ABSTRACT We study the following semi‐linear heat equation in the Heisenberg group : where denotes the fractional sub‐Laplacian of order on . We establish that the Fujita exponent, the critical threshold that delimits different dynamical regimes of this equation, is where is the homogeneous dimension of . We prove the existence of global‐in‐time solutions for the supercritical case and the nonexistence of global‐in‐time solutions for the subcritical case For the critical case we provide a class of functions for which blows up in finite time. These results extend the classical Fujita phenomenon to a sub‐Riemannian setting with the nonlocal effects of the fractional sub‐Laplacian. Our proof methods intertwine analytic techniques with the geometric structure of the Heisenberg group.
Oza et al. (Fri,) studied this question.
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