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:
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:
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:

updated: 08/22/2008