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Aslihan Demirkaya

Associate Professor

Mathematics

College of Arts and Sciences
860.768.4052 D 220A
Education

PhD, University of Kansas

BS, Industrial Engineering/Mathematics, METU, Turkey


Aslihan Demirkaya joined the College of Arts and Sciences in 2011.

Teaching

Courses Taught:

  • M 114: Everyday Statistics
  • M 140: PreCalculus
  • M 144: Calculus I
  • M 145: Calculus II
  • M 220: Linear Algebra & Matrix Theory
  • M 242: Ordinary Differential Equations
  • M 340: Introductory Analysis
  • M 344: Advanced Engineering Mathematics
  • M 480: Independent Study in Mathematics

Research

My work has been in the analysis of equations: the Kuramoto-Sivashinsky (KS) equation, Burger-Sivashinsky (BS) equation, Klein-Gordon KG type equations, Schrödinger equations, Beam equations and the Spruce-Budworm equation.

Published:

  • Demirkaya, M. Stanislavova, Numerical results on existence and stability of standing and traveling waves for the fourth order beam equation, to appear in Journal Discrete and Continuous Dynamical System-B.
  • Hala Al-Khalil, C. Brennan, R. Decker, A. Demirkaya, J. Nagode, Numerical Existence and Stability of Steady State Solutions to the Distributed Spruce Budworm Model, Involve: A Journal of Mathematics, Vol. 10 (2017), No. 5, 857—879
  • A. Demirkaya, S. Hakkaev, On the spectral stability of periodic waves of the coupled Schrödinger equations, Physics Letters A, Vol 379 (2015), Issues 45-46, 2908-2914
  • A. Demirkaya, P.G. Kevrekidis, M. Stanislavova, A. Stefanov, Spectral stability analysis for standing waves of a perturbed Klein-Gordon equation, Dynamical Systems, Differential Equations and Applications AIMS Proceedings, (2015), 359-368
  • A. Demirkaya, S. Hakkaev, M. Stanislavova, A. Stefanov, On the spectral stability of periodic waves of the Klein-Gordon equation,Differential  and Integral Equations, Vol 28 (2015), 431-454
  • A. Demirkaya, T. Kapitula, P.G. Kevrekidis, M. Stanislavova, A. Stefanov, On the spectral stability of kinks in some PT-symmetric variants of the classical Klein-Gordon Field Theories, Studies in Applied Mathematics, Vol. 133, Issue 3, pp.298-317, 2014
  • M. Aron, P. Bowers, N. Byer, R. Decker, A. Demirkaya,Jun Hwan Ryu, Numerical Results using Spectral Methods on Existence and Stability of Steady State Solutions for the Reaction Diffusion and Klein-Gordon Equations, Involve: A Journal of Mathematics, Vol. 7, No. 6, pp.723-742, 2014
  • A. Demirkaya, D. J. Frantzeskakis, P. G. Kevrekidis, A. Saxena, A. Stefanov, Effects of PT -symmetry in Nonlinear Klein-Gordon Field Theories and Their Solitary Waves, Phys. Rev. E 88, 023203, 2013
  • A. Demirkaya, M. Stanislavova, Conditional stability theorem for the one dimensional Klein-Gordon equation, J. Math. Phys. 52, 112703, 2011.
  • A. Demirkaya, M. Stanislavova, Long Time Behavior for Radially Symmetric Solutions of Kuramoto-Sivashinsky Equation in Dimension 3, Dynamics of PDE, Vol.7, No. 2, pp.161-173, 2010.
  • A. Demirkaya, The Existence of a Global Attractor for a Kuramoto-Sivashinsky type Equation in 2D, Discrete and Continuous Dynamical Systems-A, pp.198-207, 2009.
  • A. Demirkaya, $L_2$ estimates for the Solutions of Burger-Sivashinsky Equation in 1D and 2D, AIPS Conference Proceedings, Vol. 1184, pp.105-112, 2009

To Appear:

  • Christov, A. Demirkaya, P.G. Kevrekidis, A. Saxena, Kink Dynamics in a Parametric φ6 Model.

Student Research Projects

Aslihan Demirkaya and Robert Decker supervised the following research conference projects.
  • Spring 2017, Robert Galvez, Matthew Bernocco, Soliton interaction for a nonlinear Neuron Equation.
  • Spring 2017, Iliana Albion-Poles, Mitchell Sugar, Yonatan Shavit, Soliton escape velocity after scattering for a nonlinear Beam Equation.
  • Spring 2016, Salem Moges and Reid Bassette ,Soliton escape velocity after scattering for a nonlinear Klein- Gordon partial differential equation.
  • Fall/Spring 2016, Damaris Zachos, Gianmarco Molino, Comparison of KDV and RLW PDE models of shallow-water waves.
  • Spring 2015, Steven Kingston, Jarrett Lagler, and Gianmarco Molino, Acoustic Waves in Neurons.
  • Spring 2014, Hala Al-Khalil and Jamie Nagode, Numerical Existence and Stability of Traveling Wave Solutions to the Distributed Spruce Budworm Model.
  • Spring 2014, Ethan Bourdeau, John Cunsole, Virginia Demske, and Scott Rubin, Numerical Existence, Stability and Simulation of Solitons to the Sine-Gordon Equation.
  • Spring 2013, Gino Cordone and Jeffrey Knecht, Existence of Period-Doubling and Chaos of nonlinear forced Klein-Gordon equation.
  • Spring 2013, Catherine Brennan and James Pellissier, Numerical Existence and Stability of Traveling Wave Solutions to the Distributed Spruce Budworm Model.
  • Spring 2013, Jessica Andersen and Cole Murphy, The forced Van der Pol Equation.
  • Spring 2013, David Arena, Karen Brzostowski, Adam Paul, and Christopher Vincent, Differential Equation Manipulation using a Matlab Graphical User Interface.
  • Spring 2012, Nicole Byer and Jun Hwan Ryu, The numerical existence and stability of the steady state solutions of the Reaction-Diffusion equation.
  • Spring 2012, Miles Aron, Peter Bowers, The numerical existence and stability of the steady state solutions of the Klein-Gordon equations.

Service

Community Outreach:

  • Students Achieving Success (SAS) Advisory Board member
    MATHCOUNT volunteer, Hartford Chapter

Scholarly Service:

  • Referee for Mediterranean Journal of Mathematics
  • Referee for European Journal of Applied Mathematics
  • Referee for Studies In Applied Mathematics
  • Referee for Advances in Difference Equations

University Service:

  • Member of the Academic Standing Committee
  • Member of the Senior Regents Award Committee
  • Member of the Curriculum Committee

Departmental Service:

  • Faculty Advisor (with Mark Turpin) for Math Club
  • Undergraduate Research Advisor (with Robert Decker)
  • Hiring Committee Member