New Integral Transformations and Their Applications to Some Boundary-Value Problems of Mathematical Physics - Popov, G. Ya. (Ukrains’kyi Matematychnyi Zhurnal, 2002)
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.