一类具有边界摄动的非线性问题的渐近解及其可解性条件

利用摄动理论,讨论一类具有边界摄动的非线性问题.在适当的条件下,得出了这类问题的渐近解及其可解性条件,推广了一类近乎圆膜的振动问题所得的结果.     

A fast solution method for the time-dependent orienteering problem

This paper introduces a fast solution procedure to solve 100-node instances of the time-dependent orienteering problem (TD-OP) within a few seconds of computation time. Orienteering problems occur in logistic situations were an optimal combination of locations needs to be selected and the routing between the selected locations needs to be optimized. In the time-dependent variant, the travel time between two locations depends on the departure time at the first location. Next to a mathematical formulation of the TD-OP, the main contribution of this paper is the design of a fast and effective algorithm to tackle this problem. This algorithm combines the principles of an ant colony system (ACS) with a time-dependent local search procedure equipped with a local evaluation metric. Additionally, realistic benchmark instances with varying size and properties are constructed. The average score gap with the known optimal solution on these test instances is only 1.4% with an average computation time of 0.5 seconds. An extensive sensitivity analysis shows that the performance of the algorithm is insensitive to small changes in its parameter settings.     

Asymptotic expansions for the Sturm-Liouville problem by homotopy perturbation method

The asymptotic formulae for the eigenvalues and eigenfunctions of Sturm-Liouville problem with the Dirichlet boundary conditions when the potential is square integrable on [0, 1] are obtained by using homotopy perturbation method.     

A singular perturbation problem with discontinuous data in a cuboid

We analyse the asymptotic behaviour of the solution of a 3Dsingularly perturbed convection–diffusion problem withdiscontinuous Dirichlet boundary data defined in a cuboid. Wewrite the solution in terms of a double series and we obtainan asymptotic approximation of the solution when the singularparameter 0. This approximation is given in terms of a finitecombination of products of error functions and characterizesthe effect of the discontinuities on the small -behaviour ofthe solution in the singular layers.     

Global existence of weak discontinuous solutions to the Cauchy problem with small BV initial data for quasilinear hyperbolic systems

In this paper, we study the Cauchy problem for quasilinear hyperbolic system with a kind of non‐smooth initial data. Under the assumption that the initial data possess a suitably small bounded variation norm, a necessary and sufficient condition is obtained to guarantee the existence and uniqueness of global weak discontinuous solution. Copyright © 2014 John Wiley & Sons, Ltd.     

Fourth order algorithms for a semilinear singular perturbation problem

Fourth order finite-difference algorithms for a semilinear singularly perturbed reaction–diffusion problem are discussed and compared both theoretically and numerically. One of them is the method of Sun and Stynes (1995) which uses a piecewise equidistant discretization mesh of Shishkin type. Another one is a simplified version of Vulanović's method (1993), based on a discretization mesh of Bakhvalov type. It is shown that the Bakhvalov mesh produces much better numerical results. This revised version was published online in June 2006 with corrections to the Cover Date.     

The evolution to a steady state for a porous medium model

An initial boundary value problem is considered for a nonlinear diffusion equation, the diffusivity being a function of the dependent variable. Dirichlet boundary conditions, independent of time, are considered and positive solutions are assumed. This paper is mainly concerned with the rate of convergence, in time, of the unsteady to the steady state. This is done by obtaining an upper estimate for a positive-definite, integral measure of the perturbation (i.e., unsteady-steady state) using differential inequality techniques.A previous result is recalled where the diffusivity k(τ)=τn (n being a positive constant) appropriate to mass transport, or filtration, in a porous medium. The present paper treats an alternative model, sharing some of the characteristics of the previous one: k(τ)=eτ−1, τ being non-negative.The paper concludes by considering a “backwards in time” initial boundary value problem for the perturbation (amenable to the same techniques) and establishes that the solution ceases to exist beyond a critical, computable time.     

An equation decomposition method for the numerical solution of a fourth‐order elliptic singular perturbation problem

In this article, we propose a tailored finite point method (TFPM) for the numerical solution of a type of fourth‐order singular perturbation problem in two dimensions based on the equation decomposition technique. Our finite point method has been tailored based on the local exponential basis functions. Furthermore, our TFPM satisfies the discrete maximum principle automatically. Our numerical examples show that our method has second order convergence rate in energy norm as $\varepsilon\to0$ . © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2011     

Uniqueness of solution to a free boundary problem from combustion

We investigate the uniqueness and agreement between different kinds of solutions for a free boundary problem in heat propagation that in classical terms is formulated as follows: to find a continuous function defined in a domain and such that

0\}. \end{displaymath}">

We also assume that the interior boundary of the positivity set, \nobreak 0\}$">, so-called free boundary, is a regular hypersurface on which the following conditions are satisfied:

Here denotes outward unit spatial normal to the free boundary. In addition, initial data are specified, as well as either Dirichlet or Neumann data on the parabolic boundary of . This problem arises in combustion theory as a limit situation in the propagation of premixed flames (high activation energy limit).

The problem admits classical solutions only for good data and for small times. Several generalized concepts of solution have been proposed, among them the concepts of limit solution and viscosity solution. We investigate conditions under which the three concepts agree and produce a unique solution.

     

Global existence of weakly discontinuous solutions to a kind of mixed initial-boundary value problem for quasilinear hyperbolic systems

In this paper, the mixed initial-boundary value problem for general first order quasi- linear hyperbolic systems with nonlinear boundary conditions in the domain D = {（t, x） ｜ t ≥ 0, x ≥0} is considered. A sufficient condition to guarantee the existence and uniqueness of global weakly discontinuous solution is given.     

Up-to boundary regularity for a singular perturbation problem of p-Laplacian type

In this paper we are interested in establishing up-to boundary uniform estimates for the one phase singular perturbation problem involving a nonlinear singular/degenerate elliptic operator. Our main result states: if Ω⊂Rn is a C1,α domain, for some 0<α<1 and uε verifies

     

On a multiple time-scales perturbation analysis of a Stefan problem with a time-dependent Dirichlet boundary condition

In this paper, a classical Stefan problem with a prescribed and small time-dependent temperature at the boundary is studied. By using a multiple time-scales perturbation method, it is shown analytically how the moving boundary profile is influenced by the prescribed temperature at the boundary and the initial conditions. Only a few exact solutions are available for this type of problems and it turns out that the constructed approximations agree very well with these exact solutions. In particular, approximations of solutions for this type of problems, with periodic and decaying temperatures at the boundary, are constructed. Furthermore, these approximations are valid on a long time scale, and seems to be not available in the literature.     

The Dirichlet problem for a conservation law with a multiplicative stochastic perturbation

In this paper, we are interested in the Dirichlet boundary value problem for a multi-dimensional nonlinear conservation law with a multiplicative stochastic perturbation. Using the concept of measure-valued solutions and Kruzhkov?s semi-entropy formulations, a result of existence and uniqueness of the entropy solution is proved.     

一类二阶非线性奇异边值问题的正解

对非线性项ｆ在ｐｙ’＝ ０奇异但在ｙ＝ ０非奇异的情形下,边值问题 正解的存在性作讨论．     

一个渐近非线性Dirichlet问题的对径解的存在性

利用锥上的不动点定理获得了一个渐近非线性Dirirchlet问题的对径解的存在定理。     

A perturbation method for optimizing matrix stability

We present the first practical perturbation method for optimizing matrix stability using spectral abscissa minimization. Using perturbation theory for a matrix with simple eigenvalues and coupling this with linear programming, we successively reduce the spectral abscissa of a matrix until it reaches a local minimum. Optimality conditions for a local minimizer of the spectral abscissa are provided and proved for both the affine matrix problem and the output feedback control problem. Experiments show that this novel perturbation method is efficient, especially for a matrix with the majority of whose eigenvalues are already located in the left half of the complex plane. Moreover, unlike most available methods, the method does not require the introduction of Lyapunov variables. The method is illustrated for a small size matrix from an affine matrix problem and is then applied to large matrices actually arising from more sophisticated control problems used in the design of the Boeing 767 jet and a nuclear powered turbo-generator.