Fujita exponent for the fractional sub-Laplace semilinear heat equation with forcing term on the Heisenberg group

2025/05/06 by Oza, Priyank, Suragan, Durvudkhan
#35A01 #35B33 #35B40 #35K58 #35R03 #47G20 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2505.03619

Abstract

In this paper, we study the semilinear heat equation with a forcing term, driven by the fractional sub-Laplacian (-Δ_\mathbbmH^N)^s of order s∈ (0,1), on the Heisenberg group \mathbbmH^N. We establish that the Fujita exponent, a critical threshold that delimits different dynamical regimes of this equation, is p_F\coloneqq(Q)/(Q-2s), where Q\coloneqq 2N+2 is the homogeneous dimension of \mathbbmH^N. We prove the existence of global-in-time solutions for the supercritical case (p>p_F), and the non-existence of global-in-time solutions for the subcritical case (1

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