共查询到20条相似文献，搜索用时 15 毫秒
1.
莫嘉琪 《应用数学和力学(英文版)》1991,12(4):399-408
In this paper,a class of singularly perturbed initial-boundary value problems for thereaction diffusion systems is considered.Using the theory of differential inequality,weprove that the initial-boundary value problems have a solution and obtain their asymptoticexpansion. 相似文献
2.
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
3.
M. Eleuteri P. Krej
í 《ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik》2007,87(4):261-277
A parabolic equation in two or three space variables with a Preisach hysteresis operator and with homogeneous Neumann boundary conditions is shown to admit a unique global regular solution. A detailed investigation of the Preisach memory dynamics shows that the system converges to an equilibrium in the state space of all admissible Preisach memory configurations as time tends to infinity. 相似文献
4.
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
5.
Kang Lian-cheng 《应用数学和力学(英文版)》1992,13(2):149-157
In this paper, we consider a singularly perturbed problem of a kind of quasilinear hyperbolic-parabolic equations, subject to initial-boundary value conditions with moving boundary: When certain assumptions are satisfied and ε is sufficiently small, the solution of this problem has a generalized asymptotic expansion (in the Van der Corput sense), which takes the sufficiently smooth solution of the reduced problem as the first term, and is uniformly valid in domain Q where the sufficiently smooth solution exists. The layer exists in the neighborhood of t=0. This paper is the development of references [3–5]. The Project supported by the National Natural Science Foundation of China. 相似文献
6.
康连城 《应用数学和力学(英文版)》1992,(2)
In this paper, we consider a singularly perturbed problem of a kind of quasilinear hyperbolic-parabolic equations, subject to initial-boundary value conditions with moving boundary. When certain assumptions are satisfied and e is sufficiently small, the solution of this problem has a generalized asymptotic expansion (in the Van der Corput sense), which takes the sufficiently smooth solution of the reduced problem as the first term, and is uniformly valid in domain Q where the sufficiently smooth solutioh exists. The layer exists in the neighborhood of t=0. This paper is the development of references. 相似文献
7.
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
8.
倪明康 《应用数学和力学(英文版)》1991,12(5):461-468
This paper deals with the problem on the periodic solution for the singularly perturbeddifferential equations of parabolic type originating from chemical kinetics in stratifiedmedia,A uniformly valid asymptotic solution is constructed and the related asymptoticestimate is given. 相似文献
9.
SINGULARLY PERTURBED BOUNDARY VALUE PROBLEMS FOR SEMI-LINEAR RETARDED DIFFERENTIAL EQUATIONS WITH NONLINEAR BOUNDARY CONDITIONS 
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下载免费PDF全文 IntroductionInthispaper,westudiedakindofboundaryvalueproblems (BVPs)forsemi_linearretardeddifferentialequationwithnonlinearboundarycondition : εx″(t) =f(t,x(t) ,x(t-ε) ,ε) , t∈(0 ,1 ) ,(1 ) x(t) =φ(t,ε) , t∈[-ε0 ,0 ] ,h(x(1 ) ,x′(1 ) ,ε) =A(ε) ,(2 )whereε>0isasmallparameterandε0 isasufficientlysmallpositiveconstant.ThereweremanyresultsofstudyingonsingularlyperturbedboundaryvalueproblemforretardeddifferentialequationinRefs.[1～5] .Butthosestudiespossessedanesse… 相似文献
10.
Kai Wang;Hongyong Zhao ;Hao Wang 《Discrete and continuous dynamical systems》2023,28(2):1279-1299
This paper is devoted to investigate the existence of traveling wave solutions for a partially degenerate Aedes aegypti model with nonlocal effects. By taking specific kernel forms and time scale transformation, we transform the nonlocal model into a singularly perturbed system with small parameters. A locally invariant manifold for wave profile system is obtained with the aid of the geometric singular perturbation theory, and then the existence of traveling wave solutions is proved provided that the basic reproduction number $ mathcal{R}_0>1 $ through utilizing the Fredholm orthogonal method. Furthermore, we study the asymptotic behaviors of traveling wave solution with the help of asymptotic theory. The methods used in this work can help us overcome the difficulty that the solution map associated with the system is not compact. Numerically, we perform simulations to demonstrate the theoretical results. 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 下载免费PDF全文
下载免费PDF全文 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.
黄蔚章 《应用数学和力学(英文版)》1992,13(8):745-754
This paper deals.with the singular perturbation of the boundary value problem of the systems for quasi-linear ordinary differential equations where x,f, y, h, A, B and C all belong to Rm, and g is an n×n matrix function. Under suitable conditions we prove the existence of the solutions by diagonalization and the fixed point theorem and also estimate the remainder. 相似文献
13.
周源泉 《应用数学和力学(英文版)》1986,7(9):887-894
In this paper the AMSAA model for multi-system simultaneous development is discussed. The maximum likelihood (ML) estimates of the parameters and the confidence intervals of the MTBF for Weibull process are presented. Crow’s formulae[1] are the special examples for this paper. 相似文献
14.
Chen Li;Jiang Liu ;Zengji Du 《Discrete and continuous dynamical systems》2023,28(3):1771-1786
In this paper, we are concerned with the existence of traveling wave solutions for the Keller-Segel model with logarithmic sensitivity. By the Hopf-Cole transformation and traveling wave transformation, the degenerate Keller-Segel system is transformed into a singularly perturbed system. By constructing an invariant region to prove the existence of the traveling wave solutions for the degenerate system, we obtain the traveling wave solutions for Keller-Segel system with small parameter by using geometric singular perturbation theory and Fredholm theory. Finally, we discuss the asymptotic behaviors of the traveling wave solutions. 相似文献
15.
本文针对板弯曲边界元方法中计算边界曲率等高阶导数项时边界积分方程中出现的高阶奇异积分项,通过对未知挠曲函数作渐近展开并加以适当摄动,获得了渐近收敛的边界积分方程。采用这一方法计算板边界上的曲率分布,获得了满意的数值结果。 相似文献
16.
李怡平 《应用数学和力学(英文版)》1992,13(8):719-723
An initially periodic motion is gradually raised out of the potential well by the effect of negative damping. The elapsed time when the motion ceases to be periodic is obtained by multiple variable expansions. An example of a strictly nonlinear system shows the result has a good approximation and is easy to calculate. 相似文献
17.
ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅａｕｔｈｏｒｓｔｕｄｉｅｄａｃｌａｓｓｏｆｓｉｎｇｕｌａｒｌｙｐｅｒｔｕｒｂｅｄｐｒｏｂｌｅｍｓｉｎ [1]- [8].Ｔｈｉｓｐａｐｅｒｉｎｖｏｌｖｅｓｔｈｅｇｅｎｅｒａｌｉｚｅｄｓｏｌｕｔｉｏｎｏｆｔｈｅｓｉｎｇｕｌａｒｌｙｐｅｒｔｕｒｂｅｄｐｒｏｂｌｅｍｓ.ＮｏｗｗｅｃｏｎｓｉｄｅｒｔｈｅｆｏｌｌｏｗｉｎｇＤｉｒｉｃｈｌｅｔｐｒｏｂｌｅｍｆｏｒｔｈｅｑｕａｓｉ＿ｌｉｎｅａｒｅｌｌｉｐｔｉｃｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｏｆｈｉｇｈｅｒｏｒｄｅｒεＬ2ｍ[ｕ] ∑ｎ… 相似文献
18.
ＩｎｔｒｏｄｕｃｔｉｏｎＡｂｏｕｔｓｉｎｇｕｌａｒｐｅｒｔｕｒｂａｔｉｏｎｏｆｂｏｕｎｄａｒｙｖａｌｕｅｐｒｏｂｌｅｍｆｏｒｓｅｃｏｎｄ＿ｏｒｄｅｒｏｒｄｉｎａｒｙｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｗｏｒｋｓｏｆａｌａｒｇｅｎｕｍｂｅｒｗｅｒｅｃｏｎｓｉｄｅｒｅｄｏｎｌｙｆｏｒｔｈｅｃａｓｅｏｆｉｎｖｏｌｖｉｎｇｏｎｅｓｍａｌｌｐａｒａｍｅｔｅｒ[1- 4].Ｏｎｌｙａｆｅｗｗｏｒｋｓｗｅｒｅｃｏｎｓｉｄｅｒｅｄｆｏｒｔｈｅｃａｓｅｏｆｉｎｖｏｌｖｉｎｇｔｗｏｓｍａｌｌｐａｒａｍｅｔｅｒｓ[5 - 8]… 相似文献
19.
陈松林 《应用数学和力学(英文版)》1996,17(11):1095-1100
ＳＩＮＧＵＬＡＲＰＥＲＴＵＲＢＡＴＩＯＮＦＯＲＡＮＯＮＬＩＮＥＡＲＢＯＵＮＤＡＲＹＶＡＬＵＥＰＲＯＢＬＥＭＯＦＦＩＲＳＴＯＲＤＥＲＳＹＳＴＥＭＣｈｅｎＳｏｎｇｌｉｎ（陈松林）（ＲｅｃｅｉｖｅｄＡｐｒｉｌ８,１９８４;ＲｅｖｉｓｅｄＡｐｒｉｌ１５,１９... 相似文献
20.
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