# Podlipenko Yu. K.

### On Green's function for the Helmholtz equation in a wedge

Mel'nik Yu. I., Podlipenko Yu. K.

Ukr. Mat. Zh. - 1993. - 45, № 9. - pp. 1312-1314

It is found that, in the spherical coordinate system, the fundamental solution of the Helmholtz equation in a wedge satisfies the Sommerfeld radiation conditions at infinity uniformly in angle coordinates.

### Potential theory for problems of diffraction on a layer between two parallel planes

Ukr. Mat. Zh. - 1993. - 45, № 5. - pp. 647–662

We investigate the boundary-value problems that appear when studying the diffraction of acoustic waves on obstacles in a layer between two parallel planes. By using potential theory, these boundary-value problems are reduced to the Fredholm integral equations given on the boundary of the obstacles. The theorems on existence and uniqueness are proved for the Fredholm equations obtained and, hence, for the boundary-value problem.

### Boundary-value problems for the helmholtz equation in an angular domain. II

Ukr. Mat. Zh. - 1993. - 45, № 4. - pp. 500–519

We investigate boundary-value problems that appear in the study of the diffraction of acoustic waves on an infinite cylinder (with a cross section of an arbitrary shape) placed inside a wedge so that the axis of the cylinder is parallel to the edge of the wedge. The potential theory which enables one to reduce these boundary-value problems to integral equations is elaborated.

### Boundary-value problems for Helmholtz equations in an angular domain. I

Ukr. Mat. Zh. - 1993. - 45, № 3. - pp. 403–418

The boundary-value problems are investigated that arise when studying the diffraction of acoustic waves on an infinite cylinder with cross-section of an arbitrary shape situated inside a wedge so that the axis of the cylinder is parallel to the edge of the wedge. The potential theory is worked out which enables one to reduce these boundary-value problems to integral equations on a one-dimensional contour — the boundary of the cross-section of this cylinder. The theorems on existence and uniqueness of solutions to the boundary-value problems and the corresponding integral equations are proved. For this case, a principle of limit absorption is established. Effective algorithms for calculating the kernels of the integral operators are constructed.

### Piecewise-polynomial approximation of the solution of the goursat problem for nonlinear equations of hyperbolic type

Ukr. Mat. Zh. - 1982. - 34, № 1. - pp. 59-65

### A method of integral equations and the Riemann boundary problem

Mel'nik Yu. I., Podlipenko S. N., Podlipenko Yu. K.

Ukr. Mat. Zh. - 1981. - 33, № 3. - pp. 382–385

### Approximate solution of integral equations in potential theory

Mel'nik Yu. I., Podlipenko S. N., Podlipenko Yu. K.

Ukr. Mat. Zh. - 1981. - 33, № 3. - pp. 385–391