Fujita-Type Results for a Coupled Parabolic System of Hénon-Type Equations on Homogeneous Carnot Groups

In this paper, we consider a coupled parabolic system with multiple Henón-type components ( ∂ ₜ u - Δ G u ) (x,t) = H(x,t,u) ∂ t u - Δ G u ( x , t ) = H ( x , t , u ) for (x,t) ∈ G × (0,T) ( x , t ) ∈ G × ( 0 , T ) , where u=(u₁,⋯ ,uₘ) u = ( u 1 , ⋯ , u m ) is the unknown, G G is a homogeneous Carnot group on RN R N , Δ G Δ G is the operator whose components are given by the sub-Laplacian on G G , and $${aligned} H(x,t ,u)=( ts_1 \ |x|Gγ _1 \ u_2p_1, ts_2 \ |x|Gγ _2 \ u_3p_2, ⋯ , t^{sₘ} \ |x|G^{γ ₘ} \ u_1^{pₘ} ) , {aligned}$$ H ( x , t , u ) = t s 1 | x | G γ 1 u 2 p 1 , t s 2