Abstract:

We obtain the subcritical Fujita exponent and nonexistence result for the Cauchy problem of the nonlinear Rockland heat equation

$\begin{eqnarray*} \left\{\begin{array}{ll} u_{t}(t,x)+{\cal R}_{x}u(t,x)=|u(t,x)|^{p}, &(t,x) \in (0,+\infty)\times{\Bbb G}:=\Omega, \\ u(0,x)=u_{0}(x), & x \in {\Bbb G}. \end{array}\right. \end{eqnarray*}$

In this paper, we consider the critical Fujita exponent and obtain the blow-up result by an ODE method. Central to our proof is the heat kernel for Rockland operator.

Key words: Rockland operator, Parabolic equation, Fujita exponent