Anna R. Ghazaryan

Office: HA 151
Phone: (919) 515-1876
e-mail: ghazarya@email.unc.edu, aghazar@ncsu.edu

Background

Research Interests:

• Stability of traveling waves
• Traveling waves exhibited by singularly perturbed systems in applications.
  I have worked on fronts in subsonic detonation and high Lewis number combustion models, KPP-type equations: existence of the fronts (geometric singular perturbation theory), spectral stability (Stability Index Bundles), nonlinear stability (interaction of norms with and without weights).
  My current research is sponsored by NSF grant DMS-0410267, PI - Chris K.R.T. Jones.
  

  Publications

  Papers in preparation
  
  • Convective Stability of combustion waves in one-dimensional solids, with Steve Schecter, Yuri Latushkin and Aparecido J. De Souza;
  • Non-generic "Hopf bifurcation" in high Lewis number combustion model.
  
  Submitted papers
  
  • On the stability of high Lewis number combustion fronts, preprint, with Chris K.R.T. Jones.
  
  Papers accepted for publication
  
  • On the convective nature of instability of a front undergoing a supercritical Turing bifurcation, preprint. Journal Mathematics and Computers in Simulation: "On Nonlinear Waves: Computation and Theory".
  
  Published papers
  
  • A. Ghazaryan, P. Gordon. The KPP type flame fronts in porous media. Nonlinearity 21 (2008) 973-992. link to the paper
  • Nonlinear stability of high Lewis number combustion fronts,  preprint at Indiana Math. Journal.
  • A. Ghazaryan, P. Gordon, and C.K.R.T. Jones. Traveling waves in porous media combustion: uniqueness of waves for small thermal diffusivity, Journal of Dynamics and Differential Equations 19 (2007) 951-966
    The link to the paper at Springer. The link to the video of the related talk given at MSRI in January 2007.
  • A. Ghazaryan, and B. Sandstede. Nonlinear convective instability of Turing-unstable fronts near onset: A case study, pdf, SIAM Journal on Applied Dynamical Systems 6 (2007) 319-347.
  • 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).
  • 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. (in Russian) Izv. Nats. Akad. Nauk Armenii Mat. 30 (1995), no. 1, 39--65 (1997); English translation in J. Contemp. Math. Analysis. 30 (1995), no. 1, 33-55.
  • A. R. Kazaryan (Ghazaryan), and I. G. Khachatryan. On the inverse scattering problem for higher-order differential operators with summable coefficients. I. (in Russian) Izv. Nats. Akad. Nauk Armenii Mat. 29 (1994), no. 5, 50--75 (1995); English translation in J. Contemp. Math. Analysis. 29 (1994), no. 5, 42-63.
  • 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.
  • 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.
  
  More:
  • PhD thesis
  
  Extended abstracts:
  
  • Spectral stability of combustion fronts: transition from high to infinite Lewis number. Submitted to Proceedings of EQUADIFF 07
  • On the uniqueness of the subsonic detonation waves in inert porous media. Published in Extended Abstracts Proceedings (ed. by Krystyna Kuperberg) of the joint Workshop of AWM and MSRI Women in Mathematics: The Legacy of Ladyzhenskaya and Oleinik, MSRI, Berkeley, CA, May 18 - 20, 2006.

  Dynamical Systems Working Groop:

  I am participating in the work of the Dynamical Systems Working Groop of the Research Triangle (recently featured in DSWeb - Dynamical Systems Magazine ). The groop combines faculty, post-docs and students with backgrounds in dynamical systems. We meet regularly to discuss various problems of common interest. Members of the groop (this is not a complete list):

  Faculty: Chris K.R.T. Jones, Xiao-Biao Lin, Steve Schecter, Michael Shearer

  Post-docs and students: Anna Ghazaryan, Vahagn Manukian, Monique Taylor

  For a description of activities of a related research group visit the site of Applied Dynamical Systems research group

  Service:

• co-organizer of the conference The Geometry and Analysis of Dynamical Systems at the Math Department (NCSU), February 2008

  Teaching at NCSU:

• Fall 2006 MA 121

Links to Professional Societies:

• AMS - American Mathematical Society
• SIAM - Society for Industrial and Applied Mathematics
• AWM - Association for Women in Mathematics