Komarenko A. N.
Self-Adjoint Operators Generated by Problems of Transmission with Inhomogeneous Conjugation Conditions
Ukr. Mat. Zh. - 2001. - 53, № 12. - pp. 1607-1622
For problems of transmission for higher-order equations with inhomogeneous conjugation conditions, we construct and investigate the corresponding operators in Hilbert spaces. We prove the self-adjointness of these operators for a spectral problem with a parameter in conjugation conditions.
Variational method for the solution of problems of transmission with the principal conjugation condition
Ukr. Mat. Zh. - 1999. - 51, № 6. - pp. 762–775
We prove the existence of a solution of a variational minimax problem that is equivalent to the problem of transmission. We propose an algorithm for the construction of approximate solutions and prove its convergence.
Asymptotics of solutions of spectral problems of hydrodynamics in the neighborhood of angular points
Ukr. Mat. Zh. - 1998. - 50, № 6. - pp. 803–811
At angular points on the boundary of a domain, we obtain an asymptotic expansion for the eigenfunctions of spectral problems that describe natural oscillations of an ideal liquid that partially fills a cavity in a solid body. We describe cases where the eigenfunctions have singularities at angular points.
Ukr. Mat. Zh. - 1996. - 48, № 3. - pp. 335-348
We apply operator methods to the investigation of an initial boundary-value problem which describes the perturbed motion of a body with cavity partially filled with an ideal liquid relative to the uniform rotation of this system about a fixed axis. We prove the existence and uniqueness of generalized solutions with finite energy and establish a sufficient condition for the stability of motion and some properties of the spectrum of the problem under consideration.
Asymptotic expansion of eigenfunctions of a problem with a parameter in the boundary conditions in a neighborhood of angular boundary points
Ukr. Mat. Zh. - 1980. - 32, № 5. - pp. 653–659
Generalized problem of Neumann and the corresponding spectral problem for equations with degeneracy on a part of the domain boundary
Ukr. Mat. Zh. - 1969. - 21, № 6. - pp. 757–767
Ukr. Mat. Zh. - 1969. - 21, № 4. - pp. 535–541
Ukr. Mat. Zh. - 1965. - 17, № 6. - pp. 22-30