Upper bound estimates for local in time solutions to the semilinear heat equation on stratified lie groups in the sub-Fujita case

In this note, we consider the Cauchy problem for the semilinear heat equation in a homogeneous stratified group G of homogeneous dimension Q and with power nonlinearity |u|p. In this framework, the heat operator is given by ât ΔH, where ΔH is the sub-Laplacian on G We prove the nonexistence of global in time solutions for exponents in the sub-Fujita case, that is for 1 < p ≤ 1 + 2/Q, under suitable integral sign assumptions for the Cauchy data. Besides, we derive upper bound estimates for the lifespan of local in time solutions both in the subcritical case and in the critical case.