Параболические уравнения переменного типа и их приложения. Спектральная теория.
Основные публикации:
Chugunova M., Karabash I., Pyatkov S.G., “On the nature of ill-posedness of the forward-backward heat equation”, Integral Equations Operator Theory, 65:3 (2009), 319–344, arXiv: 0803.2552v2
Karabash, I., “Abstract kinetic equations with positive collision operators”, Spectral Theory in Inner Product Spaces and Applications, Oper. Theory Adv. Appl., 188, Birkhäuser, Basel, 2008, 183–203, arXiv: 0708.2510v2
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
Karabash I., Kostenko A., “Indefinite Sturm-Liouville operators with the singular critical point zero,”, Proc. Roy. Soc. Edinburgh, 138A (2008), 801–820, arXiv: 0612173v1
Karabash I., “$J$-selfadjoint ordinary differential operators similar to selfadjoint operators”, Methods of Functional Analysis and Topology, 6:2 (2000), 22–49