On Initial Value Problem for Semilinear Second-order Parabolic Equations on Spheres

The paper concerns the existence, uniqueness, and regularity of weak solutions to initial value problems for semilinear second-order partial differential equations on spheres are considered. The equations under consideration are parabolic and are inhomogeneous analogs of the Fischer-Kolmogorov-Petrovsky-Piskunov equation on spheres.