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1.
The purpose of this paper is to investigate problems of the Navier-Stokes approximation to kinetic equations in terms of the
so-called Chapman-Enskog projection. One considers properties of the Chapman-Enskog projection for the Cauchy problem for
moment approximations of the kinetic equation and primarily the Chapman-Enskog projection for the Boltzmann-Peierls kinetic
equation. The existence of the Chapman-Enskog projection for the Cauchy problem is proved for the phase space of conservative
variables (phenomena of nonlinear diffusion) and for the phase space of physical variables (the second sound projection).
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Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 25, pp. 184–225, 2005. 相似文献
2.
E. V. Radkevich 《Journal of Mathematical Sciences》2004,123(5):4428-4455
The paper is devoted to the study of the asymptotic behavior of solutions to linearized systems of equations of the so-called nonequilibrium thermodynamic moments. 相似文献
3.
This article concerns the nonlinear asymptotic analysis of the mathematical model of a multi-component poroelastic medium with the porosity balance equation. It is proved that there exist soliton-like solutions for porosity and kink-like solutions for phase velocities under conditions similar to the entropy one. It is shown that solutions appear that describe a regime of stable displacement (so-called piston displacement) and a regime similar to the Saffman–Taylor instability. It is established that the diffusion force of interaction between phases of the inner friction type causes a decrease in the amplitudes of the discontinuities. This leads to the damping of initial perturbations of stable states. Such regimes have some properties similar to those of the pendulum model in the vicinity of a stable equilibrium point. 相似文献
4.
In this paper, we study the linearization of the Cauchy problem and the mixed problem for the system of Grad--Hermite moments in nonequilibrium thermodynamics in the neighborhood of the equilibrium state. Stability conditions for solutions of the Cauchy problem are proved as a generalization of the classical Hermite--Biller theorem on stable polynomials. For the mixed problem, we prove an analog of the Vishik--Lyusternik theorem on small singular perturbations of general elliptic problems. The last observation allows us to introduce the Shapiro--Lopatinskii condition, which implies the well-posedness of the mixed problem. 相似文献
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6.
V. A. Batanov V. S. Petriv A. O. Radkevich A. L. Telyatnikov A. Yu. Volkov 《International Journal of Infrared and Millimeter Waves》1991,12(7):703-715
High power IR pumping beams self focusing and defocusing in NH3 Raman laser is investigated by numerical methods on the basis of the solution of nonlinear quasioptical equations. The analysis of self focusing have been done for a wide range of parameters of radiation and of active medium. Spatial evolution of the beam configuration have been investigated for different regimes of nonlinear diffraction. Developed model enables to allow exactly for the spectroscopic features of active molecules and may be applied to the analysis of the properties of powerful optically pumped FIR lasers. 相似文献
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V. Z. Radkevich A. Yu. Volodin M. F. Gorbatsevich V. P. Sokol Yu. G. Egiazarov 《Russian Journal of Applied Chemistry》2012,85(12):1887-1892
A procedure is suggested for determining the degree of palladium reduction in fibrous anion exchangers from data on the quantitative recovery of Pd(II) from samples with a hydrochloric acid solution of thiourea before and after the reduction stage. 相似文献
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