Kateryna KHALINA

Citizenship:	Ukraine
Birth:	March 2, 1982, Kharkiv, Ukraine
Address:	Mathematical Division, B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine, 47 Nauky Ave., Kharkiv, 61103, Ukraine
E-mail:	khalina@ilt.kharkov.ua, khalina@meta.ua

EDUCATION

• Ph.D.: V.N. Karazin Kharkiv National University, October 4, 2013. Title: "The method of transformation operators in controllability problems for the wave equation". Supervisor L.V. Fardigola.
• M.S.: Faculty of Mechanics and Mathematics, V.N. Karazin Kharkiv National University, 2004.

PROFESSIONAL CAREER

• Senior Research Fellow, Mathematical Division, B.Verkin Institute for Low Temperature Physics & Engineering of the National Academy of Sciences of Ukraine, Kharkiv, Ukraine, 07.2023 – present time.
• Research Fellow, Mathematical Division, B.Verkin Institute for Low Temperature Physics & Engineering of the National Academy of Sciences of Ukraine, Kharkiv, Ukraine, 07.2019 – 06.2023.
• Junior Research Fellow, Mathematical Division, Institute for Low Temperature Physics & Engineering of the National Academy of Sciences of Ukraine, Kharkiv, Ukraine, 11.2007 – 06.2019.

SCHOLARSHIPS AND AWARDS

• 2011 ― Scholarship of the Akhiezer Foundation.
• 22.03.2022 – 21.05.2022 ― Pauli Postdoc in the “Pauli Ukraine Project”, funded in the WPI Thematic Program “Quantum Equations and Experiments” (2021/2022)
• 01.05.2023 - 31.10.2023 ― Scholarship of the Akhiezer Foundation

GRANTS

• 01.06.2015 – 31.12.2016 ― Project leader of the grant of the National Academy of Sciences of Ukraine for young scientists, project “Linear evolution equations in Hilbert spaces and the Boltzmann equation”.
• 04.01.2022 – 30.12.2022 ― Grant of the National Academy of Sciences of Ukraine, Project “Analytical and asymptotic methods in theory of integrable nonlinear differential equations and mathematical control theory”.

PROFESSIONAL AFFILIATIONS

• Secretary of the Editorial Office of  “Journal of Mathematical Physics, Analysis and Geometry”.
• Member of Kharkiv Mathematical Society

 RESEARCH INTERESTS

Partial Differential Equations: Control Theory, Qualitative Properties of Solutions, Boundary-Value Problems.

CONFERENCES PARTICIPATED

1. 6-th International Conference "Differential Equations and Control Theory" (online format). October 11-13, 2023, Kharkiv, Ukraine.
2. The International Scientific online Conference "Algebraic and geometric methods of analysis" dedicated to the memory of Dmytro Grave. May 29 – June 01, 2023, Odesa, Ukraine.
3. The online International Scientific Conference "Algebraic and geometric methods of analysis" dedicated to the memory of Yuriy Trokhymchuk.  May 25-28, 2021, Odesa, Ukraine.
4. 5-th International Conference "Differential Equations and Control Theory". September 27-29, 2021, Kharkiv, Ukraine.
5. International Conference “Geometry, Differential Equations and Analysis” in memory of Aleksei Vasilyevich Pogorelov. June 17-21, 2019, Kharkiv, Ukraine.
6. 3-rd International Scientific Conference “Differential Equations and Control Theory”. September 25-27, 2018, Kharkiv, Ukraine.
7. VI International Conference “Analysis and Mathematical Physics”. June 18-22, 2018, Kharkiv, Ukraine.
8. International Conference “Spectral Theory and Differential Equations” International Conference in honor of Vladimir A. Marchenko’s 90th birthday. August 20-24, 2012, Kharkiv, Ukraine.
9. 3-rd International Conference for Young Scientists “Low Temperature Physics”. May 14-18, 2012, Kharkiv, Ukraine.
10. The International Skorobohat’ko Mathematical Conference. September 19-23, 2011, Drohobych, Ukraine.
11. 2-nd International Conference for Young Scientists “Low Temperature Physics”. June 6-10, 2011, Kharkiv, Ukraine.
12. 1-st International Conference for Young Scientists “Low Temperature Physics”. June 7-11, 2010, Kharkiv, Ukraine.
13. Lyapunov Memorial Conference. June 24-30, 2007, Kharkiv, Ukraine.
14. Conference for Young Scientist and Researches “Low Temperature Physics”. June 5-7, 2007, Kharkiv, Ukraine.
15. XI International Scientific Kravchuk Conference. May 18 - 20, 2006, Kyiv, Ukraine.

PUBLICATIONS

1. Larissa Fardigola and Kateryna Khalina, Controllability Problems for the Heat Equation with Variable Coefficients on a Half-Axis Controlled by the Neumann Boundary Condition. J. Math. Phys. Anal. Geom. 19 (2023), No. 3, 616-641.

2. Larissa Fardigola and Kateryna Khalina, Controllability problems for the heat equation with variable coefficients on a half-axis, ESAIM Control Optim. Calc. Var. 28 (2022), Art. No. 41.

3. Larissa Fardigola and Kateryna Khalina, Controllability Problems for the Heat Equation in a Half-Plane Controlled by the Dirichlet Boundary Condition with a Point-Wise Control, J. Math. Phys. Anal. Geom. 18 (2022), No. 1, 75–104.

4. Larissa Fardigola and Kateryna Khalina, Controllability problems for the heat equation on a half-axis with a bounded control in the Neumann boundary condition, Math. Control Relat. Fields 11 (2021), No. 1, 211-236

5. L.V. Fardigola, K.S. Khalina, Reachability and Controllability Problems for the Heat Equation on a Half-Axis, J. Math. Phys. Anal. Geom. 15 (2019), No. 1, 57-78.

6. K.S. Khalina, On the controllability over Dirichlet boundary conditions for an inhomogeneous string on the half-axis, Dopov. Nats. Akad. Nauk Ukr. Mat. Prirodozn. Tekh. Nauki (2012), No. 10, 24-29. (Ukrainian)

7. K.S. Khalina, On the Neumann boundary controllability for the non- homogeneous string on a half-axis, J. Math. Phys. Anal. Geom. 8 (2012), No. 4, 307-335.

8. K.S. Khalina, Boundary controllability problems for the equation of oscillation of an inhomogeneous string on a semiaxis, Ukrain. Mat. Zh. 64 (2012), No. 4, 525-541 (Ukrainian); Engl. translations in Ukrainian Math. J. 64 (2012), No. 4, 594-615.

9. K.S. Khalina, On the Neumann boundary controllability for the non- homogeneous string on a segment, J. Math. Phys. Anal. Geom. 7 (2011), No. 4, 333-351.

10. K.S. Khalina, Controllability problems for the non-homogeneous string that is fixed at the right end point and has the Dirichlet boundary control at the left end point, J. Math. Phys. Anal. Geom.7 (2011), No. 1, 34-58.

11. K.S. Khalina, The controllability problem for the wave equation and the Markov trigonometric moment problem, Visn. Khark. Univ., Ser. Math., Appl. Math. and Mech. 826 (2008), No. 58, 38-51. (Ukrainian)

12. K.S. Khalina, The controllability problems for the equation of an inhomogeneous string with the fixed right end, Dopov. Nats. Akad. Nauk Ukr. Mat. Prirodozn. Tekh. Nauki (2008), No. 8, 31-35. (Ukrainian)

13. L.V. Fardigola, K.S. Khalina, Controllability problems for the string equation, Ukrain. Mat. Zh. 59 (2007), No. 7, 939-952 (Ukrainian); Engl. translations in Ukrainian Math. J. 59 (2007), No. 7, 1040-1058.