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1.
运用合成展开法,构造了一类具非线性边值条件的双参数奇摄动问题的形式渐近解,并利用微分不等式理论,证明了该问题解的存在性和渐近解的一致有效性.  相似文献   

2.
研究了一类两参数非线性反应扩散积分微分奇摄动问题.利用奇摄动方法,构造了问题的外部解、内部激波层、边界层及初始层校正项,由此得到了问题解的形式渐近展开式.最后利用积分微分方程的比较定理证明了该问题解的渐近展开式的一致有效性.  相似文献   

3.
该文研究了具有快慢层的非光滑奇异摄动问题的空间对照结构.利用边界层函数法构造了该问题的形式渐近解,并运用"缝接法"证明了问题光滑解的存在性以及渐近解的一致有效性.最后,通过例子验证了所得结果的有效性.  相似文献   

4.
研究了一类奇摄动半线性Robin问题.在适当的条件下,分析了该问题出现多重解现象.利用合成展开法构造出问题的形式渐近解,并应用微分不等式理论证明了解的存在性以及当ε→0时解的渐近性质.  相似文献   

5.
研究了一类非线性三阶微分方程的奇摄动问题.运用合成展开法构造了问题的形式渐近解,并运用不动点原理证明了原问题解的存在性及所得形式渐近解的一致有效性.  相似文献   

6.
莫嘉琪 《数学进展》2008,37(1):85-91
讨论了一类具有超抛物型方程的反应扩散问题.首先,证明了比较定理.其次,构造了形式渐近解.然后,利用微分不等式方法,研究了问题解的存在、唯一性和渐近性态.最后得到了原问题解的渐近展开式.  相似文献   

7.
本文研究带慢变量的右边不连续的拟线性奇异摄动方程组的空间对照结构.利用边界层函数法构造了该方程组的形式渐近解,并运用"缝接法"证明问题解的存在性以及渐近解的一致有效性.最后,通过例子验证了所得结果的有效性.  相似文献   

8.
研究了一类含双参数的非线性高阶微分方程的奇摄动问题.运用合成展开法构造了问题的形式渐近解,并运用微分不等式理论证明了原问题解的存在性及所得形式渐近解的一致有效性.  相似文献   

9.
对一类拟线性流体模型进行研究,借助Linard变换将所研究问题转化为可以用边界函数法处理的问题,进而用边界函数法对该方程组进行分析,构造其(n+1)阶形式渐近解,并证明解的存在唯一性和形式渐近解的一致有效性.  相似文献   

10.
研究了一个三阶半线性微分方程的奇摄动非线性混合边值问题.利用边界层函数法构造了该问题的形式渐近解,并采用微分不等式理论证明了解的存在性,给出了渐近解的误差估计,最后得出了边界层函数指数型衰减的结论.  相似文献   

11.
D. Medková 《Acta Appl Math》2011,116(3):281-304
A weak solution of the Neumann problem for the Stokes system in Sobolev space is studied in a bounded Lipschitz domain with connected boundary. A solution is looked for in the form of a hydrodynamical single layer potential. It leads to an integral equation on the boundary of the domain. Necessary and sufficient conditions for the solvability of the problem are given. Moreover, it is shown that we can obtain a solution of this integral equation using the successive approximation method. Then the consequences for the direct boundary integral equation method are treated. A solution of the Neumann problem for the Stokes system is the sum of the hydrodynamical single layer potential corresponding to the boundary condition and the hydrodynamical double layer potential corresponding to the trace of the velocity part of the solution. Using boundary behavior of potentials we get an integral equation on the boundary of the domain where the trace of the velocity part of the solution is unknown. It is shown that we can obtain a solution of this integral equation using the successive approximation method.  相似文献   

12.
本以Signorini接触问题为背景,讨论了变分不等式与边值问题的等价性,利用Green公式,基本解和基本解法向导数的性质,将区域型变分不等式化成等价的边界型变分不等式,并证明了边界变分不等式解的存在唯一性,为使用边界元方法数值求解提供理论依据。  相似文献   

13.
Numerical Solution for the Helmholtz Equation with Mixed Boundary Condition   总被引:1,自引:0,他引:1  
We consider the numerical solution for the Helmholtz equation in R~2 with mixed boundary conditions.The solvability of this mixed boundary value problem is estab- lished by the boundary integral equation method.Based on the Green formula,we express the solution in terms of the boundary data.The key to the numerical real- ization of this method is the computation of weakly singular integrals.Numerical performances show the validity and feasibility of our method.The numerical schemes proposed in this paper have been applied in the realization of probe method for inverse scattering problems.  相似文献   

14.
In this paper an inverse method for solving elastostatic problems with incomplete boundary conditions is presented. In general, inverse problems are ill-posed boundary value problems whose stability and uniqueness of solution and sensitivity-based formulations require additional constraints. In the development we use the Betti-reciprocal theorem to represent the boundary traction field in terms of the boundary and field displacements in an integral form. Initially, we assume the unknown boundary conditions and deformations required to solve the problem. In this way we equate the work done by the exact solution (unknown) to the work done by an assumed solution. Discretizing the resulting equations and using an iterative procedure each step in the solution process becomes the solution to a well-posed problem. Thus, with sufficient perturbations the correct boundary conditions are reconstructed.  相似文献   

15.
We apply the trial method for the solution of Bernoulli's free boundary problem when the Dirichlet boundary condition is imposed for the solution of the underlying Laplace equation, and the free boundary is updated according to the Neumann boundary condition. The Dirichlet boundary value problem for the Laplacian is solved by an exponentially convergent boundary element method. The update rule for the free boundary is derived from the linearization of the Neumann data around the actual free boundary. With the help of shape sensitivity analysis and Banach's fixed‐point theorem, we shed light on the convergence of the respective trial method. Especially, we derive a stabilized version of this trial method. Numerical examples validate the theoretical findings.Copyright © 2014 John Wiley & Sons, Ltd.  相似文献   

16.
In this paper, we propose a method for the numerical solution of self adjoint singularly perturbed third order boundary value problems in which the highest order derivative is multiplied by a small parameter $\varepsilon$. In this method, first we introduce the derivatives of two scale relations satisfied by the subdivision schemes. After that we use these derivatives to construct the subdivision collocation method for the numerical solution of singularly perturbed boundary value problems. Convergence of the subdivision collocation method is also discussed. Numerical examples are presented to illustrate the proposed method.  相似文献   

17.
具有多重解的非线性Robin问题的奇摄动[英文]   总被引:12,自引:0,他引:12  
欧阳成 《应用数学》2002,15(3):149-153
本文利用边界层法,研究了具有多重解的非线性Robin问题εx″ f(t,x)x′ g(t,x)=0,0≤t≤1,x′(0,ε)-ax(0,ε)=A,x′(1,ε) bx(1,ε)=B其中ε为正的小参数。在适当的假设下,我们通过给出外部解展开式系数的一般表达式,得到了退化问题的边值为某方程的多重根时的渐近解,推广了有关结果。  相似文献   

18.
In this paper, we propose a simple and robust numerical method for the forced Korteweg–de Vries (fKdV) equation which models free surface waves of an incompressible and inviscid fluid flow over a bump. The fKdV equation is defined in an infinite domain. However, to solve the equation numerically we must truncate the infinite domain to a bounded domain by introducing an artificial boundary and imposing boundary conditions there. Due to unsuitable artificial boundary conditions, most wave propagation problems have numerical difficulties (e.g., the truncated computational domain must be large enough or the numerical simulation must be terminated before the wave approaches the artificial boundary for the quality of the numerical solution). To solve this boundary problem, we develop an absorbing non-reflecting boundary treatment which uses outward wave velocity. The basic idea of the proposing algorithm is that we first calculate an outward wave velocity from the solutions at the previous and present time steps and then we obtain a solution at the next time step on the artificial boundary by moving the solution at the present time step with the velocity. And then we update solutions at the next time step inside the domain using the calculated solution on the artificial boundary. Numerical experiments with various initial conditions for the KdV and fKdV equations are presented to illustrate the accuracy and efficiency of our method.  相似文献   

19.
In this paper, we propose a fundamental solution method for three-dimensional viscous flow problems with obstacles in a periodic array. Our problem is mathematically a boundary value problem of the Stokes equation with periodic boundary conditions, to which it is difficult to give a good approximation by the ordinary fundamental solution method. Our method gives an approximate solution by a linear combination of the periodic fundamental solutions. In addition, we can compute the drag forces on the obstacles by using the data obtained in our method. Numerical examples for the problems of flows past spheres show the effectiveness of our method.  相似文献   

20.
In this paper we deal with the general boundary value problems for quasilinear higherorder elliptic equations with a small parameter before higher derivatives.By using themethod of multiple scales,we have proved that if the solution of degenerated boundary valueproblem exists,then under certain assumptions as the small parameter is sufficiently small,the solution of the origional boundary value problem exists as well and it is unique in a certainfunction space.Besides,the asymptotic expansion of the solution has been constructed.  相似文献   

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