Dr. Kateryna Buryachenko

Associate Professor, Senior Researcher

Education

1994-1999 Donetsk NationalUniversity

1999-2002 Post graduate course, Institute of Applied Mathematics & Mechanics of National Academy of Sciences of Ukraine

Qualifications

1999 Diploma in Mathematics („with excellence“).

Theme: Some investigations of nontrivial solvability of homogeneous boundary value problems for the partial differentialequations.

2003 PhD Diploma in Differential equations (01.01.02), Institute of Applied Mathematics and Mechanics of National Academy of Sciences of Ukraine.

Theme ofPhD thesis: Solvabilityofboundary value problems for the high order differential equations of a principal type in a disk.

2011 Docent Diploma, (Department ofDifferential Equations).

Employment:

2000-2006 Junior researcher, Institute of Applied Mathematics and Mechanics of National Academy of Sciences of Ukraine.

2002- 2003 Assistant in department ofMathematicalPhysics, Donetsk National University

2003 –till now: Associate Professor in department ofDifferential Equation (in 2013 renamed as. Department ofMathematical Analysis and Differential Equation, in 2019 renamed as Department of Applied Mathematics)

2019-till now Senior Researcher at the Science and Research Department ofthe Vasyl’ Stus Donetsk National University

Teaching experience

Courses for Students

• DifferentialEquatios
• Mathematical Physics
• Theoryof nonlinear operators
• Function theoryand Functional Analysis
• SQL
• Theoryofgeneralized functions (by Lars Hormander)      Analytical and DifferentialGeometry
• Calculus of variation and methods of optimization      Mathematical modeling
• English for Science and Technology

Research experience

2019-till now Senior Researcher at the Science and Research Department of the Vasyl’ Stus Donetsk National University

Scientific interests:

• PDEs
• Nonlinear elliptic and parabolic differential equations and boundaryproblems      Functional and operator’s methods in the theoryof differential equations
• Mathematical modeling ofphysical processes   
• Applications ofPDEs

Research Projects:

Grants Supported by Ministry of Education and Science of Ukraine:

• Metric spaces, harmonic analysis of functions and operators, singular and non-classical boundary problems for PDEs (2015-2017)
• Qualitative analysis ofdifferentialequations in abstract spaces with applications in physical processes simulation (2016-2018)
• Properties ofsingular solutions ofdifferential equations, spectralanalysis ofdifference systems and nonlinear processes simulation (2018-2020)
• Singular solutions of mathematical physics equations in anisotropic and inhomogeneous media, simulation of diffusion and absorption processes (2019-2021)

Grants Supported by State Fund forFundamentalResearch of Ukraine:

Regularity and pointwise estimates of singular solutions to quasilinear elliptic and parabolic equations ofdiffusion-strong nonlinear absorption structure (2016-2017)

Grants supported by National Academy of Science of Ukraine:

Grant for young scientists, 2006-2007.

InternationalResearch Projects

“FromModeling and Analysis to Approximation” (2020-2022) byVolkswagen Foundation.

Professional training (with travel grants)

2009, 2012 – teaching experience, Ivan Franko National UniversityofLviv, Lviv, Ukraine 2012- Data Science training, Soft Serve, Lviv, Ukraine

(https://career.softserveinc.com/uk-ua/technology)

2013– Workshop and School “Recent Advances in PDEs”,Universita DegliStudiDiMilano, Italy.

2016 – Workshop and School “PDEs and Applications” , Naples University, (http://cvgmt.sns.it/event/349/)

2016-Workshop ofNonlinear PDEs, Lecce University, Italy.

2019 – CIME Foundation Summer Schoolon Applied Mathematics in Geophysics. (http://web.math.unifi.it/users/cime/)

Organizational experience

1. Initiator ofregular international conferences for young researchers (since 2006, http://icl.donnu.edu.ua/)
2. DEMPhA conference (2017, https://sites.google.com/view/demph17)

List of main publication:

Textbooks:

1. Buryachenko K.O., Applications of Nonlinear Functional Analysis to the Theory of DifferentialEquations/K.O. Buryachenko, V.M. Shramenko, D.V. Limanskii, Donetsk, 2011, 188 p. (Textbook is recommended by Ministry of Education and Science of Ukraine)
2. Buryachenko K.O., Calculus ofVariation and Methods ofOptimization /K/O/ Buryachenko, D.V. Limanskii, Donetsk, 2013, 99 p. (in Ukrainian)
3. Buryachenko K.O., Lectures and Tasks on the TheoryofMathematical Physics/K.O. Buryachenko, M.O. Shan, Vinnytsia, 2015, 113 p. (in Ukrainian)
4. Buryachenko K.O. Lectures and Tasks on DifferentialEquations/ K.O. Buryachenko, V.M. Tyshlek, Vinnytsia, 2017, 217 p. (in Russian)
5. 5. Buryachenko K.O., Taranets R.M., Savchenko M. Qualitative analysis of dynamical systems, Vinnytsia, 2022, 130 p. (in English).