Asymptotic behaviour of the solution to a singularly perturbed partially dissipative system with a multiple root of the degenerate equation

Asymptotic formulae for the solution of the initial-boundary value problem for a singularly perturbed partially dissipative system of reaction-diffusion type are constructed and justified. The system consists of a parabolic and an ordinary differential equation in the case when the corresponding degenerate equation has a root of multiplicity two. The behaviour of the boundary layer functions and the algorithm for constructing them are significantly distinct from the case of a simple (multiplicity-one) root of the degenerate equation.
Bibliography: 8 titles.