部分Hénon型方程组解的渐近性(英文)

本文主要讨论部分Hénon型方程组解的渐近性,其中Ω=Bk(0,1)×Bn-k(0,1)Rn及x=(y,z)∈Rk×Rn-k.我们研究当n≥3,2<p+q<2*=2n/(n-2)且p+q趋于临界指数2*=2n/(n-2)时方程组的基态解的渐近性及当2<p+q<2*且α→+∞时解的渐近性.

重调和方程“最好的”13点近似差分方程

一九五七年D.Greenspan曾导出和证明了差分方程-20U0+4（U1+U2+U3+U4）+U5+U6+U7+U8=0为拉普拉斯方程Uxx+Uyy=0的“最好的”9点近似差分方程。一九五九年我国彭清泉试图导出和证明差分方程20U0-8（U1+U2+U3+U4）+2（U5+U6+U7+U8）+U9+U10+U11+U1

管道凸起激波/湍流边界层干扰的数值模拟

采用基于部分平均的湍流方程组,模拟了管道凸起流动中两种不同强度的激波-湍流边界层干扰现象,对流场的时均参数与实验值进行了比较,计算得到的壁面压力分布、摩阻系数分布、边界层厚度和速度型与实验值比较吻合很好。结果表明基于部分平均的湍流方程组既能够准确模拟小分离的激波/湍流边界层干扰流动又能够准确模拟大分离的激波/湍流边界层干扰流动,较好地预测了典型的λ激波结构。

Propagation and attenuation of P-waves in patchy saturated porous media

We establish a patchy saturation model and derive the seismic wave equations for patchy saturated porous media on the basis of Biot＇s equations and Johnson＇s bulk modulus. We solve the equations, obtain the attenuation coefficients, and analyze the characteristics of wave attenuation in the seismic frequency range. The results suggest that seismic waves show attenuation and dispersion in partially saturated rocks in the low frequency range. With frequency increasing, attenuation increases. The attenuation of P-waves of the second kind is more pronounced in agreement with Biot＇s theory. We also study the effect of porosity, saturation, and inner sphere radius on the attenuation of the P-waves of the first kind and find that attenuation increases with increasing frequency and porosity, and decreases with increasing frequency and degree of saturation. As for the inner sphere radius, wave attenuation is initially increasing with increasing frequency and inner sphere radius less than half the outer radius. Subsequently, wave attenuation decreases with increasing frequency and inner sphere radius is higher than half the outer sphere radius.

New Exact Solutions for Konopelchenko-Dubrovsky Equation Using an Extended Riccati Equation Rational Expansion Method

Taking the Konopelchenko-Dubrovsky system as a simple example, some familles of rational formal hyperbolic function solutions, rational formal triangular periodic solutions, and rational solutions are constructed by using the extended Riccati equation rational expansion method presented by us. The method can also be applied to solve more nonlinear partial differential equation or equations.

Fission and Fusion of Localized Coherent Structures for a Higher-Order Broer-Kaup System

Starting from a Backlund transformation and taking a special ansatz for the function f, we can obtain a much more generalexpression of solution that includes some variable separated functions for the higher-order Broer-Kaup system. From this expression, we investigate the interactions of localized coherent structures such as the multi-solitonic excitations and find the novel phenomenon that their interactions have non-elastic behavior because the fission/fusion may occur after the interaction of each localized coherent structure.

Numerical simulation of calm water entry of flatted-bottom seafloor mining tool

The hydrodynamic problem of a two-dimensional model of seafloor mining tool entering still water vertically at constant speed was analyzed based on the velocity potential theory. For the assumption that the water entry occurs with very short time interval, the viscosity and gravity of fluid were neglected. Considering the characteristic shape of it, the seafloor mining tool was simplified as a flat-bottom body. The governing equations were the Reynolds time-averaged equations and the k-e model. Finite element analysis was undertaken using the CFD software, Fluent. The impact pressures on the bottom of the mining tool were computed based on the improved volume of fuid method （VOF）. The pressure distribution, the maximum impact pressure, and the impact duration time during the water entry of mining tool are presented at various deploying velocities, the two peak pressures in the impact process are observed, and the relationship between the maximum impact pressure and the deploying velocity is obtained. The results are compared with those based on other prediction theories and methods.

On Direct Transformation Approach to Asymptotical Analytical Solutions of Perturbed Partial Differential Equation

In this article, we will derive an equality, where the Taylor series expansion around ε= 0 for any asymptotical analytical solution of the perturbed partial differential equation （PDE） with perturbing parameter e must be admitted. By making use of the equality, we may obtain a transformation, which directly map the analytical solutions of a given unperturbed PDE to the asymptotical analytical solutions of the corresponding perturbed one. The notion of Lie-Bgcklund symmetries is introduced in order to obtain more transformations. Hence, we can directly create more transformations in virtue of known Lie-Bgcklund symmetries and recursion operators of corresponding unperturbed equation. The perturbed Burgers equation and the perturbed Korteweg-de Vries （KdV） equation are used as examples.

Existence of Positive Solution to a Singular System of Nonlinear Fractional Differential Equation

In this paper,we discuss a singular system of nonlinear fractional differential equation,in which the inhomogeneous term depends on the fractional derivative of lower order.By using the Krasnoselskii＇s fixed point theorem and the Leray-Schauder nonlinear alternative method,some suffcient conditions for the existence of positive solution of the singular system are obtained.

Components Admissible Solution of Algebraic Differential Equations Systems

Using the Nevanlinna value distribution theory of meromorphic function,we investigate the existence problem of admissible solutions of higher-order algebraic differential equations systems,and obtain a result concerning admissible components of solution.

SOLUTIONS OF INTEGRAL EQUATIONS OF A CLASS IN A LOCALLY SEMI-CONVEX SPACE

n this paper, solutions of vector-valued integral equations of a class on an interval (a,b) to a complete Hausdorff locally semi--convex space are presented by the fixed point method.

A Study of Acetylene Production by Methane Flaming in a Partial Oxidation Reactor

The partial oxidation of hydrocarbons is an important technical route to produce acetylene for chemical industry.The partial oxidation reactor is the key to high acetylene yields.This work is an experimental and numerical study on the use of a methane flame to produce acetylene.A lab scale partial oxidation reactor was used to produce ultra fuel-rich premixed jet flames.The axial temperature and species concentration profiles were measured for different equivalence ratios and preheating temperatures,and these were compared to numerical results from Computational Fluid Dynamics(CFD)simulations that used the Reynolds Averaged Navier-Stokes Probability Density Function(RANS-PDF)approach coupled with detailed chemical mechanisms.The Leeds 1.5,GRI 3.0 and San Diego mechanisms were used to investigate the effect of the detailed chemical mechanisms.The effects of equivalence ratio and preheating temperature on acetylene production were experimentally and numerically studied.The experimental validations indicated that the present numerical simulation provided reliable prediction on the partial oxidation of methane.Using this simulation method the optimal equivalence ratio for acetylene production was determined to be 3.6.Increasing preheating temperature improved acetylene production and shortened greatly the ignition delay time.So the increase of preheating temperature had to be limited to avoid uncontrolled ignition in the mixing chamber and the pyrolysis of methane in the preheater.

The Effect of the Under-dense Magnetized Plasma on Electron Density Distribution and Field Profile

Propagation of a high frequency electromagnetic wave in under-dence plasma in presence of an external magnetic field is investigated. When a constant magnetic field perpendicular to the motion of electrons is applied, then the electrons rotate around the magnetic field lines and generate electromagnetic part in the wake with a nonzero group velocity. Using of the Maxwell equations and nonlinear differential equation for the electric field a direct one dimensional （ID） procedure for calculating wake equations are developed and the electric and magnetic field profile in the plasma are investigated.

Non-unitary Scattering Theory against Generalized Unitary Scattering Theory

Comparison of non-unitary and generalized unitary scattering theories is done by means of nuclear monodromy （equivalence of Schrodinger and Maxwell time-independent equations）, tunneling and radioactivity. Radioactivity is important part of physics and our life. Its importance stretches from medicine as far as to war strategies. We present theoretical approach to achieve better understanding of the radioactive decay when modified quantum theory is applied. It can be done by updating existing codes to understand better construction of the world and terms and conditions of our existence. The theory modifications are strictly connected with the unimodular M matrix and Wronskian matrices （i.e. their determinants named Wronskians） which create underpinning of so called monodromy being two track wave-function evolution.

Study on （2＋1）-Dimensional Nizhnik-Novikov-Veselov Equation by Using Extended Mapping Approach

Extended mapping approach is introduced to solve （2＋1）-dimensional Nizhnik-Novikov Veselov equation. A new type of variable separation solutions is derived with arbitrary functions in the model. Based on this excitation, rich localized structures such as multi-lump soliton and ring soliton are revealed by selecting the arbitrary function appropriately.

Damage and progressive failure of concrete structures using non-local peridynamic modeling

Peridynamics (PD), a recently developed theory of solid mechanics, which employs a non-local model of force interaction and makes use of integral formulation rather than the spatial partial differential equations used in the classical continuum mechanics theory, has shown effectiveness and promise in solving discontinuous problems at both macro and micro scales. In this paper, the peridynamics theory is used to analyze damage and progressive failure of concrete structures. A non-local peridynamic model for a rectangular concrete plate is developed, and a central pairwise force function is introduced to describe the interior interactions between particles within some definite distance. Damage initiation, evolution and crack propagation in the concrete model subject to in-plane uni-axial tension, in-plane uni-axial compression and out-of-plane impact load are investigated respectively. The numerical results show that discontinuities appear and grow spontaneously as part of the solution to the peridynamic equations of motion, and no special failure criteria or re-meshing techniques are required, which proves the potential of peridynamic modeling as a promising technique for analyzing the progressive failure of concrete materials and structures.

EQUIVALENCE BETWEEN EXACT INTERNAL CONTROLLABILITY OF THE KIRCHHOFF PLATE-LIKE EQUATION AND THE WAVE EQUATION

When the rotatory inertia is taken into account, vibrations of a linear plate can be described by the Kirchhoff plate equation. Consider this equation with locally distributed control forces and some boundary condition which is the simply supported boundary condition for a rectangular plate. In this paper, the authors establish exact controllability of the system in terms of the equivalence to exact internal controllability of the wave equation, by means of a frequency domain characterization of exact controllability introduced recently in [11].

BIFURCATIONS OF ROUGH 3-POINT-LOOP WITH HIGHER DIMENSIONS

The authors study the bifurcation problems of rough heteroclinic loop connecting threesaddle points for the case β1 ＞ 1, β2 ＞ 1, β3 ＜ 1 and β1β2β3 ＜ 1. The existence, number, co-existence and incoexistence of 2-point-loop, 1-homoclinic orbit and 1-periodic orbit are studied.Meanwhile, the bifurcation surfaces and existence regions are given.

Maximum Principle for Partially-Observed Optimal Control Problems of Stochastic Delay Systems

This paper is concerned with partially-observed optimal control problems for stochastic delay systems. Combining Girsanov's theorem with a standard variational technique, the authors obtain a maximum principle on the assumption that the system equation contains time delay and the control domain is convex. The related adjoint processes are characterized as solutions to anticipated backward stochastic differential equations in finite-dimensional spaces. Then, the proposed theoretical result is applied to study partially-observed linear-quadratic optimal control problem for stochastic delay system and an explicit observable control variable is given.