# Timokha A. N.

### On one variational criterion of stability of pseudoequilibrium forms

Lukovsky I. O., Mykhailyuk O. V., Timokha A. N.

Ukr. Mat. Zh. - 1996. - 48, № 11. - pp. 1494-1500

We establish a variational criterion of stability for the problem of the vibrocapillary equilibrium state which appears in the theory of interaction of limited volumes of liquid with vibrational fields.

### One version of the Linearized theory of nonstationary boundary-value problems with free boundary

Ukr. Mat. Zh. - 1996. - 48, № 6. - pp. 791-804

We analyze the principle of linearization and linear boundary-value problems obtained by using this principle in the nonlinear theory of motion for a bounded volume of liquid with free surface subjected to the action of a nonstationary oscillating load. We formulate and study the problem of vibrocapillary equilibrium state, spectral problems in the theory of linear waves, and problems of stability of equilibrium states, including the problem of bifurcation of equilibrium states.

### Variational formulations of nonlinear boundary-value problems with a free boundary in the theory of interaction of surface waves with acoustic fields

Ukr. Mat. Zh. - 1993. - 45, № 12. - pp. 1642–1652

Variational problems equivalent to nonlinear evolutionary boundary-value problems with a free boundary are formulated. These problems arise in the theory of interaction of limited volumes of liquid, gas, and their interface with acoustic fields. It is proved that the principle of separation of motions can be applied to these variational problems. The problem of a capillary-acoustic equilibrium form is given in a variational formulation.

### Bateman variational principle for a class of problems of dynamics and stability of surface waves

Ukr. Mat. Zh. - 1991. - 43, № 9. - pp. 1181–1186

### Self-adjointness of a certain integrodifferential operator

Ukr. Mat. Zh. - 1990. - 42, № 3. - pp. 421-423