Global well-posedness of coupled parabolic systems

The initial boundary value problem of a class of reaction-diffusion systems(coupled parabolic systems)with nonlinear coupled source terms is considered in order to classify the initial data for the global existence,finite time blowup and long time decay of the solution.The whole study is conducted by considering three cases according to initial energy:the low initial energy case,critical initial energy case and high initial energy case.For the low initial energy case and critical initial energy case the sufficient initial conditions of global existence,long time decay and finite time blowup are given to show a sharp-like condition.In addition,for the high initial energy case the possibility of both global existence and finite time blowup is proved first,and then some sufficient initial conditions of finite time blowup and global existence are obtained,respectively.     

Partial uniform boundedness of solutions of systems of differential equations with partly controlled initial conditions

We introduce the notion of partial uniform boundedness of solutions with partially controlled initial conditions in the general case, that is, the case in which the part of variables with respect to which the boundedness of solutions is studied is a subset of the part of variables with respect to which the initial conditions are controlled. We obtain a criterion for the partial uniform boundedness of solutions with partly controlled initial conditions. We introduce the notion of partial total boundedness of solutions with partly controlled initial conditions. We obtain a sufficient condition for the partial total boundedness of solutions with partly controlled initial conditions.     

取油管振动方程解的整体不存在性

讨论推广的海底取油管振动方程的初边值问题和初值问题解的整体不存在性,对初边值问题推广了Gmira和Guedda得到的结果,对初值问题的结果是新的.     

Consistent Initialization of Sensitivity Matrices for a Class of Parametric DAE Systems

A class of parametric semi-explicit differential algebraic equation (DAE) systems up to index 2 is considered. It is well known that initial value problems with DAE systems do not have a solution for every initial value. The initial value has to be consistent. Therefore, a method for the calculation of consistent initial values for this class of systems is introduced. In addition, various applications need information about the dependency of the solution of an initial value problem with respect to given parameters. This question leads to a linear matrix DAE system, the sensitivity DAE system, for which consistent initial values have to be provided as well. An appropriate consistent initialization method based on the solution differentiability of parametric nonlinear optimization problems in combination with Newton's method is developed. An illustrative example shows the capability of the method.     

A depletion of assets model of organizational learning*

This research investigates how population heterogeneity with respect to initial assets affects the rate of failure (or change) of organizations and social relationships. Organizations and social relationships are assumed to be endowed with initial assets which buffer against initial risks of failure. Failure is seen as the outcome of a process in which the assets are depleted and finally become exhausted. The core idea is that the assets of a unit become depleted through learning experiences which incur search costs and setbacks. Two settings are explored: A constant rate of depletion, and a declining rate of depletion of assets. The study explores additionally how the distribution of initial assets affects the failure rate of the population. It is found that the type of distribution of initial assets has a strong impact on the time dependence of the failure rate. A Normal distribution of initial assets leads to positive time dependence if the depletion rate is constant, and to negative time dependence if the depletion rate declines. The results show that population heterogeneity with respect to initial assets has effects on the time dependence of failure rates which are quite different from the popular case of population heterogeneity with respect to fit.     

On the application of genetic algorithms and gradient methods to the problem of the reconstruction of the initial stress field in a poroelastic inhomogeneous column

Initial stress fields play an important role in deformational processes in porous structures. Accurate modeling of dynamics behavior of the porous medium taking initial stresses into account requires an appropriate mathematical model. One of the common approaches for the construction of a mathematical model of the dynamic behavior of a medium taking the initial state into account is linearization. This paper presents equations of longitudinal vibrations of a poroelastic inhomogeneous body in the presence of the initial stress field. The influence of the initial stress rate and Biot’s modulus on the dynamic behavior of the environment is analyzed. The problem of reconstructing the initial stress field for the poroelastic inhomogeneous column based on the genetic algorithm and nonlinear optimization with the use of modern packages of numerical simulation is studied. A series of numerical experiments on the reconstruction of different initial stress field distribution laws using the described methods is carried out.     

Effects of initial stress on guided waves in orthotropic functionally graded plates

Because of the limitation of the manufacturing technology, initial stress in functionally graded materials (FGM) and structures is inevitable. Based on the theory of “Mechanics of Incremental Deformations”, the guided wave propagation in FGM plates under gravity, homogeneous initial stress in the thickness direction and inhomogeneous initial stress in the wave propagation direction is investigated. The Legendre polynomial series method is used to solve the coupled wave equations with variable coefficients. The convergence of the polynomial series method is discussed through the numerical examples. The effects of the initial stress on the Lamb-like wave and on the SH wave are investigated respectively and the numerical results show they are quite distinct. The effect of the gravity on the wave propagation can be ignored. The effects of the initial stress in the thickness direction are very different from those of the initial stress in the wave propagation direction, both on the dispersion curves and on the displacement and stress distributions.     

Large time behavior of solutions to a nonlinear hyperbolic relaxation system with slowly decaying data

We consider the large time asymptotic behavior of the global solutions to the initial value problem for the nonlinear damped wave equation with slowly decaying initial data. When the initial data decay fast enough, it is known that the solution to this problem converges to the self-similar solution to the Burgers equation called a nonlinear diffusion wave, and its optimal asymptotic rate is obtained. In this paper, we focus on the case that the initial data decay more slowly than previous works and derive the corresponding asymptotic profile. Moreover, we investigate how the change of the decay rate of the initial values affect its asymptotic rate.     

Initial Opening of a Compressor Valve

The initial opening of a compressor valve is investigated. The motion of the valve plate is essentially determined by the pressure distribution in the valve gap. Since the initial gap is extremly narrow a conventional CFD solution fails. Therefore the initial stages of the opening process are modelled by using an asymptotic expansion with respect to a small asepct ratio of the valve gap. The purpose of the analysis is to provide an initial condition for a CFD simulation of the valve dynamics. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Blowup of smooth solutions to the compressible Navier-Stokes equation with compact density

We present a sufficient condition on the blowup of smooth solutions to the compressible Navier-Stokes equations in arbitrary space dimensions with initial density of compact support. As an immediate application, it is shown that any smooth solutions to the compressible Navier-Stokes equations for polytropic fluids in the absence of heat conduction will blow up in finite time as long as the initial densities have compact support, and an upper bound, which depends only on the initial data, on the blowup time follows from our elementary analysis immediately. Another implication is that there is no global small (decay in time) or even bounded (in the case that all the viscosity coefficients are positive) smooth solutions to the compressible Navier-Stokes equations for polytropic fluids, no matter how small the initial data are, as long as the initial density is of compact support. This is in contrast to the classical theory of global existence of small solutions to the same system with initial data being a small perturbation of a constant state that is not a vacuum. The blowup of smooth solutions to the compressible Euler system with initial density and velocity of compact support is a simple consequence of our argument. © 1998 John Wiley & Sons, Inc.     

Macroscopic parameters of three-dimensional flows in free shear turbulence

The initial stage of the onset of turbulence in a three-dimensional compressible inviscid shear flow is studied. An initial deterministic velocity perturbation in the form of one or several Fourier modes leads to the development of a cascade of instabilities, which is numerically simulated. The influence exerted on the formation of the cascade of instabilities and the transition to turbulence by the size of the computational domain, the shear layer width, and the initial conditions is analyzed. It is shown that the mechanism of turbulence onset is essentially three-dimensional. The influence of various flow parameters and initial conditions on the formation of the turbulence cascade is studied numerically.     

初值修正灰色Verhulst模型的参数估计

研究了初值修正项为αz(1)(1)(其中α为修正参数)的灰色Verhuslt模型的修正参数估计方法.针对相关文献中,修正参数α求解无现成公式情况,通过最小化原始序列的一次累加序列与模拟序列之差,建立并求解一个非约束优化模型,获得了初值修正参数α的一个简单有效的计算公式,完善了相关文献中建立的初值修正灰色Verhuslt模型.最后,通过计算实例验证了修正参数公式可以有效提高初值修正灰色Verhuslt模型的精度.     

The numerical experiment in the study of polynomial quasisolutions of linear differential-difference equations

In this paper we consider the initial problem with an initial point for a scalar linear inhomogeneous differential-difference equation of neutral type. For polynomial coefficients in the equation we introduce a formal solution, representing a polynomial of a certain degree (“a polynomial quasisolution”); substituting it in the initial equation, one obtains a residual. The work is dedicated to the definition and the analysis (on the base of numerical experiments) of polynomial quasisolutions for the solutions of the initial problem under consideration.     

非线性扰动Klein-Gordon方程初值问题的渐近理论

在二维空间中研究一类非线性扰动Klein-Gordon方程初值问题解的渐近理论. 首先利用压缩映象原理,结合一些先验估计式及Bessel函数的收敛性,根据Klein-Gordon方程初值问题的等价积分方程,在二次连续可微空间中得到了初值问题解的适定性;其次,利用扰动方法构造了初值问题的形式近似解,并得到了该形式近似解的渐近合理性;最后给出了所得渐近理论的一个应用,用渐近近似定理分析了一个具体的非线性Klein-Gordon方程初值问题解的渐近近似程度．     

On the behaviour of solutions of degenerated nonlinear parabolic equations

The aim of this work is to study the behaviour of solutions of the initial boundary problem for degenerated nonlinear parabolic equations of the second order. The conditions of existence and non-existence solutions are established. Moreover, the behaviour of the solution is studied. We obtain the estimations in terms of characterizing the initial and weight functions on infinity, without a lower bound on the initial function.     

一类线性规划问题初始可行基产生的新方法

本对一类特殊的线性规划问题提出了利用最优基的启发性刻划产生初始基，进而用无比检验规则产生初始可行基的方法，并给出了此方法在单纯形表上实现的步骤。     

Spatial behaviour of solutions of the three-phase-lag heat equation

In this paper we study the spatial behaviour of solutions for the three-phase-lag heat equation on a semi-infinite cylinder. The theory of three-phase-lag heat conduction leads to a hyperbolic partial differential equation with a fourth-order derivative with respect to time. First, we investigate the spatial evolution of solutions of an initial boundary-value problem with zero boundary conditions on the lateral surface of the cylinder. Under a boundedness restriction on the initial data, an energy estimate is obtained. An upper bound for the amplitude term in this estimate in terms of the initial and boundary data is also established. For the case of zero initial conditions, a more explicit estimate is obtained which shows that solutions decay exponentially along certain spatial-time lines. A class of non-standard problems is also considered for which the temperature and its first two time derivatives at a fixed time T₀ are assumed proportional to their initial values. These results are relevant in the context of the Saint-Venant Principle for heat conduction problems.     

Variation formulas of solutions and optimal control problems for differential equations with retarded argument

The authors prove a theorem on the continuous dependence of solutions of nonlinear systems of differential equations with variable delay on the perturbations of initial data (initial instant, initial function, and initial value of the trajectory) and the right-hand side in the case where these perturbations are small in the Euclidean and integral topology, respectively. The variation formulas of solutions of a differential equation with discontinuous and continuous initial condition are deduced; as compared with those known earlier, these formulas take into account the variation of the initial instant and the discontinuity and continuity of the initial data. A necessary condition for criticality of mappings defined on a finitely locally convex set is obtained. The quasiconvexity of filters in studying optimal problems with delays in controls is proved. Necessary optimality conditions and existence theorems are proved for optimal problems with variable delays in phase coordinates and controls having a nonfixed initial instant, a discontinuous and a continuous initial condition, and functional and boundary conditions of general form. Necessary optimality conditions are obtained for optimal problems with variable structure and delays. __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 25, Optimal Control, 2005.     

Solution of weighted Cauchy problem for a class of Huygens equations

The paper studies the initial value problem for a class of equations satisfying Huygens’ principle. Since this equations have singularities at t = 0, it is necessary first to determine the form of the initial conditions and then the solution of the corresponding problem is constructed in a finite number of steps. Examples of natural initial data are presented.     

飞机初始备件品种优化的集对-粗糙集方法

飞机初始备件品种的确定是飞机初始使用和维修工作的必要条件.本文针对初始备件品种影响因素信息不完备的特点,依据集对分析方法在系统中的某一特性上具有同异反定量刻画的优势,结合经典粗糙集理论,提出初始备件品种优化的集对-粗糙集方法,最终得到初始备件品种优化的决策规则.实例计算表明,该方法能够为军方优化初始备件清单提供科学合理的决策.