Lifespan of Local-In-Time Solutions to Semilinear Nonlocal Heat Equation in the Heisenberg Group
Oza P.
June 2025Springer
Journal of Mathematical Sciences (United States)
2025#291Issue 183 - 96 pp.
The paper focuses on the lifespan of local-in-time solutions to the inhomogeneous semilinear heat equation driven by the fractional sub-Laplacian on the Heisenberg group HN : ∂tu+(−ΔHN)su = |u|p+f in HN ×(0, T). In the subcritical range 1 < p < Q/(Q − 2s), we establish an upper bound on the maximal existence time, where Q = 2N + 2 is the homogeneous dimension of HN.
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