Blow-up of radially symmetric solutions for a semilinear heat equation on hyperbolic space

Abstract

In this paper radially symmetric solutions of a semilinear heat equation $$u_{t}=\Delta u + u^{p}$$ on the hyperbolic space are considered. First universal bounds of the nonnegative solution are obtained to know the blow-up rate at the final blow-up time under the exponent p which is subcritical in the Sobolev sense. Next we derive its local blow-up profile and also analyze blow-up set of solutions.