When solving problems with contact conditions of the form (1), the rate of convergence of a homogeneous difference scheme becomes very low [19]. In addition, the values of the coefficients at the contact boundary of the two media were. However, they can still be opened by clicking on the corresponding buttons in the mobile version of the application [25].

The data stream is automatically translated to the database and the administrative part of the application. Moreover, the characteristics of the tasks to be solved can be expanded according to the choice of the customer - the company itself. Numerical solution of the system of equations (1), i.e. the gas phase, is carried out in two phases.

The solution of the algebraic equation (8) for temperature is found using the Newton-Raphson iteration method [15].

## Introduction

A proof of a global existence in time of solutions of initial-boundary value problems for nonlinear equations is mostly not easy, even in some cases it is impossible. But by establishing some qualitative properties of its solutions, one can find answers to such questions. For example, by establishing the explosion of a solution in a finite time property, one can show that a solution does not exist globally in time.

Thus, the investigation into the qualitative properties of solutions such as localization and/or inflation in a finite time has developed rapidly. In this work, we study the nonlinear initial boundary value problem for the generalized Kelvin-Voigt equations describing the motion of incompressible viscoelastic non-Newtonian fluids. The equations generalized by replacing the diffusion and relaxation terms in comparison with p(x)-Laplacian and q(x)- Laplacian, respectively, and adding a non-linear absorption term with variable exponents and coefficients.

Under suitable conditions for variable exponents and coefficients, and data for the problem, the blowup of weak solution is established. The name of the Kelvin-Voigt equations has appeared in the works of Oskolkov [4-8], although neither Kelvin nor Voigt proposed any system of equations, and these equations have been used in some cases even before the above works of Oskolkov. For example, in 1966 Ladyzhenskaya [9] has proposed these classical Kelvin-Voigt equations as a regularization to the 3-dimensional Navier-Stokes equations to ensure the existence of unique global solutions, see also and references therein.

Various initial boundary value problems for classical linear and nonlinear Kelvin-Voigt equations have been studied by several authors, for example, for homogeneous fluids, i.e. in recent years, as the generalized PDE by p-Laplacian and nonlinear damping terms, a Research of the modified hydrodynamics equations, in particular, the modified Navier-Stokes equations with p-Laplacian diffusion and with a damping term is being developed with speed, see [16-19]. The system (1)-(4) with a convective term, when all exponents and coefficients are constant, is studied where the existence and uniqueness and qualitative properties of weak solutions such as large time behavior and bursting in a finite time are established .

Organization of this article: In Part 2 we introduce functional spaces, the inequalities and preliminary results used in the analysis. Later, in section 3, we state and prove our main result, in which we identify the conditions under which the weak.

Notation and Preliminaries

## Main result

AP08052425 from Ministry of Education and Science of the Republic of Kazakhstan (MES RK), Kazakhstan. The numerical solution of this model is based on the D2Q9 scheme of the lattice Boltzmann equation method. Calculated phase shifts for the elastic 𝛼𝛼𝛼𝛼+𝑑𝑑𝑑𝑑 scattering of the orbital momentum 𝐿𝐿𝐿𝐿= 0 and 2 , the total angular momentum 𝐽 2 is presented in 2.

They observed that the propagation properties of the obtained DA solitary waves are significantly modified due to the polarization force effect. Finally, Poisson's equation for the given quantum-dusted plasma system can be written as After integrating (13), φ = +∫φdφ′ −V(φ′), the existence and propagation of the fully nonlinear structures in our plasma system can be accurately identified.

Online) International Journal of Mathematics and Physics maximum and minimum values of the Mach number. V , phase portrait (φ,dφ/dζ ), electrostatic potential φ(ζ) and associated electric field E(ζ) are shown graphically for different values of the Mach number M. The profiles and properties of the solitary waves φ(ζ) and the corresponding electric field E(ζ) are shown graphically in figures (lc) and (ld).

The existence of the double layer can be seen as a sudden change of the electrostatic potential pulse φ(ζ) due to the presence of the space charge. 34; tails" of RCC absorption bands with maxima in the short wavelength (SWL) and LWL regions. In general, there are no papers on systematic studies of LWL RIA properties in the scientific literature.

Summary: We study the movement of test particles in the gravitational field of a rotating and deformed object within the framework of the adiabatic theory. The influence of the central body rotation and deformation on the trajectory of the test particles was shown. As an example, the results of this work were applied to the inner planets of the Solar System.

The correspondence between the Erez-Rosen solution and the Hartle Thorne solution in the limiting case ~𝑄𝑄𝑄𝑄 and ~𝑀𝑀𝑀𝑀2”.

The presence of the Fe2O3 phase in the nanocomposite structure is characteristic of Fe3O4 → Fe2O3 type phase transformations that occur at sintering temperatures above 300°C. Increasing the annealing temperature to 600°С leads to an increase in the contribution of NdFeO3. Meanwhile, changes in the shape of the diffraction lines are also observed, which indicate the ordering of the structure.

The general appearance of the obtained spectra depending on the annealing temperature is characterized by two types of changes. As can be seen from the presented data, an increase in the annealing temperature of nanocomposites leads to an increase in the contribution of the seaman sextet characteristic of a. The decrease in the contribution of the quadrupole double characteristic of the disordered regions confirms the results of the X-ray phase analysis of the investigated samples.

At the same time, the change in the phase composition of nanocomposites leads to an increase in the value of the superfine magnetic field, which also indicates the order of the magnetic textures of samples. This article is devoted to the study of the relationship between structural and magnetic ordering as a result of phase transformations in Fe3O4/Nd2O3. The paper considers some cosmological solutions of the Starobinsky model for a flat inhomogeneous viscous universe.

One of the most common examples of F(R) gravity with a high degree of curvature is the Starobinsky model. The relevant equations of motion are determined and the evolution of the Hubble parameter is obtained for two types of viscous fluids. The dependence of the function F(R) on the Ricci scalar is given in this paper similarly to the Starobinsky model F(R)=α +R βR2, where α ,β =const.

For our model, we study the general form of the equation of state for an inhomogeneous viscous fluid [17-20]. Figure 2 – Dynamics of the Hubble parameter for different solutions for the blue line, for the red line. Thus, in this work, we discussed some cosmological solutions of the Starobinsky model for a flat and homogeneous universe.