Panayotis Smyrnelis
Παναγιώτης Σμυρνέλης
Assistant Professor at the Institute of Mathematics of the Polish Academy of Sciences
Researcher at the Basque Center for Applied Mathematics
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In 2013, in the Department of Mathematics with a cosmonaut

Previous positions
Center for Mathematical Modeling, University of Chile (August 2015–October 2018)
Principal investigator of a multidisciplinary project on the structure of vortices in liquid crystals (sponsoring researcher: Prof. M. Kowalczyk).
University of Athens (September 2012–May 2015)
Postdoctoral position in a research program 'Aristeia' supervised by Prof. Alikakos.
Areas of interest

Elliptic systems of PDEs, Nonlinear ODEs, Calculus of Variations, Harmonic maps, Applications in Physics
(nonlinear optics, liquid crystals, superconductivity)
Publications

Double layered solutions to the extended Fisher-Kolmogorov P.D.E.
Submitted

Vortex solutions in the Ginzburg-Landau-Painlevé theory of phase transition
Submitted

Connecting orbits in Hilbert spaces and applications to P.D.E.
Communications on Pure and Applied Analysis 19 No. 5 (May 2020) pp. 2797–2818

On the origin of the optical vortex lattices in nematic liquid crystal light valve
(with E. Calisto, M. G. Clerc and M. Kowalczyk)
Optics Letters
44 No. 12 (2019) pp. 2947–2950.

Gradient theory of domain walls in thin, nematic liquid crystals films
(with M. G. Clerc and M. Kowalczyk)
Communications in Contemporary Mathematics. 22 No. 7 (2020) 1950063 (27 pages)

The connecting solution of the Painlevé phase transition model
(with M. G. Clerc and M. Kowalczyk) To appear in Annali della Scuola normale superiore di Pisa,
Classe di scienze.

Minimal heteroclinics for a class of fourth order O.D.E. systems
Nonlinear Analysis, 173 (2018) pp. 154–163

Elliptic systems of phase transition type Monograph with N. D. Alikakos and G. Fusco .
Progress in Nonlinear Differential Equations and their Applications, Vol. 91
Springer-Birkhäuser (2018).

Symmetry breaking and restoration in the Ginzburg-Landau model
of nematic liquid crystals
(with M. G. Clerc and M. Kowalczyk)
Journal of Nonlinear Science (2018)

On Abrikosov lattice solutions of the Ginzburg-Landau equations
(with I. Chenn and I. M. Sigal)
Mathematical Physics, Analysis and Geometry. 21 :7 (2018)

Theory of light-matter interaction in nematic liquid crystals and the second Painlevé equation
(with M. G. Clerc, J. D. Dávila, M. Kowalczyk, and E. Vidal-Henriquez)
Calc. Var. 56:93 (2017)

On minimizers of the Hamiltonian system u'' = ∇W (u ), and on the existence of heteroclinic, homoclinic and periodic orbits
(with P. Antonopoulos)
Indiana University Mathematics Journal 65 No. 5 (2016) pp. 1503–1524.

A maximum principle for the system Δu − ∇W (u ) = 0
(with P. Antonopoulos)
C. R. Acad. Sci. Paris, Ser. I 354 (2016) pp. 595–600.

Gradient estimates for semilinear elliptic systems and other related results
Proceedings of the Royal Society of Edinburgh 145A (2015) pp. 1313–1330.

Multiphase solutions to the vector Allen-Cahn equation: crystalline and other complex
symmetric structures
(with P. Bates and G. Fusco)
Archive for Rational Mechanics and Analysis
225 No. 2 pp. 685–715 (2017).

Entire Solutions with Six-fold Junctions to Elliptic Gradient Systems with Triangle Symmetry
(with P. Bates and G. Fusco) Advanced Nonlinear Studies 13 No. 1 (2013) pp. 1–11.

The harmonic map problem with mixed boundary conditions
Proceedings of the American Mathematical Society 143 No. 3 (2015) pp. 1299–1313.

Existence of lattice solutions to semilinear elliptic systems with periodic potential
(with N. D. Alikakos) Electron. J. Diff. Equations 2012 No. 15 (2012) pp. 1–15.

Teaching
January 2020, Basque Center for Applied Mathematics
PhD course: Connecting solutions in second order phase transition models

Spring 2016, University of Chile
Fourier Analysis: undergraduate course (with Prof. M. Kowalczyk)

Spring 2015, University of Athens
Multivariable Calculus: undergraduate course (with Prof. L. Dalla)

Απειροστικός Λογισμός III - Τύποι του Taylor και Ακρότατα

Μάθημα 1 ,
Μάθημα 2 ,
Μάθημα 3 ,
Μάθημα 4

Spring 2014, University of Athens
Methods of Applied Mathematics ΙΙ: postgraduate course (with Dr K. Liaskos)

Winter 2013-2014, University of Athens
EM.14 Nonlinear Analysis and Calculus of Variations: postgraduate course (with Prof. N. D. Alikakos)
Visits to Foreign Universities

July 15–August 23, 2020, visit to the University Sorbonne Paris Nord, France (upon invitation of Dr. Jacek Jendrej)

August 15–29, 2019, visit to the University of Chile, Chile (upon invitation of Prof. Michał Kowalczyk)

April 7–12, 2019, visit to the Basque Center for Applied Mathematics, Spain (upon invitation of Prof. Arghir Zarnescu)

April 26–May 1, 2014, visit to the Michigan State University, U.S.A. (upon invitation of Prof. Peter Bates)

October 19–November 4, 2012, visit to the University of Minnesota, U.S.A. (upon invitation of Prof. Peter Bates)

May 13–June 3, 2012, visit to the University of L'Aquila, Italy (upon invitation of Prof. Giorgio Fusco)