Abstract
Under certain assumptions, the existence of two families of solutions to the stationary problem is proved and asymptotic expansions with respect to a small parameter are established. The stability of these families of solutions is shown. The problem under consideration has a solution connected with the so-called interior transition layer. In the case of a nonstationary problem, the existence and uniqueness of a solution are established for any t>0. Under certain assumptions, the nonstationary problem defines a dynamical system in some compact set. Bibliography: 5 titles.
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