Solvability of a semilinear heat equation on Riemannian manifolds

Abstract

We study the solvability of the initial value problem for the semilinear heat equation u t − ∆u = u p in a Riemannian manifold M with a nonnegative Radon measure µ on M as initial data. We give sharp conditions on the local-in-time solvability of the problem for complete and connected M with positive injectivity radius and bounded sectional curvature.