2018
Том 70
№ 11

All Issues

Bazalii B. V.

Articles: 8
Article (Russian)

On one boundary-value problem for a strongly degenerate second-order elliptic equation in an angular domain

Bazalii B. V., Degtyarev S. P.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2007. - 59, № 7. - pp. 867–883

We prove the existence and uniqueness of a classical solution of a singular elliptic boundary-value problem in an angular domain. We construct the corresponding Green function and obtain coercive estimates for the solution in the weighted Hölder classes.

Article (Russian)

Classical Solvability of the First Initial Boundary-Value Problem for a Nonlinear Strongly Degenerate Parabolic Equation

Bazalii B. V., Krasnoshchok M. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2004. - 56, № 10. - pp. 1299-1320

We prove the existence of a classical solution global in time for the first initial boundary-value problem for a nonlinear strongly degenerate parabolic equation.

Article (Russian)

On the Solvability of the Hele–Shaw Model Problem in Weighted Hölder Spaces in a Plane Angle

Bazalii B. V., Vasil'eva N. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2000. - 52, № 11. - pp. 1446-1457

We study a nonstationary boundary-value problem for the Laplace equation in a plane angle with time derivative in a boundary condition. We obtain coercive estimates in weighted Hölder spaces.

Article (Russian)

On one proof of the classical solvability of the Hele-Shaw problem with free boundary

Bazalii B. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1998. - 50, № 11. - pp. 1452–1462

We consider the Stefan problem for a parabolic equation with a small parameter as the coefficient of the derivative with respect to time. We justify the limit transition as the small parameter tends to zero, which enables us to prove the classical solvability of the Hele-Shaw problem with free boundary in the small with respect to time.

Article (Russian)

Stefan problem for the laplace equation with regard for the curvature of the free boundary

Bazalii B. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1997. - 49, № 10. - pp. 1299–1315

We consider a nonstationary problem with free boundary for an elliptic equation in the case where the value of the required function on an unknown boundary is proportional to the curvature of this boundary. We prove the existence of a solution in the small with respect to time in the spaces of smooth functions.

Article (Ukrainian)

Symmetrization and initial boundary-value problems for certain classes of nonlinear second order parabolic equations

Bazalii B. V., Tedeev A. F.

Full text (.pdf)

Ukr. Mat. Zh. - 1993. - 45, № 7. - pp. 884–892

Article (Ukrainian)

Solvability of a problem with an unknown boundary between the domains of a parabolic and an elliptic equations

Bazalii B. V., Degtyarev S. P.

Full text (.pdf)

Ukr. Mat. Zh. - 1989. - 41, № 10. - pp. 1343–1349

Article (Ukrainian)

On a nonstationary problem with a free surface

Bazalii B. V.

Full text (.pdf)

Ukr. Mat. Zh. - 1973. - 25, № 3. - pp. 332—336