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On the relation between the Maslov-Whitham method and the weak asymptotics method
P. 55-65.
We explain the relation between the weak asymptotics method introduced by the author and V. M. Shelkovich and the classical Maslov-Whitham method for constructing approximate solutions describing the propagation of nonlinear solitary waves.
In book
Vol. 88. , Warsz. : PWN, 2010
Л.И. Кузьмина, Осипов Ю. В., Вестник Московского государственного строительного университета 2015 № 1 С. 54-62
The mechanical-geometric model of the suspension filtering in the porous media is considered. Suspended solid particles of the same size move with suspension flow through the porous media - a solid body with pores - channels of constant cross section. It is assumed that the particles pass freely through the pores of large diameter and ...
Added: February 9, 2015
Кузьмина Л.И., Осипов Ю. В., В кн. : Вопросы прикладной математики и вычислительной механики: сборник научных трудов. Т. 18.: М. : Издательство АСВ, 2015. С. 270-275.
Filtering the suspension in porous media is important for long-term assessment of the strength of soil in the construction of underground and hydraulic engineering structures. The geometrical and mechanical model of filtering is considered: solid particles pass freely through the larger pores, and get stuck at the entrance of tiny pores smaller than the diameter ...
Added: February 26, 2016
Кузьмина Л.И., Осипов Ю. В., В кн. : Вопросы прикладной математики и вычислительной механики. Сборник научных трудов. Вып. 17.: М. : Национальный исследовательский Московский государственный строительный университет, 2014. С. 295-304.
A mathematical model of particle motion in the filter based on mechanical-geometrical interaction of particles with a porous medium is considered. Near the wave front an asymptotic solution of a quasi-linear system of partial differential equations for suspended and deposited particle concentrations is constructed. For a linear filtration coefficient asymptotics is compared with the exact ...
Added: September 7, 2014
Bruning J., Grushin V. V., Dobrokhotov S. Y., Математические заметки 2012 Т. 92 № 2 С. 163-180
An example of Schrodinger and Klein-Gordon equations with fast oscillating coefficients is used to show that they can be averaged by an adiabatic approximation based on V.P. Maslov's operator method. ...
Added: December 24, 2012
Радиальный подшипник конечной длины, обладающий повышенной несущей способностью с учетом сил инерции
Ахвердиев К. С., Kovalenko E. V., Мукутадзе М. А., Вестник Ростовского государственного университета путей сообщения 2011 № 2 С. 155-160
On the basis of full stationary Navier-Stokes and Darcy equations an asymptotic solution of the hydrodynamic calculation of the porous bearing of finite length is presented. On the basis of numerical analysis obtained in the analytical expression for the bearing capacity is established that when the permeability of the porous layer varies according to the ...
Added: December 14, 2012
Кузьмина Л.И., Осипов Ю. В., Вестник Московского государственного строительного университета 2016 № 2 С. 49-61
The problem of filtering a suspension of tiny solid particles in a porous medium is con-sidered. The suspension with constant concentration of suspended particles at the filter inlet moves through the empty filter at a constant speed. There are no particles before the front; behind the front of the fluid flow solid particles interact with ...
Added: February 26, 2016
Кузьмина Л.И., Осипов Ю. В., В кн. : Вопросы прикладной математики и вычислительной техники. Сборник трудов. Вып. 19.: М. : Издательский дом АСВ, 2016. С. 275-288.
The flow of monodispersed suspension in porous media with geometric capture mechanism of solid particles in filter pores is considered. Based on the integral representation of the solution the asymptotic solution of deep bed filtration problem near the concentration front is constructed and proved. ...
Added: September 11, 2016
Danilov V., Mitrovic D., Bojkovic V., Mathematical Methods in Applied Sciences 2010 Vol. 33 P. 904-921
Using the weak asymptotic method, we approximate a triangular system of conservation laws arising from the so-called generalized pressureless gas dynamics by a diagonal linear system. Then, we apply the usual method of characteristics to find approximate solution to the original system. As a consequence, we shall see how the delta shock wave naturally arises ...
Added: April 12, 2012
Ludmila I. Kuzmina, Osipov Y., International Journal for Computational Civil and Structural Engineering 2016 Vol. 12 No. 1 P. 158-163
Asymptotic model of suspension filtration in a porous media is considered. Asymptotic solution of the fil-tration problem is constructed for large values of time. To determine the asymptotics an integral form of solution is used. The asymptotics is compared with numerical solution. ...
Added: April 4, 2016
Пиковский А., Chaos 2020 Vol. 30 No. 053119 P. 1-8
In the present paper, we study phase waves of self-sustained oscillators with a nearest-neighbor dispersive coupling on an infinite lattice. To analyze the underlying dynamics, we approximate the lattice with a quasi-continuum (QC). The resulting partial differential model is then further reduced to the Gardner equation, which predicts many properties of the underlying solitary structures. ...
Added: October 31, 2020
Liudmila Kuzmina, Osipov Y., , in : IOP Conference Series: Materials Science and Engineering, Volume 365, Safety in Construction XXI International Scientific Conference on Advanced in Civil Engineering "Construction - The Formation of Living Environment" (FORM 2018). Vol. 365.: IOP Publishing, 2018. Ch. 042003. P. 1-7.
Modelling of the suspended particles transport in a porous medium is used in the analysis of methods for strengthening foundations. To strengthen the porous soil, a low concentration cement-based grout is pumped into it under pressure. The suspension is filtered in a porous medium and fills the cavity of the soil. Grains of the grout ...
Added: November 2, 2018
Kurkina O. E., Singh N., Stepanyants Y., Physics Letters A 2014
A new model equation describing weakly nonlinear long internal waves at the interface between two thin layers of different density is derived for the specific relationships between the densities, layer thicknesses and surface tension between the layers. The equation derived and dubbed here the Gardner–Kawahara equation represents a natural generalisation of the well-known Korteweg–de Vries ...
Added: June 3, 2014
Ludmila I.Kuzmina, Osipov Y., Galaguz Y., International Journal for Computational Civil and Structural Engineering 2017 Vol. 13 No. 3 P. 70-76
The study of filtration as one of the problems of underground hydromechanics is necessary for the design and construction of tunnels, underground and hydraulic structures. Deep bed filtration of suspension in a porous medium with variable porosity and permeability and with an initial deposit is considered. An asymptotic solution to a model with small limit ...
Added: January 6, 2018
Ludmila I. Kuzmina, Osipov Y., Procedia Engineering 2015 Vol. 111 P. 491-494
Filtering the suspension in a porous soil is important for long-term evaluation of soil strength in the construction of underground and hydrotechnical structures. A size-exclusion model of solid particle capture for a flow of suspension in a porous media is considered: particles pass freely through the large pores and get stuck at the inlet of ...
Added: August 15, 2015
LIUDMILA I. KUZMINA, OSIPOV Y., International Journal for Computational Civil and Structural Engineering 2021 Vol. 17 No. 2 P. 43-49
During the construction of hydraulic and underground structures, a grout solution is pumped into the ground
to create waterproof partitions. The liquid grout is filtered in the porous rock and clogs the pores when hardened. The
mathematical model of deep bed filtration describes the transfer of suspension particles and colloids by a fluid flow through
the pores of ...
Added: October 18, 2021
Ludmila I. Kuzmina, Osipov Y., International Journal for Computational Civil and Structural Engineering 2014 Vol. 10 No. 3 P. 17-22
A size-exclusion model of solid particle capture for a flow of suspension in a porous media is considered. For a quasi-linear system of equations for the concentration of suspended and retainrd particles the asymptotic solution is constructed near the filter inlet. For linear filtration coefficient the numerical comparison of the asymptotics and the exact solution ...
Added: September 14, 2014
Дмитриев М.Г., Сачков Ю. Л., Дифференциальные уравнения 2013 Т. 49 № 11 С. 1381-1389
В одной задаче оптимального управления, связанной с восстановлением поврежденного изображения, при регуляризации простейшего функционала энергии показывается, с помощью построения и анализа асимптотики решения соответствующей сингулярно возмущенной задачи, что оптимальное управление наряду с магистральным участком содержит и зоны быстрого изменения на границах интервала. ...
Added: November 15, 2013
Pelinovsky E., Talipova T. G., Terletska K. et al., Physics of Fluids 2013 No. 25 P. 032110
Internal solitary wave transformation over the bottom step: loss of energy. ...
Added: November 23, 2013
Сипайло П. А., В кн. : Научно-техническая конференция студентов, аспирантов и молодых специалистов МИЭМ, посвященная 50-летию МИЭМ. : М. : Московский государственный институт электроники и математики, 2012. С. 32-32.
В статье рассматриваются асимптотические решения волнового уравнения с вырождающейся скоростью. ...
Added: April 4, 2013
Osipov Y., Kuzmina L., , in : Procedia Engineering, 153 (2016), XXV Polish – Russian – Slovak Seminar “Theoretical Foundation of Civil Engineering". Vol. 153.: Elsevier, 2016. P. 366-370.
Problems of deep bed filtration of the suspension in a porous soil are important for the design and construction of tunnels and hydrotechnical structures. A size-exclusion model of solid particle capture in a porous media is considered. For deep bed filtration equations an asymptotic solution for the concentrations of suspended and retained particles is constructed ...
Added: June 22, 2018
L I Kuzmina, Osipov Y., Zheglova Y., , in : VII International Symposium Actual Problems of Computational Simulation in Civil Engineering. Vol. 456.: IOP Publishing, 2018. Ch. 012051. P. 1-6.
The solution of the filtration problem allows calculating the injection of the grout
into a loose ground to create a solid foundation. The basic deep bed filtration model of a
monodisperse suspension in a porous medium is considered. Based on the synthesis of the
standard asymptotic solution for a short time and the asymptotics of the filtration problem ...
Added: January 18, 2019
V.S.Samovol, Mathematical notes 2015 Vol. 97 No. 1-2 P. 100-110
Emden-Fowler type equations of arbitrary order are considered. The paper contains asymptotic estimates of nonoscillating continuable and noncontinuable solutions of such equations. ...
Added: October 8, 2015
Л.И. Кузьмина, Осипов Ю. В., International Journal for Computational Civil and Structural Engineering 2017 Т. 13 № 1 С. 63-68
Filtration of the suspension in a porous medium with a geometric particle capture mechanism is considered. The porous medium has an initial deposit unevenly distributed across the filter. The nonlinear model of deep bed filtration suggests that the porosity and permeability of the porous medium depend on the deposit. The asymptotics of the movable boundary ...
Added: January 6, 2018