Romanov, V. G. Bugueva, T. V. Dedok, V. A.
Published in
Journal of Applied and Industrial Mathematics

Abstract Given a hyperbolic equation with variable coefficients, we construct a regularizing algorithm to solve the problem of continuation of the wave field from the boundary of the half-plane inside it. We introduce some \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{...

Voblyi, V. A.
Published in
Journal of Applied and Industrial Mathematics

Abstract We deduce an explicit formula for the number of labeled series-parallel \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k $$\end{document}-cyclic \documentclas...

Musabekov, K. S.
Published in
Journal of Applied and Industrial Mathematics

Abstract We consider an optimal control problem for some mathematical problem of a chemical reactor. We prove the existence of a solution to the system in variations which arises in deriving a necessary optimality condition in the form of the Pontryagin Maximum Principle.

Senashov, S. I. Savostyanova, I. L.
Published in
Journal of Applied and Industrial Mathematics

Abstract We consider the equations of nonlinear elasticity assuming that the components of the deformation vector depend only on the two space coordinates each of which has the two corresponding coordinates. Some system of the three differential equations for three tangent components of the stress tensor is obtained in result of this study. This sy...

Rudoy, E. M. Itou, H. Lazarev, N. P.
Published in
Journal of Applied and Industrial Mathematics

Abstract The equilibrium problem for an elastic body having an inhomogeneous inclusion with curvilinear boundaries is considered within the framework of antiplane shear. We assume that there is a power-law dependence of the shear modulus of the inclusion on a small parameter characterizing its width. We justify passage to the limit as the parameter...

Ustiuzhaninova, A. S. Turbin, M. V.
Published in
Journal of Applied and Industrial Mathematics

Abstract We study the qualitative behavior of weak solutions to an autonomous modified Kelvin–Voigt model on the base of the theory of attractors for noninvariant trajectory spaces. For the model under consideration, we determine the trajectory space, introduce the notions of a trajectory attractor and a global attractor, and prove the existence of...

Mamontov, A. E. Prokudin, D. A.
Published in
Journal of Applied and Industrial Mathematics

Abstract We consider the equations of a multivelocity model of a binary mixture of viscous compressible fluids (the two-fluid medium) in the case of one-dimensional barotropic motions. We prove the time global existence and uniqueness of a strong solution to the initial-boundary value problem describing the motion in a bounded space domain.

Neshchadim, M. V. Chupakhin, A. P.
Published in
Journal of Applied and Industrial Mathematics

Abstract Complete integration is carried out of the matrix Riccati equation arising in continuum mechanics in the two-dimensional case. The method of commutators is used to obtain some compatibility conditions.

Neverov, V. V.
Published in
Journal of Applied and Industrial Mathematics

Abstract We prove the theorem of global existence of a weak solution to an one-dimensional initial-boundary value problem for the micropolar fluid equations under the condition of axial symmetry. The micropolar fluid model is a well-known generalization of the classical Navier–Stokes equations for the case when the rotation of the continuum particl...

Razvenskaya, O. O. Malyshev, D. S.
Published in
Journal of Applied and Industrial Mathematics

Abstract The weighted vertex coloring problem for a given weighted graph is to minimize the number of colors so that for each vertex the number of the colors that are assigned to this vertex is equal to its weight and the assigned sets of vertices are disjoint for any adjacent vertices. For all but four hereditary classes that are defined by two co...