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1.
In this paper, we consider the boundary control problem of the unforced generalized Korteweg–de Vries–Burgers (GKdVB) equation
when the spatial domain is [0,1]. Three control laws are derived for this equation and the L
2-global exponential stability of the solution is proved analytically. Numerical results using the finite element method (FEM)
are presented to illustrate the developed control schemes. 相似文献
2.
An extended traffic flow model on a gradient highway with the consideration of the relative velocity
In this paper, an extended traffic flow model on a single-lane gradient highway is proposed with the consideration of the relative velocity. The stability condition is obtained by the use of linear stability analysis. It is shown that the stability of traffic flow on the gradient varies with the slope and the coefficient of the relative velocity: when the slope is constant, the stable regions increase with the increase of the coefficient of the relative velocity; when the coefficient of the relative velocity is constant, the stable regions increase with the decrease of the slope in downhill and increase with the increase of the slope in uphill. The Burgers, Korteweg-de Vries, and modified Korteweg-de Vries equations are derived to describe the triangular shock waves, soliton waves, and kink-antikink waves in the stable, metastable, and unstable region, respectively. The numerical simulation shows a good agreement with the analytical result, which shows that the traffic congestion can be suppressed by introducing the relative velocity. 相似文献
3.
Rathinasamy Sakthivel 《Nonlinear dynamics》2009,58(4):739-744
The problem of robust global stabilization by nonlinear boundary feedback control for the Korteweg–de Vries–Burgers equation
on the domain [0,1] is considered. The main purpose of this paper is to derive nonlinear robust boundary control laws which
make the system robustly globally asymptotically stable in spite of uncertainty in the system parameters. Furthermore, we
show that the proposed boundary controllers guarantee L
2-robust exponential stability, L
∞-robust asymptotic stability and boundedness in terms of both L
2 and L
∞. 相似文献
4.
This paper considers the boundary control problem of the generalized Korteweg–de Vries–Burgers (GKdVB) equation on the interval
[0, 1]. We derive a control law of the form and α is a positive integer, and prove that it guarantees L
2-global exponential stability, H
1-global asymptotic stability, and H
1-semiglobal exponential stability. Numerical results supporting the analytical ones for both the controlled and uncontrolled
equations are presented using a finite element method. 相似文献
5.
The process of propagation of shock waves in two-component mixtures is considered. The studies were performed within the framework
of the two-velocity approximation of mechanics of heterogeneous media with account of different pressures of the components.
The stability of propagation of all types of stationary shock waves (fully dispersed, frozen-dispersed, dispersed-frozen,
and frozen shock waves of two-front configuration) to infinitesimal and finite perturbations is shown numerically, using the
method of coarse particles. The problem of initiation of shock waves (the formation of different types of shock waves from
stepwise initial data) is solved. Flows in the transonic range relative to the speed of sound in the first component are obtained.
Institute of Theoretical and Applied Mechanics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated
from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 1, pp. 55–63, January–February 1999. 相似文献
6.
S.A. Bystrov H. Honma V.I. Ivanov J. Koreeda K. Maeno F.V. Shugaev H. Yanagisawa 《Shock Waves》1998,8(3):183-189
Using a diffraction approach the convolution-type integral equation for the laser schlieren signal created by an arbitrary
disturbance at low pressure, where refractive index of disturbance is close to unity, in a shock tube (thin optical layer)
has been deduced. In the equation electric circuit relaxation processes were taken into account by a response function. The
equation was solved with the aid of the regularization method worked out for ill-posed problems. The density structures of
the strong shock waves in air have numerically been reconstructed from experimental data ranging shock wave Mach number of
–30, and –30 Pa.
Received 7 April 1996 / Accepted 20 June 1996 相似文献
7.
The hydrodynamics of processes occurring in explosion of condensed explosives in air is considered. The physical model, computation
technique, and results of simulation of a two-dimensional hydrodynamic flow arising in explosion of cylindrical charges are
discussed. In this case, the explosions are considered at some distance above the ground. To close the gas-dynamics equations,
the Jones–Wilkins–Lee equation of state is used. The results of calculation allow one to obtain a detailed space–time pattern
of the arising flow and to study the origination, propagation, and subsequent attenuation of shock waves. Cylindrical charges
of the same mass but with different diameter-to-length ratios are considered. It is shown that the charge shape can render
essential influence on dynamics of flow and the parameters of shock waves (in the near and medium fields of explosion). 相似文献
8.
Zh. L. Mal’tseva 《Journal of Applied Mechanics and Technical Physics》1999,40(5):824-830
Solitary waves on an interface between two fluids are considered. A uniform asymptotic expansion is constructed for internal
solitary waves with flat crests (of the plateau type) that degenerate into a bore in the limit. It is shown that, in this
case, in contrast to a Korteweg-de Vries wave, the wave amplitude is of the same order of smallness as the longwave approximation
parameter.
Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from
Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 5, pp. 55–61, September–October, 1999. 相似文献
9.
The purpose of the present investigation is to analyze the phenomenon of shock wave formation in gas-liquid foams and to explain the qualitative differences which are found when comparing results from shock tube experiments performed with foams and bubbly liquids. It is well known that oscillatory pressure waves in bubbly liquids may reach an amplitude twice as large as that of the original pressure impulse. However, experiments showed that pressure disturbances in foams always attenuate without significant change in the wave pressure profile. In the present study this behavior is explained by analyzing shock wave formation using the Burgers equation which is derived from the conservation laws for a bubbly liquid. It is shown that the parameter of non linearity in the Burgers equation describing wave propagation in bubbly liquids is about 40 times higher than in foams. At the same time coefficient of bulk viscosity of a foam is about 103 times greater than that of a bubbly liquid. This explains why in shock tube experiments with foams shock waves are not detected while they are easily observed when bubbly liquids are used under similar conditions. 相似文献
10.
Nonlinear wave dynamics of an elastically deformed saturated porous media is investigated following the Biot approach. Mathematical models under research are the Biot model and its generalization by consideration of viscous stresses inside liquids. Using two-scales and linear WKB methods, the classical Biot system is transformed to a first-order wave equation. To construct the solution of the other system, an asymptotic modified two-scales method is developed. Initial system of equations is transformed to a nonlinear generalized Korteweg–de Vries–Burgers equation for quick elastic wave. Distinctions of wave propagation in the context of the Biot model and its generalization are shown. 相似文献
11.
Paulo Amorim João-Paulo Dias Mário Figueira Philippe G. LeFloch 《Journal of Dynamics and Differential Equations》2013,25(1):49-69
We investigate the coupling between the nonlinear Schrödinger equation and the inviscid Burgers equation, a system which models interactions between short and long waves, for instance in fluids. Well-posedness for the associated Cauchy problem remains a difficult open problem, and we tackle it here via a linearization technique. Namely, we establish a linearized stability theorem for the Schrödinger–Burgers system, when the reference solution is an entropy-satisfying shock wave to Burgers equation. Our proof is based on suitable energy estimates and on properties of hyperbolic equations with discontinuous coefficients. Numerical experiments support and expand our theoretical results. 相似文献
12.
S. S. Kutateladze V. E. Nakoryakov V. V. Sobolev I. R. Shreiber 《Journal of Applied Mechanics and Technical Physics》1974,15(5):638-642
Results are presented of a numerical solution of the Korteweg-de Vries-Burgers equation that describes the propagation and establishment process for a stationary structure to a shock wave in a gas-liquid medium. Data are obtained on the time for the establishment of a stationary structure of a shock wave, propagation velocity, and amplitude oscillations in the front of the shock wave. Experiments are discussed on the basis of the results obtained for the study of shock waves in a liquid containing gas bubbles. 相似文献
13.
M. Mond I. Rutkevich E. Zaretsky 《Archive of Applied Mechanics (Ingenieur Archiv)》2001,71(4-5):317-326
Summary The role of free electrons in the stability of strong shock waves in metals under spontaneous acoustic emission is investigated.
For that purpose, a three-term form of the equation of state is employed in order to describe the cold pressure, the thermal
atomic pressure and the thermal pressure of free electrons. The equation of state enables the calculation of the sound velocity
behind the shock, which in turn is utilized in the Dyakov–Kontorovich criteria for the shock stability. The integral over
the Fermi–Dirac distribution function that describes the specific internal energy of free electrons is replaced by a model
algebraic function that possesses correct asymptotic limits at low and high temperatures. It is shown that strong shock waves
in all metals are prone to instability under spontaneous emission. However, the threshold for that instability is shifted
to higher Mach numbers if free electrons are taken into account. It is further shown that the stabilizing effect of free electrons
is vastly overestimated if the expressions for degenerate electron gas are employed for temperatures that are larger than
the Fermi temperature.
Received 22 November 1999; accepted for publication 12 July 2000 相似文献
14.
Mathematical techniques are proposed which make it possible to reduce the system of magnetohydrodynamic equations for a viscous heat-conducting gas with finite electric conductivity and a general equation of state to the model Burgers equation. On the basis of this equation the structure of weakly nonlinear magnetohydrodynamic shock waves is studied. In particular, the width of the shock wave is estimated.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.4, pp. 43–48, May–June, 1993. 相似文献
15.
R. S. Srivastava 《Shock Waves》2007,17(3):209-212
Lighthill (Proc. R. Soc. A 198, 454–470, 1949) considered the diffraction of a normal shock wave passing over a small bend. The bend being small Lighthill
was able to linearize the flow equations and solved the problem through several mathematical techniques. Following Lighthill
(Proc. R. Soc. A 198, 454–470, 1949), Srivastava and Chopra (J. Fluid Mech. 40, 821–831, 1970) extended the work to the diffraction of oblique shock waves. Srivastava (AIAAJ 33, 2230–2231, 1995) considered the problem of starting point of curvature and extended the work to yawed wedges (Srivastava
in Proceedings of the 14th International Mach reflection symposium Sun Marina Hotel, Yonezawa, Japan, 1–5 October 2000, pp.
225–249, 2002). Srivastava (Shock waves 13, 323–326, 2003) considered the problem for starting point of curvature when the relative outflow behind reflected shock before
diffraction has been subsonic and sonic. The present work is an extension of the work published in Srivastava (Shock waves
13, 323–326, 2003) when the wedge has been yawed through an angle. The results have been obtained for two angles χ = 60° and
χ = 40° (χ is the angle of yaw).
相似文献
16.
A. A. Lugovtsov 《Journal of Applied Mechanics and Technical Physics》2009,50(2):327-335
Equations describing the propagation of waves of small but finite amplitude in a liquid with gas bubbles are derived. The
bubble distribution density is a continuous function of bubble size and spatial coordinates. It is found that, for a uniform
bubble distribution, the obtained equations become the Korteweg-de Vries, Kadomtsev-Petviashvili and Khokhlov-Zabolotskaya
equations.
__________
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 2, pp. 188–197, March–April, 2009. 相似文献
17.
The effect of shock pressures on the inactivation of a marine Vibrio sp. was studied experimentally and numerically. In the experiment, an aluminum impactor plate accelerated by a gas gun was
used to induce shock waves in a sealed aluminum container with cell suspension liquid inside. The shock pressures in the container
were measured by a piezofilm gauge. Several 10–100 MPa of pressure were measured at the shock wave front. An FEM simulation,
using the Johnson–Cook model for solid aluminum and the Tait equation for the suspension liquid, was carried out in order
to know the generation mechanism of shock pressures in the aluminum container. The reflection, diffraction and interaction
of shock waves at the solid–liquid boundaries in the aluminum container were reasonably predicted by the numerical simulation.
The changes in shock pressures obtained from the computational simulation were in good agreement with those from the experiment.
The number of viable cells decreased with the increase of peak pressures of the shock waves. Peak pressures higher than 200 MPa
completely inactivated the cells. At this pressure, the cell structures were deformed like the shape of red blood cells, and
some proteins leaked from the cells. These results indicate that the positive and negative pressure fluctuations generated
by shock waves contribute to the inactivation of the marine Vibrio sp.
相似文献
18.
V. V. Lunyov 《Fluid Dynamics》2000,35(3):443-448
Second-order differential equations of the hyperbolic type are derived for describing the local law of shock wave propagation.
The shock waves are assumed to be two-dimensional unsteady in a stationary gas flow and three-dimensional steady in a supersonic
flow. The behavior of the characteristics of these equations is investigated as a function of the governing flow parameters
and their relative position with respect to the typical bicharacteristics of the characteristic cone behind the shock is analyzed.
Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 159–165, May–June, 2000. 相似文献
19.
The initial boundary value problem for the compressible Navier–Stokes equation is considered in an infinite layer of . It is proved that if the Reynolds and Mach numbers are sufficiently small, then strong solutions to the compressible Navier–Stokes equation around parallel flows exist globally in time for sufficiently small initial perturbations. The large time behavior of the solution is described by a solution of a one-dimensional viscous Burgers equation. The proof is given by a combination of spectral analysis of the linearized operator and a variant of the Matsumura–Nishida energy method. 相似文献
20.
A system of nonlinear equations for describing the perturbations of the pressure and radius in fluid flow through a viscoelastic tube is derived. A differential relation between the pressure and the radius of a viscoelastic tube through which fluid flows is obtained. Nonlinear evolutionary equations for describing perturbations of the pressure and radius in fluid flow are derived. It is shown that the Burgers equation, the Korteweg-de Vries equation, and the nonlinear fourth-order evolutionary equation can be used for describing the pressure pulses on various scales. Exact solutions of the equations obtained are discussed. The numerical solutions described by the Burgers equation and the nonlinear fourth-order evolutionary equation are compared. 相似文献