Research interests

Qualitative aspects of nonlinear boundary problems;

Free boundary problems;

Elliptic and parabolic boundary value problems in nonsmooth domains;

Diplomas

June 1998, Master of Sciences (Donetsk State University, masters thesis: “On regularity of solutions of Hele-Shaw problem with free boundary”, supervisor: Professor Borys Bazaliy); 

 January 2003, PhD in Mathematics (Institute of Applied Mathematics and Mechanics of National Academy of Sciences of Ukraine, Donetsk, PhD thesis: “The elliptic and parabolic boundary value problems with the time derivative in the boundary condition in a plane corner and their application to free boundary problems”, supervisor: Professor Borys Bazaliy)

Career

2006 to present time  Researcher at the Department of Mathematical Physics at the Institute of Applied Mathematics and Mechanics of National Academy of Sciences of Ukraine, Donetsk;

             2004-2006 Adjunct Lecturer (concurrently) at the Physics
             Department of Donetsk National University;

2003- 2006 Junior Researcher at the Department of Mathematical Physics at the Institute of Applied Mathematics and Mechanics of National Academy of Sciences of Ukraine, Donetsk;

2001-2003 Engineer at the Department of Mathematical Physics at the Institute of Applied Mathematics and Mechanics of National Academy of Sciences of Ukraine, Donetsk;

2001-2002 Assistant Professor (concurrently) at the Department of Mathematics at Donbass State Academy of Building and Architecture;

1998-2001 Graduate student at the Institute of Applied Mathematics and Mechanics of National Academy of Sciences of Ukraine, Donetsk

Publications

1. B. Bazaliy, N. Vasylyeva, On the solvability of a transmission problem for the Laplace operator with a dynamic boundary condition on a nonregular interface, Journal of Mathematical Analysis and Applications (submitted), 25 p. 2011.
    
2. B. Bazaliy, N. Vasylyeva, The initial-boundary value problems in a plane corner for the heat equation, Electronic Journal of Diff. Equations, 2010, n. 90, (2010), 1-32.
    
3. B. Bazaliy, N. Vasylyeva, The Muskat problem with surface tension and a nonregular initial interface, Journal of Nonlinear Analysis: Theory, Methods and Applications, 72 (2011), 6074-6096.
    
4. B. Bazaliy, N. Vasylyeva, The transmission problem in domains with a corner point for the Laplace operator in weighted Hölder spaces, Journal of Differential Equations, 249 (2010), 2476-2499.
    
5. B.V. Bazaliy, N.V. Vasil’eva, On solvability of the model Hele-Shaw problem in weight Holder spaces in a plane corner. Ukr. Math.J., 52 (11), (2000), pp. 1446-1457 (in Russian).
    
6. B.V. Bazaliy, N.V. Vasylyeva, Estimates of solutions of Hele-Shaw model problem in nonsmooth domains.- Donetsk: 1999, 21 p. (Preprint).
    
7. N. Vasylyeva, On a linear boundary value problem with the time derivative respect to time in the boundary condition arising in the investigation of Hele-Shaw problem. Proceeding of IAMM NASU, 7 (2002), pp. 33-44.(in Russian)
    
8. N. Vasylyeva, On a solvability of the model Stefan problem in a plane corner. Nonlinear Boundary Problem, 12(2002), pp. 52-59.(in Russian).
    
9. N. Vasylyeva, On existence of smooth solutions in the Hele-Shaw problem in nonsmooth domains, Nonlinear Boundary Problems, 19, (2009), 12-28.
    
10. N. Vasylyeva, On solvability of the Hele-Shaw problem in weighted Hölder spaces in a plane domain with a corner point. UMB 2 №3 (2005), 317-343.(Russian and English)
     
11. N. Vasylyeva, On solvability of the initial boundary value problem for the heat equation in a plane corner with dynamic boundary condition. VI Ogólnopolskie Warsztaty dla Młodych Matematyków Teoria Operatorów, Kraków, 22-28 September 2003, pp. 111-122
     
12. N. Vasylyeva, On the solvability of some nonclassical boundary-value problem for the Laplace equation in the plane corner. J. Advances and Differential Equations, v.12, n.10 (2007), 1167-1200.
     
13. N. Vasylyeva, To a symmetrized method in Hele-Shaw problem. Nonlinear Boundary Problem, 10 (2000), pp. 204-208. (in Russian).
     
14. N.V. Vasylyeva, “The elliptic and parabolic boundary value problems with the time derivative in the boundary condition in a plane corner and their application to free boundary problems” - Manuscript, PhD thesis, Donetsk, 2002.