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Dnipro National University
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- Professor (Associate)
Publications
Publications (22)
Some discrete models for a simplified (compared to that published earlier in JODEA, 28 (1) (2020), 1 – 42) initial boundary value problem for a 1D linear degenerate wave equation, posed in a space-time rectangle and solved earlier exactly (JODEA, 30 (1) (2022), 89 – 121), have been considered. It has been demonstrated that the correct evaluation of...
The separation of variables based solution to a simplified (compared to that published earlier in JODEA, 28 (1) (2020), 1-42) initial boundary value problem for a 1D linear degenerate wave equation, posed in a space-time rectangle, has been presented in a fully complete form. Degeneracy of the equation is due to vanishing its coefficient in an inte...
![Fig. 7.2. The rectangular region [−2.5, +2.5] × [0.0, 25.0] ∈ C in...](profile/Peter-Kogut/publication/357228718/figure/fig2/AS:1103615045451777@1640133739589/The-rectangular-region-25-25-00-250-C-in-which-the-lines-of-zero-values_Q320.jpg)
A 1-parameter initial-boundary value problem for a linear spatially 1-dimensional
homogeneous degenerate wave equation, posed in a space-time rectangle, in case of strong degeneracy, was reduced to a linear integro-differential equation of convolution type (JODEA, 29(1) (2021), pp. 1–31). The former was then solved by applying the Laplace transform...
A 1-parameter initial boundary value problem (IBVP) for a linear homogeneous
degenerate wave equation (JODEA, 28(1), 1) in a space-time rectangle is considered. The origin of degeneracy is the power law coefficient function with respect to the spatial distance to the symmetry line of the rectangle, the exponent being the only parameter of the probl...
A 1-parameter initial boundary value problem for the linear homogeneous degenerate wave equation u tt (t, x; α)−(a(x; α) u x (t, x; α)) x = 0 (JODEA, 27(2), 29-44), where: 1) (t, x) ∈ [0, T ] × [−l, +l]; 2) the weight function a(x; α): a) a 0 x c α , 0 |x| c; b) a 0 , c |x| l; c) a 0 is a constant reference value; and 3) the parameter α ∈ (0, +∞);...
![Fig. 5.3. A structured grid in space-time rectangle [0, T ] × [−l, +l]...](publication/338780805/figure/fig3/AS:850667543465985@1579826355264/A-structured-grid-in-space-time-rectangle-0-T-l-l-is-composed-of-N-K-nodes_Q320.jpg)
Initial boundary value problems in space-time rectangle for the following linear inhomogeneous degenerate wave equation of the second order smooth coefficient function a(x) vanishes in single points of segment.
The well-posedness of the initial boundary value problems is achieved using some approaches to regularization of the equation and the theor...
Some implications concerning an unobservable medium whose micro-motion
(rotational motion in Faraday vortex tubes) produces magnetic phenomena after Maxwell, used in a previous article on the origin of Maxwell’s equation for the magnetic induction (JODEA, 26 (1), 29 – 44) are clarified and explained.
It is shown that `a free function' in the evolution equation of Hornig & Schindler for the magnetic induction (Physics of Plasmas, 3 (3), 781 - 791) has a unique representation, obtained in an explicit form. Some conclusions of the explicit formulation of the evolution equation are discussed.
The representation u(x) = F2(x)Qm-2(x)+Qm(x) for the solution to the Dirichlet problem for the Laplace equation in a disk: F2(x) = jx - x0j2 - c2 6 0, is proved using the Poisson integral; Qm(x) being the polynomial boundary function of degree m, Qm-2(x) being the uniquely determined polynomial of degree m - 2.
The Boltzmann correction to the Maxwell induction law for a moving medium
lled with vortex tubes of Faraday has been implemented.
Доказано, что решение задачи Дирихле в круге, на границе F2(x1, x2) = 0 которо- го задано условие в виде многочлена Qm(x1, x2) степени m, допускает однозначное пред- ставление u(x1, x2) = F2(x1, x2) Pm−2(x1, x2) + Qm(x1, x2), где Pm−2(x1, x2) — многочлен степени m − 2.
Publications of V. I. Perekhrest with numerous applications of a class of exact vortex solutions to the Euler equations for incompressible media to celestial mechanics, cosmogony, and cosmology, have been studied.
The three-shock configuration is quite typical for the aircraft internal and external aerodynamics. For example, it appears at supersonic steady free-stream conditions in intakes (Fig. 1, left) and unsteady shock wave reflection from 2D wedges (Fig. 1, right). In the latter case the resulting flow is experimentally proven to be pseudo-stationary, a...
Numerical computations of inviscid flows over series of caret waveriders at angles of attack from no incidence up to on-design values α* and at on-design Mach numbers M* have been performed. Both explicit and implicit time-asymptotic shock-capturing finite-volume techniques and different numerical fluxes (Van Leer, Roe, HLLE and AUSM families) comb...
Flow over a concave cone-shaped wing at M = 3 and angles of attack α of 0, 5 and 10° is evaluated in the quasiconical approximation for Navier-Stokes equations, employs the direct McCormack method. The results reveal new elements in the structure of the flow on the windward side of the wing.
The interference of supersonic flows on the concave surface of conical wings was experimentally investigated in [1] for various values of the camber and angles of attack. In order to establish the detailed structure of the interference flow the laminar flow past a wing model in the form of half the surface of a circular cone with vertex angle 2k =...
