Podlipenko Yu. K.
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.
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.
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
Ukr. Mat. Zh. - 1981. - 33, № 3. - pp. 382–385
Ukr. Mat. Zh. - 1981. - 33, № 3. - pp. 385–391