Research interests

The classical solvability of nonlinear free boundary problems for elliptic and parabolic equations ( Stefan problem, Hele-Shaw problem, Muskat-Verigin problem ), boundary value problems with higher derivatives in the boundary conditions, degenerate parabolic equations, free boundary problems in nonsmooth domains, the application of variation methods to the free boundary problems arising in the theory of thermal conductivity, problems of equilibrium and stabilization of the free boundary solutions for large times, applications of symmetrization methods to obtain the estimates for the solutions of the nonlinear parabolic equations, investigation of the singular integral equations.

Diplomas

1988, Doctor of Science in mathematics, V.A.Steklov Mathematical Institute (Leningrad Branch) Academy of Science of USSR.

1968, Ph.D. in mathematics, Institute of Mathematics Academy of Science of Ukraine.

1961, MS in Aircraft Engineering, Aviation Institute, Kharkov, Ukraine

Career

1989-present, Professor of Department of Mathematical Physics, Institute of Applied Mathematics and Mechanics Academy of Science, Donetsk, Ukraine. Mathematical description of the processes of fluid dynamics, liquid-solid phase transitions, filtration in porous media, free boundary problems.

1970-1989,   Senior Researcher, Institute of Applied Mathematics and Mechanics. Description of surface waves with complicated interface properties. Investigation of the free boundary problems.

Publications

1. The Hele-Shaw problem with surface tension in a half plane: A model problem. J. Diff. Eq., 216 (2005) –p. 387-438. (A. Friedman).
    
2. The Hele-Shaw problem with surface tension in a half plane. J. Diff. Eq., 216 (2005) –p. 439-469. (A.Friedman).
    
3. A free boundary problem for an elliptic-parabolic system: an application to a model of tumor growth. Communication PDE, 2003, v.28, nos.3&4, pp. 627-675 (A.Friedman).
    
4. Classical solvability of the first initial boundary value problem for super degenerate parabolic equation, Ukrainian Math. J. 56 (10), (2004) p.1299-1321 (N.V.Krasnoschok).
    
5. Coercive estimate of solutions to the many-dimensional model problem in the theory of nonlinear filtration with free boundary, Dopovidi Acad. Sc. of Ukraine, 2001, n.1, 7-11.
    
6. Energy consideration in a model of nematode sperm crawling, Mathematical Biosciences and Engineering, v.3, n.2 (2006), pp.347-370. (Yar. Bazaliy, A. Friedman and B. Hu).
    
7. Global existence and asymptotic stability for an elliptic-parabolic free boundary problem: an application to a model of tumor growth. Indiana Univ. Math. J., 2003, v. 52, n. 5, 1265-1304 (A.Friedman).
    
8. On one boundary problem for strong degenerate elliptic equation of the second order, Ukr. Math. J. to appear (Degtyarev S.P.)
    
9. One-dimensional free boundary problem for actin-based propulsion of Listeria, J.Math.Anal. Appl. to appear (Yar.Bazaliy and A.Friedman)
    
10. Regularity of a solution to the many-dimensional free boundary problem for the porous medium equation. Siberian Advances in Math, 2003, v. 13, n. 3, pp. 1-53 (N.V. Krasnoschok).
     
11. Regularity of a weak solution to the first initial boundary value problem for a nonlinear degenerate parabolic equation, Ukr. Math. Bulletin, (2006), n.2 (Krasnoschek N.V.)
     
12. The model free boundary Hele-Shaw problem in a nonregular domain. Ukraine Math. J. 2001, v.48, n.12 (N.V. Vasil’eva).