Fractional elliptic reaction-diffusion systems with coupled gradient terms and different diffusion
In this work, we study the existence and nonexistence of nonnegative solutions to a class of nonlocal elliptic systems set in a bounded open subset of $\mathbb{R}^N$. The diffusion operators are of type $u_i\mapsto d_i(-\Delta)^{s_i}u_i$ where $0<s_1\neq s_2<1$, and the gradients of the unknowns act as source terms. Existence results are obtained by proving some fine estimates when data belong to weighted Lebesgue spaces. Those estimates are new and interesting in themselves.
Authors
- Maha Daoud
- Kheireddine Biroud (ORCID: https://orcid.org/0000-0002-0972-5265)
- Somia Atmani
- El-Haj Laamri (ORCID: https://orcid.org/0000-0001-8204-7483)
Institutions
- University of Abou Bekr Belkaïd (DZ)
- Institut Élie Cartan de Lorraine (FR)
- École Supérieure en Sciences Appliquées de Tlemcen (DZ)
- Laboratoire d’Analyse et de Mathématiques Appliquées (FR)
- Institut Polytechnique de Paris (FR)
- Université de Lorraine (FR)
- University of Hassan II Casablanca (MA)
Publication Details
- Journal
- Complex Variables and Elliptic Equations
- Published
- 2025-08-26
- DOI
- https://doi.org/10.1080/17476933.2025.2549908
- Primary Topic
- Advanced Mathematical Modeling in Engineering
- Type
- article
- Field-Weighted Citation Impact
- 0.00