# Minenko A. S.

### Investigation of one convective Stefan problem by the Ritz method

Ukr. Mat. Zh. - 2007. - 59, № 11. - pp. 1546–1556

A plane stationary convective Stefan problem is analyzed in the case where the convection is caused by the presence of a prescribed rotation of intensity μ. A method of studying this problem is proposed which consists in a series expansion of the solution in terms of powers of a small parameter μ. The null expansion term is defined by the Rietz method. The formula describing the dependence of free boundary equation on μ is obtained.

### On minimization of one integral functional by the Ritz method

Ukr. Mat. Zh. - 2006. - 58, № 10. - pp. 1385–1394

Using the variational method, we investigate a nonlinear problem with a Bernoulli condition in the form of an inequality on a free boundary. We prove a solvability theorem and establish the convergence of an approximate solution obtained by the Ritz method to the exact solution in certain metrics.

### Analyticity of a free boundary in one problem of axisymmetric flow

Ukr. Mat. Zh. - 1998. - 50, № 12. - pp. 1692–1700

We prove the solvability of a boundary-value problem in the case where the Bernoulli condition is given on a free boundary in the form of an inequality. We establish the analyticity of the free boundary.

### Axially symmetric flow with free boundary

Ukr. Mat. Zh. - 1995. - 47, № 4. - pp. 477–487

We prove the solvability of a boundary-value problem with the Bernoulli condition in the form of an inequality on a free boundary. By using the Rietz method, we construct an approximate solution that converges to an exact solution in the integral metric.