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1.
Applying the theory of stratification, the solution space structure about a class of deformed Navier-Stokes equation isdetermined.
It is proved that such kind of equation has no Ck (k≥2) stable solution by the fact that the strate transversale is a null set.
Foundation item: the National Natural Science Foundation of China (19971054), Shanghai Natural Science Foundation (99ZA14034)
Biography: HE You-hua (1960-) 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 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
6.
For the generalized inverse function-valued Padé approximants, its intact computation formulas are given. The explicit determinantal
formulas for the denominator scalar polynomials and the numerator function-valued polynomials are first established. A useful
existence condition is given by means of determinant form.
Foundation item: the National Natural Science Foundation of China (19871054)
Biography: Gu Chuan-qing (1955-), Professor, Doctor Director 相似文献
7.
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
8.
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
9.
IntroductionDuringthestudyofshallowwaterwaves,peopleobtainedmanywell_knowncompletelyintegrablemodels,suchasKdVequation,mKdVequation,Boussinesqequation,Whitham_Broer_KaupequationandKhokhlov_Zabolotskayaequationetc.[1~8].For2 1_dimensionalvariablecoefficientg… 相似文献
10.
Bifurcations of one kind of reaction-diffusion equations, u″+μ(u-uk)=0(μ is a parameter,4≤k∈Z+), with boundary value condition u(0)=u(π)=0 are discussed. By means of singularity theory based on the method of Liapunov-Schmidt reduction, satisfactory results can be acquired. 相似文献
11.
The criterion for the points in the parameter space being on the stability boundary of linear Hamiltonian system depending
on arbitrary numbers of parameters was given, through the sensitivity analysis of eigenvalues and eigenvectors. The results
show that multiple eigenvalues with Jordan chain take a very important role in the stability of Hamiltonian systems.
Foundation item: the National Natural Science Foundation of China (10072012); the National Natural Science Foundation of Russia
Biography: QI Zhao-hui (1964-) 相似文献
12.
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
13.
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
14.
Ding Xie-ping 《应用数学和力学(英文版)》2003,24(6):659-672
A new family of set-valued mappings from a topological space into generalized convex spaces was introduced and studied. By
using the continuous partition of unity theorem and Brouwer fixed point theorem, several existence theorems of maximal elements
for the family of set-valued mappings were proved under noncompact setting of product generalized convex spaces. These theorems
improve, unify and generalize many important results in recent literature.
Contributed by DING Xie-ping
Foundation items: the National Natural Science Foundation of China (19871059); the Natural Science Foundation of Education Department of Sichuan
Province of China ([2000]25)
Biography: DING Xie-ping (1938∼) 相似文献
15.
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
16.
Uniform Analytic Construction of Wavelet Analysis Filters Based on Sine and Cosine Trigonometric Functions 总被引:1,自引:0,他引:1
1 Introduction1 .1IntroductionofbackgroundWaveletanalysisanditsapplicationshavebecomeoneofthefastestgrowingresearchareasinrecentyears[1- 9].Especially ,thewavelettransformsbasedonorthonormalbasesofcompactlysupportedwaveletarewidelyusedinimagecompression ,com… 相似文献
17.
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
18.
IntroductionThedynamicequationsofmotionofmultibodysystemswithconstraintsarethefollowingdifferential/algebraicequations,i.e.,E... 相似文献
19.
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
20.
A class of nonlinear boundary value problems (BVP) for the second-order E2 class elliptic systems in general form is discussed. By introducing a kind of transformation, this kind of BVP is reduced
to a class of generalized nonlinear Riemann-Hilbert BVP. And then some singular integral operators are introduced to establish
the equivalent nonlinear singular integral equations. The solvability is proved under some suitable hypotheses by means of
the properties of singular integral operators and the function theoretic methods.
Foundation items: the National Natural Science Foundation of China (19671056); Shanghai Municipal Natural Scientific Foundation (99ZA14030,
01ZA14023); Jiangxi Provincial Natural Scientific Foundation (981102, 0211014)
Biographies: LI Ming-zhong (1935−); XU Ding-hua (1967−) 相似文献