Blow-up of Solutions of Nonlinear Heat Equation with Hypoelliptic Operators on Graded Lie Groups

Abstract

In this paper we show blow-up of solutions of the nonlinear heat equation with the Rockland operators on the graded Lie groups. In addition, we give the necessary conditions for the existence of local or global solutions of the nonlinear heat equation with hypoelliptic operators on Heisenberg groups.