http://dspace.nbuv.gov.ua:80/handle/123456789/10109 Fri, 10 Apr 2026 13:29:54 GMT 2026-04-10T13:29:54Z http://dspace.nbuv.gov.ua:80/bitstream/id/265842/ http://dspace.nbuv.gov.ua:80/handle/123456789/10109 http://dspace.nbuv.gov.ua:80/handle/123456789/124265 Averaging of the Dirichlet problem for the spectral hyperbolic quasilinear equation Sidenko, N.R. In this paper we establish su cient conditions on the data of the problem which guarantee a convergence of its solution to a limit solution. The domains where we consider the problem has a ne-grained structure.We use S.I.Pohozhaev's method for the proof of the unique solvability in entire and the D.Cioranescu-F.Murat hypothesis for the description of the domain milling. Tue, 01 Jan 2008 00:00:00 GMT http://dspace.nbuv.gov.ua:80/handle/123456789/124265 2008-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/124264 The behavior of solutions of the mixed boundary value problem for a linear second-order elliptic equation in a neighbourhood of intersecting edges Plesha, M. In this paper we deals with the mixed boundary value problem for secondorder elliptic equations in a polyhedral domain. We obtain exact estimates for solutions of the problem in a neighbourhood of an vertex. A special section is dedicated to the examples. Tue, 01 Jan 2008 00:00:00 GMT http://dspace.nbuv.gov.ua:80/handle/123456789/124264 2008-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/124263 The Stefan problem Borodin, M.A. The Stefan problem in its classical statement is a mathematical model of the process of propagation of heat in a medium with di erent phase states, e.g., in a medium with liquid and solid phases.The process of propagation of heat in each phase is described by the parabolic equations. In this work we prove the existence of the global classical solution in a two-phase multidimensional Stefan problem. We apply a method which consists of the following. First, we construct approximating problems, then we prove some uniform estimates and pass to the limit. Tue, 01 Jan 2008 00:00:00 GMT http://dspace.nbuv.gov.ua:80/handle/123456789/124263 2008-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/124262 Asymptotic analysis of a vibrating system containing stiff-heavy and flexible-light parts Babych, N.; Golovaty, Yu. A model of a strongly inhomogeneous medium with simultaneous perturbation of the rigidity and mass density is studied. The medium has strongly contrasting physical characteristics in two parts with the ratio of rigidities being proportional to a small parameter ". Additionally, the ratio of mass densities is of order " ε⁻¹. We investigate the asymptotic behaviour of the spectrum and eigensubspaces as ε → 0. Complete asymptotic expansions of eigenvalues and eigenfunctions are constructed and justified. We show that the limit operator is nonself-adjoint in general and possesses two-dimensional Jordan cells in spite of the singular perturbed problem is associated with a self-adjoint operator in appropriated Hilbert space Lε. This may happen if the metric in which the problem is self-adjoint depends on small parameter " in a singular way. In particular, it leads to a loss of completeness for the eigenfunction collection. We describe how root spaces of the limit operator approximate eigenspaces of the perturbed operator. Tue, 01 Jan 2008 00:00:00 GMT http://dspace.nbuv.gov.ua:80/handle/123456789/124262 2008-01-01T00:00:00Z