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Том 239, № 5 (2019)
- Год: 2019
- Статей: 6
- URL: https://ogarev-online.ru/1072-3374/issue/view/15009
Article
Morse–Smale Systems and Topological Structure of Carrier Manifolds
Аннотация
We review the results describing the connection between the global dynamics of Morse–Smale systems on closed manifolds and the topology of carrier manifolds. Also we consider the results related to topological classification of Morse–Smale systems.
549-581
Oldroyd Model for Compressible Fluids
Аннотация
In this paper, mathematical models of compressible viscoelastic Maxwell, Oldroyd, and Kelvin–Voigt fluids are derived. A model of rotating viscoelastic barotropic Oldroyd fluid is studied. A theorem on strong unique solvability of the corresponding initial-boundary value problem is proved. The spectral problem associated with such a system is studied. Results on the spectrum localization, essential and discrete spectra, and spectrum asymptotics are obtained. In the case where the system is in the weightlessness state and does not rotate, results on multiple completeness and basis property of a special system of elements are proved. In such a case, under the assumption the viscosity is sufficiently large, an expansion of the solution of the evolution problem with respect to a special system of elements is obtained.
582-607
Abstract Mixed Boundary-Value and Spectral Conjugation Problems and their Applications
Аннотация
Based on the abstract Green formula, we study a general approach to abstract boundary value conjugation problems. We consider examples of some configurations of docked domains for conjugation problems, using the generalized Green formula for the Laplace operator. Also, we consider spectral problems with two complex parameters: one of them can be treated as a fixed one, while the other can be treated as the spectral one. By means of the proposed general approach, we reduce those problems to the spectral problem for operator bundles with self-adjoint operator coefficients acting in Hilbert space and depending on two parameters.
608-643
On the Volume Formula for a Hyperbolic Octahedron with mm2-Symmetry
Аннотация
In this paper, explicit integral volume formulas for arbitrary compact hyperbolic octahedra with mm2-symmetry are obtained in terms of dihedral angles. Also, we provide an algorithm to compute the volume of such octahedra in spherical spaces.
644-653
Topological Algebras of Measurable and Locally Measurable Operators
Аннотация
In this paper, we review the results on topological ∗-algebras S(M), S(M, τ), and LS(M) of measurable, τ -measurable, and locally measurable operators affiliated with the von Neumann algebra M. Also, we consider relations between those algebras for different classes of von Neumann algebras and establish the continuity of operator-valued functions with respect to the local convergence in measure. We describe maximal commutative ∗-subalgebras of the algebra LS(M) as well.
654-705
On Coercive Solvability of Parabolic Equations with Variable Operators
Аннотация
In a Banach space E, the Cauchy problem
is considered for a differential equation with linear strongly positive operator A(t) such that its domain D = D(A(t)) does not depend on t and is everywhere dense in E and A(t) generates an analytic semigroup exp{−sA(t)}(s ≥ 0). Under natural assumptions on A(t), we prove the coercive solvability of the Cauchy problem in the Banach space \( {C}_0^{\beta, \upgamma} \) (E). We prove a stronger estimate for the solution compared with estimates known earlier, using weaker restrictions on f(t) and v0.
706-724