Biography
I joined UNNC in August 2015. Before that I worked for 3 years at Xi’an Jiaotong-Liverpool University in Suzhou (PR China) and for 7 years at Max Planck Institute for Mathematics in the Sciences in Leipzig (Germany).
Expertise Summary
I am an applied mathematician working on non-linear partial differential equations. Of my particular interest are problems with geometric “side effects”, like free boundaries and free discontinuities.
Teaching
Differential Equations and Calculus for Engineers (HG2M13 CN)
Linear Mathematics (G11LMA CN)
Past teaching
Advanced Mathematical Techniques in Ordinary Differential Equations for Engineers (HG3MOD UNNC)
Analytical and Computational Foundations (G11ACF UNNC)
Applied Mathematics (G11APP UNNC)
Calculus (G11CAL UNNC)
Engineering Mathematics II (HG1M12 UNNC)
Engineering Mathematics I (MTH101 XJTLU)
Methods of Applied Mathematics (MTH106 XJTLU)
Partial Differential Equations (MTH210 XJTLU)
Principal research interests
Nonlinear Analysis / Partial differential equations / Free boundary problems / Free discontinuity problems
Research Grants
2017-2018 “Free Discontinuity Problems and Applications in Fracture Mechanics“. NSFC 400K RMB
2014-2015 “The asymptotic behaviour of minimizers of Mumford-Shah functional at the crack-tip” XJTLU-RDF 44K RMB
Events organized
International Conference “Free boundary / free discontinuity problems and applications”, Ningbo China, June 24-26, 2018
Research Summer School “Free discontinuity problems and applications in fracture mechanics”, Ningbo China, August 14-18, 2017
International workshop "Non-linear PDEs and Applications", Suzhou, China, May 18-19, 2015
UNESCO-CIMPA Summer-School “Nonlinear analysis and Geometric PDE”, Tsaghkadzor, Armenia, June 15-24, 2008
Recent Publications
Lemenant, Antoine; Mikayelyan, Hayk
Stationarity of the crack-front for the Mumford-Shah problem in 3D. J. Math. Anal. Appl. 462 (2018), no. 2, 1555–1569
Mikayelyan, Hayk
Cylindrical optimal rearrangement problem leading to a new type obstacle problem. ESAIM: Control, Optimisation and Calculus of Variations (accepted) https://doi.org/10.1051/cocv/2017047
Emamizadeh, Behrouz; Farjudian, Amin; Mikayelyan, Hayk
An Elliptic Optimal Control Problem and its Two Relaxations. J. Optim. Theory Appl. 172 (2017), no. 2, 455–465
Li, Zhilin; Mikayelyan, Hayk
Fine numerical analysis of the crack-tip position for a Mumford-Shah minimizer. Interfaces and Free Bound. 18 (2016), no. 1, 1–18
Mikayelyan, Hayk
Stabilization technique applied to curve shortening flow in the plane. Zap. Nauchn. Sem. St.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) vol. 444 (2016), 89-97
reprinted in Journal of Mathematical Sciences, 2017, Volume 224, Issue 3, pp 442–447
Mikayelyan, Hayk; Shahgholian, Henrik
Hopf's lemma for a class of singular/degenerate PDE-s. Ann. Acad. Sci. Fenn. Math. 40 (2015), no. 1, 475–484
Andersson, John; Mikayelyan, Hayk
The zero level set for a certain weak solution, with applications to the Bellman equations. Trans. Amer. Math. Soc. 365 (2013), no. 5, 2297–2316
Mikayelyan, Hayk; Shahgholian, Henrik
Convexity of the free boundary for an exterior free boundary problem involving the perimeter. Commun. Pure Appl. Anal. 12 (2013), no. 3, 1431–1443
Andersson, John; Mikayelyan, Hayk
On the non-tangential touch between the free and the fixed boundaries for the two-phase obstacle-like problem. Math. Ann. 352 (2012), no. 2, 357–372
Andersson, John; Mikayelyan, Hayk
C1,α regularity for solutions to the p-harmonic thin obstacle problem. Int. Math. Res. Not. IMRN 2011, no. 1, 119–134
External Activities
Visiting Fellowship (Feb. 3 - Apr. 13, 2014). Research program on “Free Boundary Problems and Related Topics”, held at the Isaac Newton Institute for Mathematical Sciences in Cambridge, UK
Visiting Fellowship (Mar. 1 - Apr. 30, 2011). Research program on “Free boundary problems and applications”, held at the Mathematical Sciences Research Institute in Berkeley, USA
Recent Invited Talks
17th International Conference CoMFoS17: Mathematical Analysis of Continuum Mechanics, Okinawa Institute of Science and Technology, Japan, September 20-22, 2017 (keynote speaker)
Analysis & Algebra Seminar, University of Nottingham (UK), August 30th 2017
14th International Conference on Free Boundary Problems: Theory and Applications, Shanghai, July 9-14, 2017 (two invited talks)
The Australian National University MATHFEST 2016, Workshop on geometric and nonlinear PDE. Kioloa Coastal Campus 9–13 December 2016
Seminar of the State Key Laboratory of Scientific and Engineering Computing. Chinese Academy of Sciences, Beijing. April 2016
Material Science Seminar of University of Michigan –Shanghai Jiaotong University Joint Institute. Shanghai, April 2016
Differential Geometry Seminar. National Centre for Theoretical Sciences, Taibei Dec. 2015
PDE Seminar, Academia Sinica, Taibei, Dec. 2015
2nd School on Analysis and PDE. IPM Tehran, Iran. May 19-21, 2015
Workshop on Non-linear Partial Differential Equations, Shanghai Jiaotong University, December 11-13, 2014
Satellite Conference on Nonlinear Elliptic and Parabolic Equations and Applications, International Congress of Mathematicians 2014, Seoul, Aug 8-12, 2014
Analysis Seminar, East China Normal University, Shanghai, May 30, 2014
Analysis Seminar, University of Edinburgh (UK), April 7, 2014
Weekly Seminar, Isaac Newton Institute for Mathematical Sciences, Cambridge (UK), March 18, 2014
Administration
Course Director of BSc Mathematics with Applied Mathematics, UNNC
Member of Advisory Taskforce of FoSE, UNNC
Member of UNNC 2020 Strategy Steering Committee, UNNC (2015-17)
Senior Tutor of BSc Mathematics with Applied Mathematics, UNNC (2017)
Applied Mathematics Program Director at XJTLU (2013-15)
Member of the Committee for Defence and Security Research of the Scientific Council of the Max Planck Society, Munich (2009-10)