spectral optimization, resonances, nonlinear and nonselfadjoint spectral theory, evolution PDE, stability of discrete systems, signal processing
Biography
Education.
June 2005, Ph.D. in Mathematics, the Institute of Applied Mathematics and Mechanics, NAS of Ukraine, Donetsk, Ukraine. Title of Ph.D. Thesis: On similarity of differential operators to selfadjoint ones.
June 1999, Diploma in Mathematics, Donetsk State University, Donetsk.
Professional Experience.
01/2013–present, Senior research fellow, Institute of Applied Mathematics and Mechanics, Donetsk, Ukraine.
05/2011–12/2012, Researcher, Institute of Applied Mathematics and Mechanics, Donetsk, Ukraine.
10/2010–05/2011, Junior research fellow, Institute of Applied Mathematics and Mechanics, Donetsk, Ukraine.
11/2008–10/2010, Pacific Institute for the Mathematical Sciences Post-doctoral Fellow, the University of Calgary, Canada.
08/2007–07/2008, Post-Doctoral Fellow, the University of Calgary.
11/2006–04/2007, Postdoctoral researcher, the University of Zurich, Switzerland.
04/2006–11/206, Junior research fellow, Institute of Applied Mathematics and Mechanics, Donetsk, Ukraine.
12/2002–08/2006, Assistant, Senior Lecturer, Donetsk National University.
Main publications:
Karabash I.M., “Pareto optimal structures producing resonances of minimal decay under L1-type constraints”, Journal of Differential Equations, 257:2 (2014), 374-414.
Karabash I., “Optimization of quasi-normal eigenvalues for 1-D wave equations in inhomogeneous
media; description of optimal structures”, Asymptotic Analysis, 81:3–4 (2013), 273-295
Karabash I., “Optimization of quasi-normal eigenvalues for Krein-Nudelman strings”, Integral Equations and Operator Theory, 75:2 (2013), 235-247
Karabash I., “Nonlinear eigenvalue problem for optimal resonances in optical cavities”, Math. Model. Nat. Phenom., 8:1 (2013), 143-155.
Karabash I., Kostenko A., Malamud M., “The similarity problem for J-nonnegative Sturm-Liouville operators”, J. Differential Equations, 246 (2009), 964–997, arXiv: 0803.1496v2
I. M. Karabash, A. S. Kostenko, “On the Similarity of a $J$-Nonnegative Sturm–Liouville Operator to a Self-Adjoint Operator”, Funktsional. Anal. i Prilozhen., 43:1 (2009), 81–84; Funct. Anal. Appl., 43:1 (2009), 65–68
I. M. Karabash, S. Hassi, “Similarity between $J$-Self-Adjoint Sturm–Liouville Operators with Operator Potential and Self-Adjoint Operators”, Mat. Zametki, 78:4 (2005), 625–628; Math. Notes, 78:4 (2005), 581–585
I. M. Karabash, A. S. Kostenko, “Similarity of $\operatorname{sgn}x\bigl(-\frac{d^2}{dx^2}+c\delta\bigr)$ Type Operators to Normal and Self-adjoint Operators”, Mat. Zametki, 74:1 (2003), 134–139; Math. Notes, 74:1 (2003), 127–131
I. M. Karabash, “On the Similarity of $J$-Self-Adjoint Differential Operators of Odd Order to Normal Operators”, Mat. Zametki, 71:3 (2002), 476–480; Math. Notes, 71:3 (2002), 436–440
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