Abstract In this paper, we consider a coupled parabolic system with multiple Henón-type components (ₜ u - ₆ 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, ₆ Δ G is the operator whose components are given by the sub-Laplacian on G G, and aligned H (x, t, u) = (t^s₁ \ |x| ₆^ ₁ \ u₂^p₁, t^s₂ \ |x| ₆^ ₂ \ u₃^p₂, , t^s₌ \ |x| ₆^ ₌ \ u₁^p₌), aligned H (x, t, u) = t s 1 | x | G γ 1 u 2 p 1, t s 2
Freire et al. (Tue,) studied this question.