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| 1 | Stability analysis of solutions to nonlinear stiff Volterra functional differential equations in Banach spaces显示文摘A series of stability, contractivity and asymptotic stability results of the solutions to nonlinear stiff Volterra functional differential equations (VFDEs) in Banach spaces is obtained, which provides the unified theoretical foundation for the stability analysis of solutions to nonlinear stiff problems in ordinary differential equations(ODEs), delay differential equations(DDEs), integro-differential equations(IDEs) and VFDEs of other type which appear in practice. | LI Shoufu | 2005 | Science China Mathematics2005，48，3： | 20 |
| 2 | B-Theory of Runge-Kutta methods for stiff Volterra functional differential equations显示文摘B-stability and B-convergence theories of Runge-Kutta methods for nonlinear stiff Volterra func-tional differential equations (VFDEs) are established which provide unified theoretical foundation for the studyof Runge-Kutta methods when applied to nonlinear stiff initial value problems (IVPs) in ordinary differentialequations (ODEs), delay differential equations (DDEs), integro-differential equations (IDEs) and VFDEs ofother type which appear in practice. | 李寿佛 | 2003 | Science China Mathematics2003，46，5： | 18 |
| 3 | Comparison principle and stability criteria for stochastic differential delay equations with Markovian switching显示文摘In the present paper we first obtain the comparison principle for the nonlinear stochastic differentialdelay equations with Markovian switching. Later, using this comparison principle, we obtain some stabilitycriteria, including stability in probability, asymptotic stability in probability, stability in the pth mean, asymptoticstability in the pth mean and the pth moment exponential stability of such equations. Finally, an example isgiven to illustrate the effectiveness of our results. | 罗交晚 邹捷中 侯振挺 | 2003 | Science China Mathematics2003，46，1： | 12 |
| 4 | The vortex dynamics of a Ginzburg-Landau system under pinning effect显示文摘It is proved that the vortices of a Ginzburg-Landau system are attracted by impurities or inhomogeneities in the super-conducting materials. The strong H1-convergence for the system is also studied. | 简怀玉 徐兴旺 | 2003 | Science China Mathematics2003，46，4： | 11 |
| 5 | High-order accurate dissipative weighted compact nonlinear schemes显示文摘Based on the method deriving dissipative compact linear schemes (DCS), novel high-order dissipative weighted compact nonlinear schemes (DWCNS) are developed. By Fourier analysis,the dissipative and dispersive features of DWCNS are discussed. In view of the modified wave number, the DWCNS are equivalent to the fifth-order upwind biased explicit schemes in smooth regions and the interpolations at cell-edges dominate the accuracy of DWCNS. Boundary and near boundary schemes are developed and the asymptotic stabilities of DWCNS on both uniform and stretching grids are analyzed. The multi-dimensional implementations for Euler and Navier-Stokes equations are discussed. Several numerical inviscid and viscous results are given which show the good performances of the DWCNS for discontinuities capturing, high accuracy for boundary layer resolutions, good convergent rates (the root-mean-square of residuals approaching machine zero for solutions with strong shocks) and especially the damping effect on the spudous oscillations which were found in the solutions obtained by TVD and ENO schemes. | 邓小刚 | 2002 | Science China Mathematics2002，45，3： | 11 |
| 6 | The 3-D non-axisymmetrical Lamb's problem in transversely isotropic saturated poroelastic media显示文摘Based on Biots theory on fluid-saturated porous media, the displacement functions are adopted to convert the 3-D Biots wave equations in the cylindrical coordinate for transversely isotropic saturated poroelastic media into two棗one 6-order and one 2-order棗uncoupling differential governing equations. Then, the differential equations are solved by the Fourier expanding and Hankel integral transform method. Integral solutions of soil skeleton displacements and pore pressure as well as the total stresses for poroelastic media are obtained. Furthermore, the systematic study on Lambs problems for the transversely isotropic saturated poroelastic media is performed. Integral solutions for surface radial, vertical and circumferential displacements are obtained in both cases of drained surface and undrained surface under the vertical and horizontal harmonic excitation force. In the end of this paper, the numerical examples are presented. The calculation results indicate that the difference between the model of isotropic saturated poroelastic media and that of transversely isotropic saturated poroelastic media is obvious. | HUANG Yi1 & WANG Xiaogang1,2 1. School of Civil Engineering, Xian University of Architecture & Technology, Xian 710055, China 2. Department of Civil Engineering, Qinghai University, Xining 810016, China Correspondence should be addressed to Huang Yi (email: huangyih@pub.xaonline.com) Received April 15, 2004 revised July 12, 2004 | 2004 | Science China(Technological Sciences)2004，47，5： | 10 |
| 7 | A preliminary study on vegetation-erosion dynamics and its applications显示文摘Vegetation-erosion dynamics is a new interdisciplinary science, studying the laws of evolution of watershed vegetation under the action of various ecological stresses. Introducing a qualitative expression of ecological stresses in this paper, the present authors establish the cou- pled differential equations for the vegetation-erosion process and derive a theoretical solution. The model is applied to the Anjiagou watershed on the Loess Pateau and the Xiaojiang water- shed and its sub-watersheds on the Yunnan Plateau. The calculated results agree well with the vegetation development processes. Abstracted from the differential equations the so-called vegetation-erosion chart is worked out, with which we can predict the development trend of vegetation under no human stresses. It is demonstrated that the erosion control is important for vegetation development and reforestation must be a long-term strategy. On the Yunnan Plateau with relatively high precipitation and temperature, vegetation can be greatly improved if erosion is controlled. On the dry and cold Loess Pateau suffering from high rate of soil erosion, however, vegetation can effectively control erosion but erosion reduction exhibits low effectiveness on vegetation development. Vegetation in the area is not stable and management is always needed to maintain the vegetation. | WANG Zhaoyin 1,2 , WANG Guangqian 1 , LI Changzhi 1 & WANG Feixin 1 1. Department of Hydraulic Engineering, Tsinghua University, Beijing 100084, China 2. International Research and Training Center on Erosion and Sedimentation, Beijing 100084, China | 2005 | Science China Earth Sciences2005，48，5： | 7 |
| 8 | Efficient parallel multivalue hybrid methods for stiff differential equations显示文摘A class of efficient parallel multivalue hybrid methods for stiff differential equations are presented,which are all extremely stable at infinity, A-stable for orders 1-3 and A(α)-stable for orders 4-8. Eachmethod of the class can be performed parallelly using two processors with each processor having almost thesame computational amount per integration step as a backward differentiation formula (BDF) of the same orderwith the same stepsize performed in serial, whereas the former has not only much better stability propertiesbut also a computational accuracy higher than the corresponding BDF. Theoretical analysis and numericalexperiments show that the methods constructed in this paper are superior in many respects not only to BDFsbut also to some other commonly used methods. | 李寿佛 | 2002 | Science China Mathematics2002，45，10： | 6 |
| 9 | Uniqueness and local stability for the inverse scattering problem of determining the cavity显示文摘Considering a time-harmonic electromagnetic plane wave incident on an arbitrarily shaped open cavity embedded in infinite ground plane, the physical process is modelled by Maxwell's equations. We investigate the inverse problem of determining the shape of the open cavity from the information of the measured scattered field. Results on the uniqueness and the local stability of the inverse problem in the 2-dimensional TM (transverse magnetic) polarization are proved in this paper. | FENG Lixin & MA Fuming LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, China School of Mathematical Sciences, Heilongjiang University, Harbin 150080, China School of Mathematical Sciences, Jilin University, Changchun 130012, China | 2005 | Science China Mathematics2005，48，8： | 6 |
| 10 | Exact Boundary Controllability for a Coupled System of Wave Equations with Neumann Boundary Controls(Dedicated to Professor Haim Brezis on the occasion of his 70th birthday)显示文摘This paper first shows the exact boundary controllability for a coupled system of wave equations with Neumann boundary controls. In order to establish the corresponding observability inequality, the authors introduce a compact perturbation method which does not depend on the Riesz basis property, but depends only on the continuity of projection with respect to a weaker norm, which is obviously true in many cases of application. Next,in the case of fewer Neumann boundary controls, the non-exact boundary controllability for the initial data with the same level of energy is shown. | Tatsien LI Bopeng RAO | 2017 | Chinese Annals of Mathematics,Series B2017，38，2： | 3 |
| 11 | The blow-up rates for systems of heat equations with nonlinear boundary conditions显示文摘This paper deals with the blow-up rate estimates of positive solutions for systems of heat equationswith nonlinear boundary conditions. The upper and lower bounds of blow-up rate are obtained. | 王明新 | 2003 | Science China Mathematics2003，46，2： | 3 |
| 12 | Existence of the solutions and the attractors for the large-scale atmospheric equations显示文摘In this paper, firstly, the proper function space is chosen, and the proper expression of the operators is introduced such that the complex large-scale atmospheric motion equations can be described by a simple and abstract equation, by which the definition of the weak solution of the atmospheric equations is made. Secondly, the existence of the weak solution for the atmospheric equations and the steady state equations is proved by using the Galerkin method. The existence of the non-empty global attractors for the atmospheric equations in the sense of the Chepyzhov-Vishik’s definition is obtained by constructing a trajectory attractor set of the atmospheric motion equations. The result obtained here is the foundation for studying the topological structure and the dynamical behavior of the atmosphere attractors. Moreover, the methods used here are also valid for studying the other atmospheric motion models. | HUANG Haiyang1 & GUO Boling2 1. Department of Mathematics, Beijing Normal University, Beijing 100875, China 2. Institute of Applied Physics and Computational Mathematics, Beijing 100080, China | 2006 | Science China Earth Sciences2006，49，6： | 2 |
| 13 | RATIONAL BASIS FOR SUSPENDED SEDIMENT MODELING显示文摘This paper presents a rational basis to model the transport of suspended sediment. The looseboundary condition for 3D models and the adjustment coefficients for both the depth-integrated 2D and laterally integrated 1D models are treated comprehensively. A combination of Dirichlet and Neumann conditions is proposed as the loose-boundary condition. The adjustment coefficient for 2D models is obtained on the basis of the proposed boundary condition and analytical solutions developed for some simple cases of non-equilibrium transport of sediment in uniform flows. The adjustment coefficient for 1D models for natural rivers is further obtained from lateral integration. Comparisons with analytical solutions and a considerable amount of laboratory and prototype data show that mathematical models developed along the proposed line of attack would well simulate the transport of suspended sediment in practical problems. | Jianjun ZHOU, Biniiang LIN and Bingnan LIN Prof, Dept. of Hydraulic Eng., Tsinghua University, Beijing 100084, P.R. China Senior Lecturer, School of Eng., Cardiff University, Queen’s Buildings, P.O.Box 686, Cardiff, CF14 9EW, UK Dir. Emeritus, China Inst. of Water Resources and Hydropower Res. Formerly, Chief of Sedimentation Panel for TGP Chairman Emeritus of Advising Council, IRTCES, P.O. Box. 366, Beijing 100044, P.R. China | 2003 | International Journal of Sediment Research2003，18，3： | 2 |
| 14 | Asymptotic behavior of the solutions of the p-Laplacian equation显示文摘The asymptotic behavior of the solutions for p-Laplacian equations as p →∞ is studied. | ZHANG Liqin ZHAO Junning | 2006 | Science China Mathematics2006，49，6： | 2 |
| 15 | New Similarity Reductions and Compacton Solutions for Boussinesq-Like Equations with Fully Nonlinear Dispersion显示文摘In this paper, similarity rcductions of Boussinesq-like equations with nonlinear dispersion (simply called B(m, n) equations) utt = (un)xx + (um) which is a generalized model of Boussinesq equation uts = (u2)xx + u and modified Bousinesq equation utt = (u3)xx + uxxxx, are considered by using the direct reduction method. As a result,several new types of similarity reductions are found. Based on the reduction equations and some simple transformations,we obtain the solitary wave solutions and compacton solutions (which are solitary waves with the property that after colliding with other compacton solutions, they re-emerge with the same coherent shape) of B(1, n) equations and B(m, m)equations, respectively. | YAN Zhen-Ya | 2001 | Communications in Theoretical Physics2001，，10： | 2 |
| 16 | The Darboux Transformation for NLS-MB Equations显示文摘The Darboux transformations for the nonlinear Schrodinger equation and Maxwell-Bloch equations areconstructed. The one-soliton solution and periodic solution are obtained from the different 'seeds'. | HE Jing-Song CHENG Yi LI Yi-Shen | 2002 | Communications in Theoretical Physics2002，，10： | 1 |
| 17 | Lagrangian description of nonlinear chromatography显示文摘Under the framework of non-equilibrium thermodynamic separation theory (NTST), Local Lagrangian approach (LLA) was proposed to deal with the essential issues of the convec- tion and diffusion (shock waves) phenomena in nonlinear chromatography with recursion equa- tions based on the three basic theorems, Lagrangian description, continuity axiom and local equilibrium assumption (LEA). This approach remarkably distinguished from the system of con- temporary chromatographic theories (Eulerian description-partial differential equations), and can felicitously match modern cybernetics. | LIANG Heng LIU Xiaolong | 2004 | Science China Chemistry2004，47，6： | 1 |
| 18 | Dynamical Running Mass of Quark in the Dyson-Schwinger Equation Approach显示文摘Based on the Dyson-Schwinger equations of QCD in the 'rainbow' approximation, the fully dressed quarkpropagator Sf(p) is investigated, and then an algebraic parametrization form of the propagator is obtained as a solutionof the equations. The dressed quark amplitudes Af and Bf built up the fully dressed quark propagator and the dynamicalrunning masses Mf defined by Af and Bf for light quarks u, d and s are calculated, respectively. Using the predictedrunning masses Mf, quark condensates <0|q(0)q(0)|0> = -(0.255 GeV)a for u, d quarks, and <0|s s|0> = 0.8<0|q(0)q(0)]0)for s quark, and experimental pion decay constant fπ = 0.093 GeV, the masses of Goldstone bosons K, π, and η are alsoevaluated. The numerical results show that the masses of quarks are dependent on their momentum p2. The fully dressedquark amplitudes Af and Bf have correct behaviors which can be used for many purposes in our future researches onnonperturbative QCD. | MA Wei-Xing SHEN Peng-Nian ZHOU Li-Juan | 2002 | Communications in Theoretical Physics2002，，11： | 1 |
| 19 | Existence of Young measure solutions of a class of singular diffusion equations显示文摘The first initial-boundary value problem of a class of singular diffusion equations with the flux sublinear growth and the potential without convexity is investigated. Such equations may be strongly degenerate, singular and forward-backward. Inspired by the idea in a recent work of Demoulini, we first discuss the regular case by introducing the Young measure solutions and prove the existence of such solutions. Consequently, we approximate the extreme case by the method of regularization. By means of some uniform estimates and some techniques, the existence of Young measure solutions with bounded variation is established. | YIN Jingxue and WANG Chunpeng(Department of Mathematics, Jilin University, Changchun 130012, China) | 2002 | Progress in Natural Science:Materials International2002，12，4： | 1 |
| 20 | On density perturbations and missing mass显示文摘In inflation the influence of short wave part of scalar field on the long wave is considered to be a nature of a random force possessing simple statistical properties. A unified cosmology is proposed. Some interesting results are obtained. | 王永久 唐智明 | 2002 | Science China Mathematics2002，45，4： | 1 |
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