New Integral Transformations and Their Applications to Some Boundary-Value Problems of Mathematical Physics
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.
English version (Springer): Ukrainian Mathematical Journal 54 (2002), no. 12, pp 1992-2005.
Citation Example: 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.