The Fujita exponent for the fractional heat equation on hyperbolic space is 1 + β/λ0^σ, with existence of non-negative bounded finite-energy solutions to the semilinear elliptic equation for 0 ≤ λ ≤ λ0 and subcritical γ, enabled by a new fractional Poincaré inequality on symmetric spaces.
Papageorgiou, Large-time behavior of two families of operators related to the fractional Laplacian on certain Riemannian manifolds,Potential Anal.61, 263–287 (2024)
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Blow-up exponents and a semilinear elliptic equation for the fractional Laplacian on hyperbolic spaces
The Fujita exponent for the fractional heat equation on hyperbolic space is 1 + β/λ0^σ, with existence of non-negative bounded finite-energy solutions to the semilinear elliptic equation for 0 ≤ λ ≤ λ0 and subcritical γ, enabled by a new fractional Poincaré inequality on symmetric spaces.