title: To the Problem on Small Oscillations of a System of Two Viscoelastic Fluids Filling Immovable Vessel: Model Problem
abstract: In this paper, we study the scalar conjugation problem, which models the problem of small oscillations of two viscoelastic fluids filling a fixed vessel. An initial-boundary value problem is investigated and a theorem on its unique solvability on the positive semiaxis is proven with semigroup theory methods. The spectral problem that arises in this case for normal oscillations of the system is studied by the methods of the spectral theory of operator functions (operator pencils). The resulting o
journal: Contemporary Mathematics Fundamental Directions