Popov G. Ya.
New Integral Transformations and Their Applications to Some Boundary-Value Problems of Mathematical Physics
Ukr. Mat. Zh. - 2002. - 54, № 12. - pp. 1642-1652
We construct new integral transformations and present their applications to the construction of exact solutions of some boundary-value problems of mathematical physics. We solve the problem of diffraction of acoustic waves in a circular cone truncated by two spherical surfaces. We also solve the initial boundary-value problem of the theory of heat conduction for the same truncated cone under nonzero initial conditions.
On Some Integral Transformations and Their Application to the Solution of Boundary-Value Problems in Mathematical Physics
Ukr. Mat. Zh. - 2001. - 53, № 6. - pp. 810-819
We obtain a formula for the expansion of an arbitrary function in a series in the eigenfunctions of the Sturm–Liouville boundary-value problem for the differential equation of cone functions. On the basis of this result, we derive a series of integral transformations (including well-known ones) and inversion formulas for them. We apply these formulas to the solution of initial boundary-value problems in the theory of heat conduction for circular hollow cones truncated by spherical surfaces.
A generalization of Carleman's equation, solved in explicit form, and its application in the theory of bending of plates
Ukr. Mat. Zh. - 1986. - 38, № 3. - pp. 315–320
Ukr. Mat. Zh. - 1986. - 38, № 2. - pp. 188–195
Ukr. Mat. Zh. - 1968. - 20, № 4. - pp. 540–547
Ukr. Mat. Zh. - 1960. - 12, № 1. - pp. 46-54