghazaryan, Y. Latushkin, X. Yang. Stability of a planar front in a multidimensional reaction-diffusion system. SIAM J. on Math. Analysis 50:5 (2018) 5569-5615. PDF.
  3. A. Ghazaryan, Y. Latushkin, A. Pogan. Spectrum of non-planar traveling waves. Integral Equations Operator Theory 90:3 (2018) 20pp. https://doi.org/10.1007/s00020-018-2447-5. Preprint. 
  4. A. Ghazaryan, S. Lafortune, V. Manukian. Stability of nonlinear waves and patterns and related topics. Philos Trans A Math Phys Eng Sci. 2018 Apr 13; 376 (2117). pii: 20180001. doi: 10.1098/rsta.2018.0001.
  5. A. Ghazaryan, S. Lafortune, P. McLarnan. Combustion waves in hydraulically resistant porous media  in a special parameter regime. Physica D: Nonlinear Phenomena, 332 (1), 2016, 23-33. Preprint.
  6. A. Ghazaryan, S. Lafortune, V. Manukian. Stability of front solutions in a model for a surfactant driven flow. Physica D: Nonlinear Phenomena.  307 (1),  2015,  1-13. Preprint.
  7. A. Ghazaryan, S. Lafortune, P. McLarnan. Stability analysis for fronts traveling in combustion in hydraulically resistant porous media.  SAIM J. on Applied Mathematics. 75 (3), 2015, 1225-1244. Preprint.
  8. A. Ghazaryan, V. Manukian, S. Schecter. Traveling waves in Holling-Tanner model with diffusion. Proceedings of the Royal Society of London A.  Preprint. http://rspa.royalsocietypublishing.org/content/471/2177/20150045.

  9. A. Ghazaryan, V. Manukian. Coherent structures in a model for mussel-algae Interaction.  SIAM J. of Dynamical Systems. 14 (2), 2015,  893-913. Preprint

  10. A. Ghazaryan, Y. Latushkin, S. Schecter. Stability of traveling waves in partly parabolic systems. Mathematical Modelling of Natural Phenomena,  Cambridge University Press. 8 (2013),  31-47. PDF.
  11. A. Ghazaryan,  S. Schecter, P.  Simon. Gasless combustion fronts with heat loss.  SIAM J. of Applied Mathematics73 (2013), No 3, 1303-1326.  PDF.
  12. A. Ghazaryan, J. Humpherys, J. Lytle. Spectral behavior of combustion fronts with high exothermicity. SIAM J. of Applied Mathematics. 73 (2013), No. 1, 422-437PDF.
  13. A. Ghazaryan, C. Jones. On the existence of high Lewis number combustion fronts. J. of Mathematics and Computers in Simulation: "On Nonlinear Waves: Computation and Theory,"   82  (2012)  1133-1141.  PDF.
  14. A. Ghazaryan, Y. Latushkin, S. Schecter. Stability of traveling waves for degenerate systems of reaction-diffusion equations. Indiana Univ. Math. J. 60 (2011) 443-472. PDF.
  15. A. Ghazaryan, Y. Latushkin, S. Schecter. Stability of traveling waves for a class of reaction-diffusion systems that arise in chemical reaction models.  SIAM J. Math. Anal.  Volume 42, Issue 6, (2010)  2434-2472. PDF.
  16. A. Ghazaryan, Y. Latushkin, S. Schecter, A. J. De Souza. Convective stability of combustion waves in one-dimensional solids.  Archive for Rational Mechanics and Analysis, 198   Issue: 3  (2010), 981-1030. PDF.
  17. A. Ghazaryan,  P.  Gordon, A. Virodov. Stability of fronts and transient behavior in KPP systems.  Proceedings of the Royal Society A 466 (2010), 1769-1788. PDF.
  18.  A. Ghazaryan. On the convective nature of instability of a front undergoing a supercritical Turing bifurcation,  J. of Mathematics and Computers in Simulation: "On Nonlinear Waves: Computation and Theory."  80 (2009), 10-19. PDF.
  19. M. Beck, A. Ghazaryan, B. Sandstede. Nonlinear convective stability of traveling fronts near Turing and Hopf instabilities.  J. of Differential Equations 246 (2009) 4371-4390. PDF.
  20.  A. Ghazaryan,  C. Jones. On the stability of high Lewis number combustion fronts.  J. of Discrete and Continuous Dynamical Systems 24, number 3, (2009) 809-826. PDF.
  21. A. Ghazaryan. Nonlinear stability of high Lewis number combustion fronts,  Indiana Univ. Math. J. 58 No. 1 (2009), 181-212. PDF.
  22. A. Ghazaryan, P. Gordon. The KPP type flame fronts in porous media. Nonlinearity 21 (2008) 973-992. PDF.
  23. A. Ghazaryan, P. Gordon, C.K.R.T. Jones. Traveling waves in porous media combustion: uniqueness of waves for small thermal diffusivity.  J. of Dynamics and Differential Equations 19 (2007) 951-966PDF.
  24. A. Ghazaryan, B. Sandstede.  Nonlinear convective instability of Turing-unstable fronts near onset: A case study. SIAM J. of Applied Dynamical Systems 6 (2007) 319-347. PDF
  25. A. R. Kazaryan (Ghazaryan), and I. G. Khachatryan. On the structure of the scattering matrix of a differential operator of arbitrary order with coefficients summable on the entire axis. (in Russian) Doklady Akad. Nauk Armenii (96) 1, (1996).
  26. A. R. Kazaryan (Ghazaryan), and I. G. Khachatryan. On the inverse scattering problem for a differential operator of arbitrary order with coefficients summable on the entire axis. II.  J. Contemp. Math. Analysis. 30 (1995), no. 1, 33-55.
  27. A. R. Kazaryan (Ghazaryan), and I. G. Khachatryan. On the inverse scattering problem for higher-order differential operators with summable coefficients. I. English translation in J. Contemp. Math. Analysis. 29 (1994), no. 5, 42-63.
  28. S. E. Bekhiri, A. R. Kazaryan (Ghazaryan), and I. G. Khachatryan. On the reconstruction of a regular two-term differential operator of arbitrary even order from the spectrum. (in Russian). Yerevan State University Press, Uchenye Zapiski 2 (1994) 181, 8-22.
  29. S. E. Bekhiri, A. R. Kazaryan (Ghazaryan) and I. G. Khachatryan. Asymptotic formula for eigenvalues of a regular binomial differential operator of arbitrary even order. (in Russian). Yerevan State University Press, Uchenye Zapiski 1 (1994), 3-18.
Publications in Conference Proceedings:  Other publications
PhD thesis