Oscillation of Higher-Order Delay Differential Equation with Applications to Hyperbolic Equations

In this paper, we consider an odd-order delay differential equation with positive and negative coefficients. New sufficient conditions that guarantee the oscillation of all solutions are presented. Our results extend and improve some known results. Next, these results are used for establishing oscillation criteria for hyperbolic delay differential equations with positive and negative coefficients corresponding to three sets of boundary conditions.     

Oscillation of a class of nonlinear partial difference equations with continuous variables

We consider a class of nonlinear partial difference equations with continuous variables. Some oscillation criteria are obtained using an integral transformation and inequalities.     

Oscillation theorems of higher order nonlinear delay differential equations

ＯＳＣＩＬＬＡＴＩＯＮＴＨＥＯＲＥＭＳＯＦＨＩＧＨＥＲＯＲＤＥＲＮＯＮＬＩＮＥＡＲＤＥＬＡＹＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＪｉｎＭｉｎｇ－ｚｈｏｎｇ（靳明忠）（ＤｅｐａｒｔｍｅｎｔｏｆＢａｓｉｃＣｏｕｒｓｅｓ,ＹｕｎｎａｎＩｎｓｔｉｔｕｔ...     

Oscillation of solutions for a class of nonlinear neutral parabolic differential equations boundary value problem

ＩｎｔｒｏｄｕｃｔｉｏｎＤｕｅｔｏｔｈｅａｃｃｕｒｅｎｃｅｏｆａｇｒｅａｔｄｅａｌｏｆｍａｔｈｅｍａｔｉｃｍｏｄｅｌｌｉｎｇｓｄｅｓｃｒｉｂｅｄｉｎｐａｒｔｉａｌｆｕｎｃｔｉｏｎａｌｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓｉｎｔｈｅａｐｐｌｉｃａｔｉｏｎｆｉｅｌｄｓｏｆｍｅｃｈａｎｉｃｓａｎｄｃｏｎｔｒｏｌｔｈｅｏｒｙ[1],ｇｒｅａｔｉｎｔｅｒｅｓｔｗａｓａｒｏｕｓｅｄａｓｔｏｔｈｅｓｔｕｄｉｅｓｏｎｔｈｅｐｒｏｐｅｒｔｙｏｆｔｈｅｓｏｌｕｔｉｏｎｓｏｆｔｈｉｓｔｙｐｅｏｆｅｑｕａｔｉｏｎｓ.Ｇ…     

Criteria for finite element algorithm of generalized heat conduction equation

To eliminate oscillation and overbounding of finite element solutions of classical heat conduction equation, the author and Xiao have put forward two new concepts of monotonies and have derived and proved several criteria. This idea is borrowed here to deal with generalized heat conduction equation and finite element criteria for eliminating oscillation and overbounding are also presented. Some new and useful conclusions are drawn.     

On self-excited oscillation of dynamic systems with gap

In this paper, the sufficient condition for self-excited oscillation of dynamic systems with gap is given by using qualitative method of differential equations.     

Boundedness and persistence and global asymptotic stability for a class of delay difference equations with higher order

ＩｎｔｒｏｄｕｃｔｉｏｎＣｏｎｓｉｄｅｒｔｈｅｆｏｌｌｏｗｉｎｇｄｅｌａｙｄｉｆｆｅｒｅｎｃｅｅｑｕａｔｉｏｎｗｉｔｈｈｉｇｈｅｒｏｒｄｅｒｘｎ+1=Ａ0ｘｐ0ｎ+ Ａ1ｘｐ1 ｎ- 1+… + Ａｋｘｐｋｎ-ｋ　　 (ｎ=0 ,1 ,2 ,… ) ,( 1 )ｗｈｅｒｅＡｉ,ｐｉ ∈ [0 ,∞ )　　 (ｉ=0 ,1 ,2 ,…ｋ;ｋ∈ 1 ,2 ,… ) ( 2 )ａｎｄｔｈｅｉｎｉｔｉａｌｃｏｎｄｉｔｉｏｎｓｘ-ｋ,ｘ-ｋ+1,… ,ｘ- 1,ｘ0 ａｒｅａｒｂｉｔｒａｒｙｐｏｓｉｔｉｖｅｎｕｍｂｅｒｓ.Ｓｏｍｅｓｐｅｃｉａｌｃａｓｅｓｏｆｋ=1ｆｏｒＥｑ .( 1 )ｈａｖｅｂｅｅｎ…     

Sufficient conditions for the oscillation of solutions of first-order neutral delay impulsive differential equations with constant coefficients

This paper is dealing with the oscillatory properties of first-order neutral delay impulsive differential equations and the corresponding inequalities with constant coefficients. The established sufficient conditions ensure the oscillation of every solution of equations of this type.     

Permanence and asymptotic properties of nonlinear delay difference equations

The asymptotic behavior of a class of nonlinear delay difference equation wax studied . Some sufficient conditions are obtained for permanence and global attractivity . The results can be applied to a claxs of nonlinear delay difference equations and to the delay discrete Logistic model and some known results are included.     

On the oscillation of solutions of hyperbolic partial functional differential equations

ＣＬＣｎｕｍｂｅｒ：Ｏ１７５．２Ｄｏｃｕｍｅｎｔｃｏｄｅ：ＡｏｌｕｔｉｏｎｓｏｆＨｙｐｅｒｂａｎｇＰｅｉｇｕａｎｇａｎｄＧｅＷｅｉｇａｏｌｕｔｉｏｎｓｏｆＨｙｐｅｒｂｏｌｉｃＦｕｎｃｔｉｏｎａＷａｎｇＰｅｉｇｕａｎｇａｎｄＧｅＷｅｉｇａｏｌｕｔｉｏｎ...     

Oscillation of all solutions of iterative equations

The paper contains sufficient conditions for the oscillation of all solutions of linear functional iterative equations. Published in Neliniini Kolyvannya, Vol. 10, No. 3, pp. 348–364, July–September, 2007.     

Periodic solution of a second order, autonomous, nonlinear system

There exist a sufficient condition for the existence of at least one periodic solution for a type of second order autonomous ordinary differential equations. The correctness of the condition has been pointed out by Schauder's fixed point theorem. In order to indicate the validity of the assumptions made, two illustrative examples, showing its application in the nonlinear vibration and relaxation oscillation are presented.     

Numerical study of the oscillations induced by shock/shock interaction in hypersonic double-wedge flows

In this paper, the shock pattern oscillations induced by shock/shock interactions over double-wedge geometries in hypersonic flows were studied numerically by solving 2D inviscid Euler equations for a multi-species system. Laminar viscous effects were considered in some cases. Temperature-dependent thermodynamic properties were employed in the state and energy equations for consideration of the distinct change of the thermodynamic state. It was shown that the oscillation results in high-frequency fluctuations of heating and pressure loads over wedge surfaces. In a case with a relatively lower free-stream Mach number, the shock/shock interaction structure maintains a seven-shock configuration during the entire oscillation process. On the other hand, the oscillation is accompanied by a transition between a six-shock configuration (regular interaction) and a seven-shock configuration (Mach interaction) in a case with a higher free-stream Mach number. Numerical results also indicate that the critical wedge angle for the transition from a steady to an oscillation solution is higher compared to the corresponding value in earlier numerical research in which the perfect diatomic gas model was used.      

Oscillation theorems for a second order nonlinear differential equation

In this paper, some new oscillation criteria for a second order nonlinear differential equation with clampings are established. These criteria improve and generalize the related results given in [1-4].     

A computational investigation of the finite-time blow-up of the 3D incompressible Euler equations based on the Voigt regularization

We report the results of a computational investigation of two blow-up criteria for the 3D incompressible Euler equations. One criterion was proven in a previous work, and a related criterion is proved here. These criteria are based on an inviscid regularization of the Euler equations known as the 3D Euler–Voigt equations, which are known to be globally well-posed. Moreover, simulations of the 3D Euler–Voigt equations also require less resolution than simulations of the 3D Euler equations for fixed values of the regularization parameter \(\alpha >0\). Therefore, the new blow-up criteria allow one to gain information about possible singularity formation in the 3D Euler equations indirectly, namely by simulating the better-behaved 3D Euler–Voigt equations. The new criteria are only known to be sufficient criterion for blow-up. Therefore, to test the robustness of the inviscid-regularization approach, we also investigate analogous criteria for blow-up of the 1D Burgers equation, where blow-up is well known to occur.     

Three-dimensional arbitrary Lagrangian–Eulerian numerical prediction method for non-linear free surface oscillation

A numerical prediction method has been proposed to predict non-linear free surface oscillation in an arbitrarily-shaped three-dimensional container. The liquid motions are described with Navier–Stokes equations rather than Laplace equations which are derived by assuming the velocity potential. The profile of a liquid surface is precisely represented with the three-dimensional curvilinear co-ordinates which are regenerated in each computational step on the basis of the arbitrary Lagrangian–Eulerian (ALE) formulation. In the transformed space, the governing equations are discretized on a Lagrangian scheme with sufficient numerical accuracy and the boundary conditions near the liquid surface are implemented in a complete manner. In order to confirm the applicability of the present computational technique, numerical simulations are conducted for the free oscillations of viscid and inviscid liquids and for highly non-linear oscillation. In addition, non-linear sloshing motions caused by horizontal and vertical excitations and a transition from non-linear sloshing to swirling are numerically predicted in three-dimensional cylindrical containers. Conclusively, it is shown that these sloshing motions associated with high non-linearity are reasonably predicted with the present numerical technique. © 1998 John Wiley & Sons, Ltd.     

Heat and mass transfer of a fuel droplet evaporating in oscillatory flow

A numerical study of the heat and mass transfer from an evaporating fuel droplet in oscillatory flow was performed. The flow was assumed to be laminar and axisymmetric, and the droplet was assumed to maintain its spherical shape during its lifetime. Based on these assumptions, the conservation equations in a general curvilinear coordinate were solved numerically. The behaviors of droplet evaporation in the oscillatory flow were investigated by analyzing the effects of flow oscillation on the evaporation process of a n-heptane fuel droplet at high pressure.The response of the time history of the square of droplet diameter and space-averaged Nusselt numbers to the main flow oscillation were investigated in frequency band of 1–75 Hz with various oscillation amplitudes. Results showed that, depending on the frequency and amplitude of the oscillation, there are different modes of response of the evaporation process to the flow oscillation. One response mode is synchronous with the main flow oscillation, and thus the quasi-steady condition is attained. Another mode is asynchronous with the flow oscillation and is highly unsteady. As for the evaporation rate, however, in all conditions is more greatly enhanced in oscillatory flow than in quiescent air.To quantify the conditions of the transition from quasi-steady to unsteady, the response of the boundary layer around the droplet surface to the flow oscillation was investigated. The results led to including the oscillation Strouhal number as a criteria for the transition. The numerical results showed that at a low Strouhal number, a quasi-steady boundary layer is formed in response to the flow oscillation, whereas by increasing the oscillation Strouhal number, the phenomena become unsteady.     

Oscillation criteria for nonlinear neutral hyperbolic equations with functional arguments

This paper is devoted to the study of oscillatory behavior of solutions of nonlinear neutral hyperbolic equations with functional arguments by using the integral averaging method and generalized Riccati techniques. First, we establish oscillation results for nonlinear neutral hyperbolic equations by reducing the multidimensional oscillation problems to one-dimensional oscillation problems for functional differential inequalities. Second, we present oscillation results for nonlinear neutral hyperbolic equations by utilizing Riccati techniques.     

Analytical evaluation of the elastic and plastic resistances of double symmetric rectangular hollow sections under axial force and biaxial bending

In the recent codes for the design of steel structures, the elastic–plastic methods of analysis are recognised to provide an efficient estimation of the ultimate resistance of some of these structures. These methods are usually based on some basic hypotheses, such as the creation of plastic hinges in the most stressed cross-sections, for instance.As the development of these plastic hinges depends on the interaction between the internal forces and on the cross-section shape, specific equations are required for the analysis of different types of cross-sections. However, most frequently, these equations are not available, or they are expressed by means of simplified expressions; this is usually the case when biaxial bending is involved.This paper presents new interaction criteria for the analysis of steel rectangular hollow sections subjected to an axial force and biaxial bending moments, at the elastic or the plastic limit states (as long as buckling phenomena are not involved). The plastic interaction criteria are presented, in a first step, for some particular combinations of the internal forces, such as axial loading with bending about a main axis, and biaxial bending without axial loading. Then, the global solution for the simultaneous combination of an axial force and bending moments about both the main axes of inertia are described in detail. All these plastic interaction criteria are compared with the corresponding plastic criteria adopted in the Eurocode 3 (EC3). Some suggestions are presented in order to improve the results given by these EC3 criteria.     

Oscillation behavior of solutions for even order neutral functional differential equations

Even order neutral functional differential equations are considered. Sufficient conditions for the oscillation behavior of solutions for this differential equation are presented. The new results are presented and some examples are also given.