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In this paper, we study a critical exponent to the semilinear heat equationwith forcing term on Heisenberg group. Our technique of proof is based onmethods of nonlinear capacity estimates specifically adapted to the nature ofthe Heisenberg group. Surprisingly, the critical exponent will be bounded forall dimensions of the Heisenberg group, in contrast to the Euclidean case whichin the 1D and 2D cases will be infinite. In addition, we give an upper boundestimate on the lifespan of local solutions.

The Fujita exponent for a semilinear heat equation with forcing term on Heisenberg Group