On Cauchy Problem for Semilinear Second-Order Parabolic Equations on Spheres

This article is devoted to solvability of the Cauchy problem for non-autonomous semilinear parabolic second-order partial differential equations on n-dimensional spheres. Such equations are non-homogeneous and non-autonomous analogs on spheres of the Kolmogorov–Petrovsky–Piskunov and Fischer equations.