Anna R. Ghazaryan

I have moved to the University of Kansas at Lawrence, KS, in August 2008. My webpage is now at www.math.ku.edu/~aghazaryan

Postdoctoral Research Fellow at University of NC-Chapel Hill
Office at UNC: PH 334
Phone: (919) 962-982
e-mail: ghazarya@email.unc.edu
Visiting Rostdoctoral fellow at NC State University
Office at NCSU: HA 151
e-mail: aghazar@ncsu.edu

Background

Mathematics (PhD), Earthquake Engineering (MS)

Teaching at NCSU:

Fall 2006 MA 121

Research Interests:

My research concerns traveling waves. In particular, I am interested in fronts. I have been working on several projects on existence, properties and stability of fronts:

Stability of traveling waves
Traveling waves in singularly perturbed systems

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
Nonlinear convective stability of traveling fronts near Turing and Hopf instabilities, with M. Beck and B. Sandstede

Submitted papers

Papers accepted for publication

A. Ghazaryan, Chris K.R.T. Jones. On the stability of high Lewis number combustion fronts, preprint. Journal of Discrete and Continuous Dynamical Systems.
A. Ghazaryan. On the convective nature of instability of a front undergoing a supercritical Turing bifurcation, preprint. Journal of 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
A. Ghazaryan. 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.
PhD thesis

Publications in Conference Proceedings:

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 Group of the Research Triangle Park:

I am participating in the work of the Dynamical Systems Working Group of the Research Triangle (recently featured in DSWeb - Dynamical Systems Magazine ). The group combines faculty, post-docs and students with backgrounds in dynamical systems. We meet regularly to discuss various problems of common interest. Members of the group (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 the Applied Dynamical Systems research group at UNC-Chapel Hill.

Picture below is from the article DSWeb - Dynamical Systems Magazine about the Dynamical Systems Group at NC State University written by Steve Schecter. From left: John Franke, Vahagn Manukian, David Long, Ming Jiang, Dmitry Zenkov, and I.

Service:

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

Links to Professional Societies:

AMS - American Mathematical Society
SIAM - Society for Industrial and Applied Mathematics
AWM - Association for Women in Mathematics
Links to Conference Calendars: ATLAS, AMS, IMACS

updated: 08/22/2008