A non-local coupling model involving three fractional Laplacians

In this paper, we study a non-local diffusion problem that involves three different fractional Laplacian operators acting on two domains. Each domain has an associated operator governs the it, and third serves as coupling mechanism between of them. The model proposed is gradient flow energy functional. first part provide results about existence solutions conservation mass. second encompasses [Formula: see text] decay solutions. devoted to study, asymptotic behavior when domains are ball its complementary. Exterior Sobolev Nash inequalities independent interest also provided in Appendix A.