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1.
张石生 《应用数学和力学(英文版)》1999,20(12):1310-1318
The purpose of this paper is to study the Mann and Ishikawa iterative approximation of solutions for m-accretive operator equations in Banach spaces. The results presented in this paper extend and improve some authors’ recent results. 相似文献
2.
Structure of nonnegative nontrivial and positive solutions was precisely studied for some singularly perturbed p-Laplace equations.
By virtue of sub- and supersolution method, it is shown that there are many nonnegative nontrivial spike-layer solutions and
positive intermediate spike-layer solutions. Moreover, the upper and lower bound on the measure of each spike-layer solutions.
Moreover, the upper and lower bound on the measure of each spike-layer were estimated when the parameter is sufficiently small.
Foundation items: the National Key Basic Research Development Project Program of China (1999032801); the National Natural Science Foundation
of China (10371095)
Biography: ZHANG Zheng-ce (1976≈) 相似文献
3.
曾六川 《应用数学和力学(英文版)》2002,23(6):686-693
1 IntroductionandPreliminariesLetXbearealBanachspacewiththenorm‖·‖ ,X bethedualspaceofX ,and〈· ,·〉bethegeneralizeddualitypairingbetweenXandX .ThenormalizeddualitymappingJ:X →2 X isdefinedbyJ(x) =f∈X :〈x ,f〉=‖x‖2 =‖f‖2 , x∈X . RecallthatthemodulusρX( ·)ofsmoothnesso… 相似文献
4.
IntroductionWiththerapiddevelopmentofscienceandtechnology ,thestudykernelofmodernscienceischangedfromlineartononlinearstepbystep .Manynonlinearscienceproblemscansimplyandexactlybedescribedbyusingthemathematicalmodelofnonlinearequation .Uptonow ,manyimpor… 相似文献
5.
The new concepts of the Z-C-X space and excellent cone are introduced. Some problems of random semiclosed 1-set-contractive operator are investigated in the Z-C-X space. At first, an important inequality is proved. Secondly, several new conclusions are proved by means of random fixed point index in the theory of random topological degree. A random solution of a class of random operator equations under conditions of imitating the parallelogram law is obtained, famous Altman’s theorem is generalized in partially ordered Z-C-X space. Therefore, some new results are obtained. 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.
Ding Xie-ping 《应用数学和力学(英文版)》2003,24(9):1017-1024
By applying existence theorems of maximal elements for a family of GB-majorized mappings in a product space of G-convex spaces, some coincidence theorem, Fan-Browder type fixed point theorem
and some existence theorems of solutions for a system of minimax inequalities are proved under noncompact setting of G-convex
spaces. These theorems improve and generalize many important known results in literature.
Contributed by Duping Xie-ping
Foundation items: the National Natural Science Foundation of China (19871059); the Natural Science Foundation of Education Department of Sichuan
Province ([2000]25)
Biography: Duping Xie-ping (1938∼), Professor (E-mail: dingxip@sichu.edu.cn) 相似文献
8.
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
9.
IntroductionForseveralhundredyears,ithasbeenbothimportantanddifficultprojecttoconstructtheanalyticalsolutionsfornonlineardifferentialequations.Manymathematiciansandtheoreticalphysicistshavedonealotofwork[1~ 5 ].However,thereexistlotsofimportantandbeingofp… 相似文献
10.
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
11.
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
12.
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
13.
Computation of super-convergent nodal stresses of timoshenko beam elements by EEP method 总被引:4,自引:1,他引:4
The newly proposed element energy projection (EEP) method has been applied to the computation of super-convergent nodal stresses of Timoshenko beam elements. Generalformul as based on element projection theorem were derived and illustrative numerical examples using two typical elements were given. Both the analysis and examples show that EEP method also works very well for the problems with vector function solutions. The EEP method gives super-convergent nodal stresses, which are well comparable to the nodal displacements in terms of both convergence rate and error magnitude. And in addition, it can overcome the “ shear locking“ difficulty for stresses even when the displacements are badly affected. This research paves the way for application of the EEP method to general onedimensional systems of ordinary differential equations. 相似文献
14.
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
15.
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
16.
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
17.
曹进德 《应用数学和力学(英文版)》1999,20(6):647-652
In this paper, by ssing the theory of Fourier series, some necessary and sufficient conditions of existence and uniqueness
of periodic solutions of a class of higher order neutral type equations are obtained. The main results by Shi Jianguo in “Discussion
on the periodic solutions for linear equation of neutral type with constant coefficients” are improved, i. e., the condition
|b0|≠1 instead of the condtion |b0|<1/2 of Theorem 1 by Shi Jianguo is given. Other theorems by Shi are rebuilt and improved according to the new assumption.
Foundation item: the Natural Science Foundation of Yunnan Province, China (97A012G) 相似文献
18.
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
19.
IntroductionHowtoobtaintravelingwavespeedsandsolutionsinnonlinearreaction_diffusionequationshasbeenaclassoffocusedquestionsformathematiciansandtheoreticalphysicists.Lineardiffusionyieldsinfinitepropagationspeed ,sodiffusioncoefficientswhichdependonthe… 相似文献
20.
CONSTITUTIVE RELATION OF UNSATURATED SOIL BY USE OF THE MIXTURE THEORY (Ⅱ)-LINEAR CONSTITUTIVE EQUATIONS AND FIELD EQUATIONS 总被引:2,自引:0,他引:2
The linear constitutive equations and field equations of unsaturated soils were obtained through linearizing the nonlinear equations given in the first part of this work. The linear equations were expressed in the forms similar to Biot’s equations for saturated porous media. The Darcy’s laws of unsaturated soil were proved. It is shown that Biot’s equations of saturated porous media are the simplification of the theory. All these illustrate that constructing constitutive relation of unsaturated soil on the base of mixture theory is rational. 相似文献