I am an applied analyst with general interest in applied dynamical systems and nonlinear PDEs.

My research Interests include:

  • Reaction-diffusion systems
  • Partially parabolic systems
  • Singularly perturbed systems
  • Traveling waves
  • Convective instability
  • Multiscale systems

Journal Publications

  1. M. Bakhshi, A. Ghazaryan, V. Manukian, N. Rodriguez. Traveling wave solutions in a model for social outbursts in a tension-inhibitive regime. Studies in Applied Mathematics. 147:2 (2021) 650-674.
  2. A. Ghazaryan, S. Lafortune, C. Linhart. Flame propagation in a porous medium. Physica D: Nonlinear Phenomena Available online 28 July 2020. Vol. 413.
  3. A. Ghazaryan, S. Lafortune, V. Manukian. Spectral analysis of fronts in a Marangoni-driven thin liquid film flow down a slope. SIAM J. on Applied Mathematics, 80(1) (2020), 95 -118.
  4. 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.
  5. 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) 5569-5615Read the article
  6. A. Ghazaryan, Y. Latushkin, A. Pogan. Spectrum of non-planar traveling waves. Integral Equations Operator Theory 90:3 (2018) 20pp. Preprint.
  7. 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.
  8. 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
  9. 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.
  10. 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.
  11. 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.
  12. A. Ghazaryan, V. Manukian. Coherent structures in a model for mussel-algae Interaction.  SIAM J. of Dynamical Systems. 14 (2), 2015,  893-913. Preprint
  13. 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.
  14. A. Ghazaryan,  S. Schecter, P.  Simon. Gasless combustion fronts with heat loss.  SIAM J. of Applied Mathematics,  73 (2013), No 3, 1303-1326. PDF
  15. A. Ghazaryan, J. Humpherys, J. Lytle. Spectral behavior of combustion fronts with high exothermicity. SIAM J. of Applied Mathematics. 73 (2013), No. 1, 422-437.  PDF.
  16. 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.
  17. 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.
  18. 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.
  19. 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.
  20. 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.
  21. 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.

Books

  • A. Ghazaryan,  S. Lafortune, V. Manukian. Introduction to Traveling Waves. Chapman & Hall/CRC. Nov 2022, 174 pages.
    Editors: J. Beery, S. Greenwald, and C. Kessel, Springer, 2021.
Order

Other Publications

Awarded Funding

  • Faculty Research Grant, Miami University, Summer 2019.
  • Research Fellowship for a Master's Student that includes paid tuition and a stipend for Academic Year 2019/2020.
  • NSF Research Grant DMS-1311313. Duration 08/15/2013 - 07/31/2016. Project Title:  On three different manifestations of instability of fronts in parabolic and partially parabolic systems.
  • Collaboration Grant for Mathematicians from Simons Foundation. Duration 09/1/2012 -08/31/2017.  Project title: Traveling waves in nonlinear coupled systems.
  • NSF GRANT DMS-0908009. Duration 07/07/2009 - 30/06/2011. Project title: Traveling Fronts with Unstable Continuous Spectrum: Geometric Structure and Nonlinear Stability Properties.
  • Miami University CELTUA Grant: Major Teaching Project for Departments/Programs. Title: Enhancing teaching and learning in MTH245: Differential Equations for Engineers.
  • Dean's Award, School of Arts and Sciences, Miami University, Summer 2012
  • Faculty Research Grant, Miami University, Summer 2011
  • Research Fellowship for a Master's Student that includes paid tuition and a stipend for Academic Year 2011/2012
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