The phenomenological equation of spin combustion, when the zone of combustion reaction spread is the ring, is considered. The action of pseudo-differential operator \((-\Delta )^{\alpha }\) , \(0<\alpha <1\) is determined by spectral decomposition, and the existence and uniqueness of global solution of initial-boundary value problem of spin combustion are proved. The equation is a singularly perturbed nonlinear parabolic equation of the Van-der-Pol’s type with Neumann conditions. Using Galerkin’s method with the Krylov-Bogoliubov-Mitropolsky-Samoilenko method, an asymptotic of solution was constructed, and a bifurcation analysis was conducted. The structure and stability of created solutions such as rotating waves were investigated. The theorem about the stability of solution of a quasi-normal form of the problem was proved. The interconnection between the given model and the model of spin combustion in a circumference is obtained.
