Duality principle which is well known in linear observability and control theory is generalized for nonlinear dynamical systems. Possibility of phase state reconstruction in analytical dynamical systems by stable discrete observation programs is proved. The solvability of the boundary-value problems of hydrogen interraction with solids with nonlinear dynamical boundary conditions is investigated. The methods of inverse problem solution of parametric identification of hydrogen permeability models are propozed.

Graduated from Faculty of Applied Mathematics-Control Processes of Leningrad State University (now St.-Petersburg State University) in 1982 (department of mechanics of control motion). Ph.D. thesis was defended in 1985. D.Sci. thesis was defended in 1998. A list of my works contains for about 60 titles.

1. Zaika Yu.V., Bormatova E.P., “Parametricheskaya identifikatsiya modeli vodorodopronitsaemosti po vremenam zapazdyvaniya”, Zhurnal tekhnicheskoi fiziki, 80:3 (2010), 31–39
2. Zaika Yu. V., Rodchenkova N.I., “Boundary-value problem with moving bounds and dynamic boundary conditions: diffusion peak of TDS-spectrum of dehydriding”, Applied Mathematical Modelling, 33:10 (2009), 3776–3791
3. Zaika Yu.V., “Identification of a hydrogen transfer model with dynamical boundary conditions”, International Journal of Mathematics and Mathematical Sciences, 2004, № 4, 195–216
4. Zaika Yu.V., “Integral observability operators of nonlinear dynamical systems”, International Journal of Mathematics and Mathematical Sciences, 2003, no. 55, 3519–3538
5. Zaika Yu.V., “Interval estimates of functionals in time-delay systems with uncertainty”, International Journal of Mathematics and Mathematical Sciences, 2003, no. 56, 3573–3590

• Institute of Applied Mathematical Research of the Karelian Research Centre RAS, Petrozavodsk
• Petrozavodsk State University