共查询到20条相似文献,搜索用时 31 毫秒
1.
A class of nonlinear nonlocal for singularly perturbed Robin initial boundary value problems for reaction diffusion equations with boundary perturbation is considered. Under suitable conditions, first, the outer solution of the original problem was obtained. Secondly, using the stretched variable, the composing expansion method and the expanding theory of power series the initial layer was constructed. Finally, using the theory of differential inequalities the asymptotic behavior of solution for the initial boundary value problems was studied, and educing some relational inequalities the existence and uniqueness of solution for the original problem and the uniformly valid asymptotic estimation were discussed. 相似文献
2.
莫嘉琪 《应用数学和力学(英文版)》2008,29(8):1105-1110
In this paper, a class of nonlinear singularly perturbed initial boundary value problems for reaction diffusion equations with boundary perturbation are considered under suitable conditions. Firstly, by dint of the regular perturbation method, the outer solution of the original problem is obtained. Secondly, by using the stretched variable and the expansion theory of power series the initial layer of the solution is constructed. And then, by using the theory of differential inequalities, the asymptotic behavior of the solution for the initial boundary value problems is studied. Finally, using some relational inequalities the existence and uniqueness of solution for the original problem and the uniformly valid asymptotic estimation are discussed. 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.
The asymptotic theory of initial value problems for semilinear ware equations in two space dimensions was dealt with. The
well-posedness and vaildity of formal approximations on a long time scale were discussed in the twice continuous classical
space. These results describe the behavior of long time existence for the validity of formal approximations. And an application
of the asymptotic theory is given to analyze a special wave equation in two space dimensions.
Foundation item: Sichuan Youth Foundation (1999-09)
Biography: LAI Shao-yong (1965−), Associate Professor 相似文献
5.
A class of singularly perturbed initial boundary value problems for semilinear reaction diffusion equations with two parameters is considered, Under suitable conditions and using the theory of differential inequalities, the existence and the asymptotic behavior of the solution to the initial boundary value problem are studied. 相似文献
6.
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
7.
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
8.
黄家寅 《应用数学和力学(英文版)》2004,25(7):817-826
By using “the method of modified two-variable”,“the method of mixing perturbation ”and introducing four small parameters, the problem of the nonlinear unsymmetrical bending for orthotropic rectangular thin plate with linear variable thickness is studied. And the uniformly valid asymptotic solution of Nth- order for ε1 and Mth- order for ε2 of the deflection functions and stress function are obtained. 相似文献
9.
The method of boundary layer with multiple scales and computer algebra were applied to study the asymptotic behavior of solution
of boundary value problems for a class of system of nonlinear differential equations. The asymptotic expansions of solution
were constructed. The remainders were estimated. And an example was analysed. It provides a new foreground for the application
of the method of boundary layer with multiple scales.
Contributed by Jiang Fu-ru, Original Member of Editorial Committe, AMM
Biography: Xie La-bing (1976∼); Jiang Fu-ru(1927∼) 相似文献
10.
Abstract A class of initial boundary value problems of differential-difference equations for reaction diffusion with a small time delay is considered. Under suitable conditions and by using the stretched variable method, a formal asymptotic solution is constructed. Then, by use of the theory of differential inequalities, the uniform validity of the solution is proved. 相似文献
11.
The initial layer phenomena for a class of singular perturbed nonlinear system with slow variables are studied. By introducing stretchy variables with different quantity levels and constructing the correction term of initial layer with different “ thickness“, the Norder approximate expansion of perturbed solution concerning small parameter is obtained, and the “ multiple layer“ phenomena of perturbed solutions are revealed. Using the fixed point theorem, the existence of perturbed solution is proved, and the uniformly valid asymptotic expansion of the solutions is given as well. 相似文献
12.
IntroductionThelimitanalysisofstructuresisoneofthemostpracticalandusefulbranchesinplasticity .Ithasimportantapplicationbackgroundforproblemssuchasthedeterminationofloadcarryingcapacityandplasticformingofmetal.Thepurposeofthelimitanalysisofstructuresistoprovidereliabletheoreticalbasesforengineeringdesignandsafetyassessment.Asasimplifiedmethodforelastoplasticproblems,limitanalysisneednotrequirethehistoryofloadandcancomputethelimitloadsdirectlyinsteadofelastoplasticincrementalcomputationwhichisus… 相似文献
13.
A class of singularly perturbed boundary value problems of weakly non- linear equation for fourth order on the interval[a,b]with two parameters is considered. Under suitable conditions,firstly,the reduced solution and formal outer solution are con- structed using the expansion method of power series.Secondly,using the transformation of stretched variable,the first boundary layer corrective term near x=a is constructed which possesses exponential attenuation behavior.Then,using the stronger transfor- mation of stretched variable,the second boundary layer corrective term near x=a is constructed,which also possesses exponential attenuation behavior.The thickness of second boundary layer is smaller than the first one and forms a cover layer near x=a. Finally,using the theory of differential inequalities,the existence,uniform validity in the whole interval[a,b]and asymptotic behavior of solution for the original boundary value problem are proved.Satisfying results are obtained. 相似文献
14.
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
15.
S. A. Nazarov 《Journal of Applied Mechanics and Technical Physics》2007,48(6):861-870
Explicit presentations for the initial terms of the asymptotic solution of the spectral problem of the elasticity theory in
a plane region with a rapidly oscillating boundary are obtained. Based on asymptotic formulas, two methods for problem modeling
are proposed: with the use of Wenzel’s boundary conditions and with the use of the principle of a smooth image of a singularly
perturbed boundary. Various approaches to justification of asymptotic presentations are discussed.
__________
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 6, pp. 103–114, November–December, 2007. 相似文献
16.
Chou Huan-wen 《应用数学和力学(英文版)》1983,4(6):855-863
In this paper,the method of composite expansions which was proposed by W. Z. Chien (1948)[5]is extended to investigate two-parameter boundary layer problems.For the problems of symmetric deformations of the spherical shells under the action of uniformly distribution load q, its nonlinear equilibrium equations can be written as follows: where ε and δ are undetermined parameters.If δ=1 and ε is a small parameter, the above-mentioned problem is called first boundary layer problem; if ε is a small parameter, and δ is a small parameter, too, the above-mentioned problem is called second boundary layer problem.For the above-mentioned problems, however, we assume that the constants ε, δ and p satisfy the following equation: εp=1-ε In defining this condition by using the extended method of composite expansions, we find the asymptotic solution of the above-mentioned problems with the clamped boundary conditions. 相似文献
17.
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
18.
Analysis of thermal post-buckling of heated elastic rods 总被引:11,自引:2,他引:9
IntroductionAxiallycompressedstresswilloccurinaconstrainedelasticcolumnsubjectedtoatemperaturerising.Ifthevalueofthecompressedstressesexceedacertainlimit,thermalbucklingoftheheatedrods,whichisoutoftheinitialstraightlineconfiguration,willtakeplace.So,the… 相似文献
19.
The conditions for determining solution of buckling eigenvalue problem are discussed. The corresponding system of integral
equations with constraint conditions and boundary variational equations with Lagrange multiplier are established. The theorems
on the existence and uniqueness of the solution for these problems are given. The corresponding boundary element method is
constructed and the error estimation for the approximation solution is obtained. Finally the numerical example is given.
Foundation item: the National Natural Science Foundation Pre-research Project (T4107015)
Biography: Ding Rui (1969-) 相似文献
20.
THE PROBLEMS OF THE NONLINEAR UNSYMMETRICAL BENDING FOR CYLINDRICALLY ORTHOTROPIC CIRCULAR PLATE(II)
THEPROBLEMSOFTHENONLINEARUNSYMMETRICAL.BENDINGFORCYLINDRICALLYORTHOTROPICCIRCULARPLATE(II)HuangJiayin(黄家寅);QinShengli(秦圣立);Xi... 相似文献