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1.
黄蔚章 《应用数学和力学(英文版)》1997,18(6):575-584
I.Intr0ducti0n'Manyresultshavebeeng0tinstudyingthesingu1arperturbation0fboundaryvalueproblemfornonlinearsystemeg#=j(t,g,y',8)(l.l)bythemethodandthetechniqueofdiagonalizationl'~'l.Thepapersarebasedonsucha.conditionthattheeigenvaluesofJacobimatrixlu'offwit… 相似文献
2.
The step-type contrast structure for a singular singularly perturbed problem is shown. By use of the method of boundary function, the formal asymptotic expansion is constructed. At the same time, based on sewing orbit smooth, the existence of the step- type solution and the uniform validity of the asymptotic expansion are proved. Finally, an example is given to demonstrate the effectiveness of the present results. 相似文献
3.
IntroductionThispaperisconcernedwiththenumericalsolution ,byfinitedifferencemethod ,ofthefollowingsingularlyperturbednonlocalboundaryvalueproblem :Lu≡-εu″ +a(x)u=f(x) ( 0 <x<l) ,( 1 )L0 u≡-εu′( 0 ) +γu( 0 ) =μ0 , ( 2 )L1u≡u(l) -δu(d) =μl ( 0 <d<l) ,( 3 )whereεisasmallpositiveparameter,… 相似文献
4.
In this paper we discuss,an initial-boundary value problem of hyperbolic type with firstderivative with respect to x.The asymptotic solution is constructed and its uniform validityis proved under weader compatibility conditions.Then we develop an exponentially fitteddifference scheme and establish discrete energy inequality.Finally,we prove that thesolution of difference problem uniformly converges to the solution of the original problem. 相似文献
5.
A uniformly convergent finite difference method for a singularly perturbed initial value problem 总被引:1,自引:0,他引:1
G. M. Amiraliyev Hakk Duru Department of Mathematics Y Y University VAN TURKEY 《应用数学和力学(英文版)》1999,20(4):379-387
IntroductionThepurposeofthispaperistodevelopacuratediferencemethodforthefolowinginitialvalueproblem,whichisinsingularperturba... 相似文献
6.
Some authors employed the method and technique of differential inequalities to obtain fairly general results concerning the existence and asymptotic behavior, as ε→n~+, of the solutions of scalar boundary value problems In this paper, we extend these results to vector boundary value problems, under analogous stability conditions on the solution u=u(t) of the reduced equation O=h(t, u) Two types of asymptotic behavior are studied, depending on whether the reduced solution u(t) has or does not have a con tinuous first derivative in (a, b) leading to the phenomena of boundary and angular layers. 相似文献
7.
I.1utroductlouWeconsidcrthenonlinearstateregulatorproblemsconsistingofthesystemontheinterval0't相似文献
8.
Interior layer behavior of boundary value problems for second order vector equation of elliptic type
In this paper, making use of the theory of partial differential inequalities, we will investigate the boundary value problems
for a class of singularly perturbed second order vector elliptic equations, and obtain the existence and asymptotic estimation
of solutions, involving the interior layer behavior, of the problems described above. 相似文献
9.
The nonlinear nonlocal singularly perturbed problems for reaction diffusion equations 总被引:4,自引:0,他引:4
A class of nonlinear nonlocal for singularly perturbed Robin initial boundary value problems for reaction diffusion equations
is considered. Under suitable conditions, firstly, the outer solution of the original problem is obtained, secondly, using
the stretched variable, the composing expansion method and the expanding theory of power series the initial layer is constructed,
finally, using the theory of differential inequalities the asymptotic behavior of solution for the initial boundary value
problems are studied and educing some relational inequalities the existence and uniqueness of solution for the original problem
and the uniformly valid asymptotic estimation is discussed.
Foundation items: the National Natural Science Foundation of China (10071048); the “Hunfred Talents Project” by Chinese Academy of Sciences
Biography: Mo Jia-qi (1937−) 相似文献
10.
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
11.
SINGULARLY PERTURBED NONLINEAR BOUNDARY VALUE PROBLEM FOR A KIND OF VOLTERRA TYPE FUNCTIONAL DIFFERENTIAL EQUATION 总被引:2,自引:0,他引:2
鲁世平 《应用数学和力学(英文版)》2003,24(12):1441-1449
IntroductionThereweresomeresultsofstudyingonboundaryvalueproblemsforfunctionaldifferentialequation[1~6 ]byemployingthetoplolgicaldegreetheoryandsomefixedpointprinciplesinrecentyears.Buttheworktostudyboundaryvalueproblemsfordelaydifferentialequationwithsmallparameterbymeansofthetheoryofsingularperturbationrarelyappeared[7~11].Thereasonforitisthattheworktoconstructtheuppersolutionandlowersolutionforthecaseofdifferentialequationwithdelayisdifficult.Theauthorhasstudiedakindofboundaryvalueproblem… 相似文献
12.
We consider the numerical solution of a singularly perturbed problem for the quasilinear parabolic differential equation, and construct a linear three-level finite difference scheme on a nonuniform grid. The uniform convergence in the sense of discrete L~2 norm is proved and numerical examples are presented. 相似文献
13.
In this paper,by using the techniques of differential inequalities,we prove the existence of the solutions of a singularly perturbed boundary value problem for the third order semilinear differential equation with a turning point. 相似文献
14.
A class of singularly perturbed reaction diffusion systems 总被引:4,自引:0,他引:4
莫嘉琪 《应用数学和力学(英文版)》1997,18(3):273-277
A class of singularly perturbed reaction diffusion systems are considered. Under suitable conditions, using the comparison
theorem the asymptotic behavior of solution for the initial boundary value problems is studied.
Project supported by the National Natural Science Foundation of China 相似文献
15.
The step-like contrast structure for a class of nonlinear singularly perturbed optimal control problems is considered. The existence of the step-like contrast structure for the singularly perturbed optimal control problem is proved by equivalence, which is based on the necessary conditions. The authors not only give the conditions under which there exists a step-like contrast structure, but also determine where the internal transition time is. Meanwhile, the uniformly valid asymptotic expansion of the step-like contrast structure solution is constructed by the direct scheme method. Finally, an example is presented to show the result. 相似文献
16.
袁镒吾 《应用数学和力学(英文版)》1996,17(1):90-98
YuanYiwu(袁镒吾)(ReceivedOct.2,1994;CommunicatedbyChienWeizang)INTERPOLATIONPERTURBATIONMETHODFORSOLVINGTHEBOUNDARYLAYERTYPEPROB... 相似文献
17.
倪守平 《应用数学和力学(英文版)》1989,10(4):329-330
In this paper the method and technique of the diagonalization are employed to transform a vector second-order nonlinear system into two first-order approximate diagonalized systems. The existence and the asymptotic behavior of the solutions are obtained for a vector second-order nonlinear Robin problem of singular perturbation type. 相似文献
18.
A class of nonlinear singularly perturbed problem of ultra parabolic equations are considered. Using the comparison theorem, the existence, uniqueness and its asymptotic behavior of solution for the problem are studied. 相似文献
19.
林宗池 《应用数学和力学(英文版)》1986,7(5):433-441
In this paper, using the method of differential inequalities, we study the existence of solutions and their asymptotic behavior, as 0+, of Dirichlt problem for second order quasilinear systems. Depending on whether the reduced solutionu(t) has or does not have a continuous first-derivative in (a, b), we study two types of asymptotic behaviour, thus leading to the phenomena of boundary and angular layers. 相似文献
20.
In this paper, we consider the upwind difference scheme for singular perturbation problem (1.1). On a special discretization mesh, it is proved that the solution of the upwind difference scheme is first order convergent, uniformly in the small parameter ε, to the solution of problem (1.1). Numerical results are finally provided. 相似文献