A study of the stability of solutions of linear parabolic equations with nearly constant coefficients and small diffusion

We study the stability of the solutions of boundary value problems for a certain class of Petrovskii-parabolic systems with sufficiently small diffusion coefficients. The dimension of the set of critical cases in the stability problem turns out to be infinite. We develop an efficient algorithm for studying stability. As examples we consider parabolic boundary value problems with delay and rapidly oscillating coefficients, the problem of parametric resonance under a double-frequency perturbation, and problems with variable leading terms and variable domain of definition. Bibliography: 21 titles.Translated fromTrudy Seminara imeni I. G. Petrovskogo, No. 15, pp. 128–155, 1991.