Fujita-Type Results for a Coupled Parabolic System of Hénon-Type Equations on Homogeneous Carnot Groups
Year: 2026
Type: article
Abstract: In this paper, we consider a coupled parabolic system with multiple Henón-type components $$\left( \partial _t \textbf{u} - \Delta _{\mathbb {G}} \textbf{u} \right) (x,t) = H(x,t,\textbf{u})$$ ∂ t u - Δ G u ( x , t ) = H ( x , t , u ) for $$ (x,t) \in \mathbb {G} \times (0,T)$$ ( x , t ) ∈ G × ( 0 , T ) , where $$\textbf{u}=(u_1,\cdots ,u_m) $$ u = ( u 1 , ⋯ , u m ) is the unknown, $$\mathbb {G}$$ G is a homogeneous Carnot group on $$\mathbb {R}^N$$ R N , $$\Delta _{\mathbb {G}}$$ Δ G is the operator whose components are given by the sub-Laplacian on $$\mathbb {G}$$ G , and $$\begin{aligned} H(x,t ,\textbf{u})=\left( t^{s_1} \ |x|_{\mathbb {G}}^{\gamma _1} \ u_2^{p_1}, t^{s_2} \ |x|_{\mathbb {G}}^{\gamma _2} \ u_3^{p_2}, \cdots , t^{s_{m}} \ |x|_{\mathbb {G}}^{\gamma _{m}} \ u_1^{p_{m}} \right) , \end{aligned}$$ H ( x , t , u ) = t s 1 | x | G γ 1 u 2 p 1 , t s 2
Source: Journal of Geometric Analysis
Authors: Ricardo Freire, Ricardo Castillo, Miguel Loayza
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,290
OpenAlex ID: W7161697409