共查询到20条相似文献,搜索用时 78 毫秒
1.
Inreference [1 ] ,wediscussedtheinstabilityofNavier_StokesequationonR3×R ,and ,intheillustrationofit,wepresentedsomeexamplesintheformofexactsolution .Thebasisoftheconstructionofthemisthe“equationsecondaire”oftheequation .Infact,theseexactsolutionsaresomelimit… 相似文献
2.
By combining Chapman-Enskog expansion with the BGK approximation to Baltzmann equation and Navier-Stokes equation was obtained.
And an expression of Darcy’s law was obtained through taking variable average over Navier-Stokes equation on some representative
space in porous media, and finally an example was taken to prove its reliability.
Foundation items: the National Natural Science Foundation of China (10372094); the Natural Science Foundation of Zhejiang Province, China
(M103082, M102053); the Science Foundation of Education Department of Zhejiang Province, China (20030871)
Biography: Xu You-sheng (1963∼), Associate Professor, Doctor 相似文献
3.
Shen Zhen 《应用数学和力学(英文版)》2003,24(5):545-554
The ill posed initial value problem of the Euler equations and the formal solvability of ill posed problem based on stratification
theory are discussed. For some ill posed initial value problems, the existence conditions of formal solutions and the methods
of how to construct a formal solution are given. Finally, an example is given to discuss the ill posedness of the initial
value problem on hyper plane {t=0} in R4, and explain that the problem has more than one solution.
Foundation item: the National Natural Science Foundation of China (19971054)
Biography: Shen Zhen (1977−) 相似文献
4.
IntroductionWiththerapiddevelopmentofscienceandtechnology ,thestudykernelofmodernscienceischangedfromlineartononlinearstepbystep .Manynonlinearscienceproblemscansimplyandexactlybedescribedbyusingthemathematicalmodelofnonlinearequation .Uptonow ,manyimpor… 相似文献
5.
The inverse problem for a class of nonlinear evolution equations of dispersive type was reduced to Cauchy problem of nonlinear
evolution equation in an abstract space. By means of the semigroup method and equipping equivalent norm technique, the existence
and uniqueness theorem of global solution was obtained for this class of abstract evolution equations, and was applied to
the inverse problem discussed here. The existence and uniqueness theorem of global solution was given for this class of nonlinear
evolution equations of dispersive type. The results extend and generalize essentially the related results of the existence
and uniqueness of local solution presented by YUAN Zhong-xin.
Contributed by Chen Yu-shu
Foundation item: the National Natural Science Foundation of China (Significance 199990510); the National Key Basic Research Special Foundation
of China (G1998020316); Liuhui Center for Applied Mathematics, Nankai University & Tianjin University
Biography: Chen Fang-qi (1963-) 相似文献
6.
The mixed finite element(MFE) methods for a shallow water equation systemconsisting of water dynamics equations, silt transport equation, and the equation of bottomtopography change were derived. A fully discrete MFE scheme for the discrete-time alongcharacteristics is presented and error estimates are established. The existence andconvergence of MFE solution of the discrete current velocity, elevation of the bottomtopography, thickness of fluid column, and mass rate of sediment is demonstrated. 相似文献
7.
The solvability of the Euler equations about incompressible inviscid fluid based on the stratification theory is discussed.
And the conditions for the existence of formal solutions and the methods are presented for calculating all kinds of ill-posed
initial value problems. Two examples are given as the evidences that the initial problems at the hyper surface does not exist
any unique solution.
Foundation item: the National Natural Science Foundation of China (19971054)
Biography: Shen Zhen (1977−) 相似文献
8.
MIXED FINITE ELEMENT METHODS FOR THE SHALLOW WATER EQUATIONS INCLUDING CURRENT AND SILT SEDIMENTATION (Ⅰ)——THE CONTINUOUS-TIME CASE 总被引:1,自引:0,他引:1
An initial-boundary value problem for shallow equation system consisting of water dynamics equations, silt transport equation, the equation of bottom topography change, and of some boundary and initial conditions is studied, the existence of its generalized solution and semidiscrete mixed finite element (MFE) solution was discussed, and the error estimates of the semidiscrete MFE solution was derived. The error estimates are optimal. 相似文献
9.
唐一鸣 《应用数学和力学(英文版)》1999,20(8):888-894
Inthispaper,whatwediscusbelongstoastabilityproblemaboutthesecondclasgeneralNavier_Stokesequations.Ittouchessomeimportantprobl... 相似文献
10.
Periodic solution of m order linear neutral equations with constant coefficient and time delays was studied. Existence and
uniqueness of 2 T-periodic solutions for the equation were discussed by using the method of Fourier series. Some new necessary
and sufficient conditions of existence and uniqueness of 2T-periodic solutions for the equation are obtained. The main result
is used widely. It contains results in some correlation paper for its special case, improves and extends the main results
in them. Existence of periodic solution for the equation in larger number of particular case can be checked by using the result,
but cannot be checked in another paper. In other words, the main result in this paper is most generalized for (1), the better
result cannot be found by using the same method.
Foundation item: the Natural Science Foundation of Yunnan Education Committee (990002)
Biography: ZHANG Bao-sheng (1962-) 相似文献
11.
IntroductionDuringthestudyofshallowwaterwaves,peopleobtainedmanywell_knowncompletelyintegrablemodels,suchasKdVequation,mKdVequation,Boussinesqequation,Whitham_Broer_KaupequationandKhokhlov_Zabolotskayaequationetc.[1~8].For2 1_dimensionalvariablecoefficientg… 相似文献
12.
THE MULTI-SYMPLECTIC ALGORITHM FOR “GOOD” BOUSSINESQ EQUATION 总被引:2,自引:0,他引:2
The multi-symplectic formulations of the “Good” Boussinesq equation were considered. For the multi-symplectic formulation,
a new fifteen-point difference scheme which is equivalent to the multi-symplectic Preissman integrator was derived. The numerical
experiments show that the multi-symplectic scheme have excellent long-time numerical behavior.
Foundation items: the Foundation for Key Laboratory of Scientific/Engineering Computing Institute of Computational Mathematics and Scientific/Engineering
Computing, Chinese Academy of Sciences; the Natural Science Foundation of Huaqiao University.
Biography: ZENG Wen-ping (1940-), Professor (E-mail: qmz@1sec.cc.ac.cn) 相似文献
13.
Weak formulation of equilibrium equations including boundary conditions of laminated cylindrical shell is presented, and thermal
stresses mixed state equation for axisymmetric problem of closed cantilever cylindrical shell is established. A unified approach
and weak solutions are obtained for closed laminated cantilever cylindrical shell of arbitrary thickness under thermal and
mechanical loadings. The equation and boundary conditions proposed in this paper are weakened, the method of this paper would
be easy to popularize in dynamics analysis of elasticity.
Foundation item: the National Natural Science Foundation of China (19392305) 相似文献
14.
刘继军 《应用数学和力学(英文版)》2003,24(5):605-613
A 3-layered explicit difference scheme for the numerical solution of 2-D heat equation is proposed. Firstly, a general symmetric
difference scheme is constructed and its optimal error is obtained. Then two kinds of condition for choosing the parameters
for optimal error and stable difference scheme are given. Finally, some numerical results are presented to show the advantage
of the schemes
Foundation items: the Science Foundation of Chinese Postdoctoral (2002031224); the Science Foundations of Southeast University (9209011148,
3007011043)
Biography: Liu Ji-jun (1965-) 相似文献
15.
IntroductionandProblemintheResearchofToroidThispaperdealswiththeexistenceof2π_periodicsolutionstothenonlinearsystemoffirst_orderdifferentialequationswithadeviatingargument x(t) =Bx(t) F(x(t-τ) ) p(t) ,( 1 )wherex(t)∈R2 , x(t) =ddtx(t) ,τ∈R ,B∈R2×2 ,F :R2 →R2 isboundedandp∈C(… 相似文献
16.
黄再兴 《应用数学和力学(英文版)》1999,20(11):1286-1290
In this paper, it is proven that the balance equation of energy is the first integral of the balance equation of momentum
in the linear theory of nonlocal elasticity. In other words, the balance equation of energy is not an independent one. It
is also proven that the residual of nonlocal body force identically equals zero. This makes the transform formula of the nonlocal
residual of energy much simpler. The linear nonlocal consitutive equations of elastic bodies are deduced in details, and a
new formula to calculate the antisymmetric stress is given.
Foundation item: the Natural Science Foundation of Jiangsu Province, China (BK97063) 相似文献
17.
孙鸿烈 《应用数学和力学(英文版)》1999,20(7):789-794
IntroductionFrompracticalproblem,wecouldconcludemanyproblemsaboutsolvingparabolicpartialdiferentialequation.Nowtherearemanynu... 相似文献
18.
1 ATrialFunctionandaRoutinetoFindAnalyticalSolutionofTwoTypesofNonlinearPDE Wetreatthenonlinearevolutionequation ,whichisformedbyaddinghighorderderivativetermsandnonlineartermstotheBurgersequation u t u u x … up u xq α1 u x … αn nu xn =0 ,( 1)whichp ,q ,nandαi(i =1,2… 相似文献
19.
Based on modern differential geometry, the symplectic structure of a Birkhoffian system which is an extension of conservative and nonconservative systems is analyzed. An integral invariant of Poincaré-Cartan’s type is constructed for Birkhoffian systems. Finally, one-dimensional damped vibration is taken as an illustrative example and an integral invariant of Poincaré’s type is found. 相似文献
20.
王文治 《应用数学和力学(英文版)》2004,25(2):236-244
Some new Saul‘ yev type asymmetric difference schemes for Burgers’ equation isgiven, by the use of the schemes, a kind of alternating group four points method for solvingnonlinear Burgers‘ equation is constructed here. The basic idea of the method is that thegrid points on the same time level is divided into a number of groups, the differenceequations of each group can be solved independently, hence the method with intrinsicparallelism can be used directly on parallel computer. The method is unconditionally stableby analysis of linearization procedure. The numerical experiments show that the method has good stability and accuracy. 相似文献