详细
An averaging method is constructed for two-component distributed kinetic systems with low diffusion in a limited one-dimensional region with impermeability conditions at the boundary. Transformations of the considered distributed system are constructed, which make it possible to allocate one “fast” and a countable number of “slow” variables. Theorems on the correspondence of stationary and periodic solutions, as well as invariant tori of averaged equations of “slow” variables, respectively, to spatially inhomogeneous periodic solutions and invariant tori of initial equations of a similar stability character are proved. Algorithms for constructing periodic solutions (cycles) and invariant tori of the initial equations in the form of a power expansion of a small parameter are proposed, providing the construction of asymptotic formulas for these self-oscillating objects. The conditions for convergence of the corresponding expansions are formulated.