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1.
On some singular perturbation problems in the theory of lubrication   总被引:1,自引:0,他引:1  
Some singular perturbation problems occurring in the theory of hydrodynamic lubrication are studied. We examine in detail the case of the very long or very short journal bearing; the asymptotic problem of small eccentricity ratio is also considered.  相似文献   

2.
We discuss the problem of the existence of periodic and almost periodic solutions in distribution of semilinear stochastic equations on a separable Hilbert space.

Under a dissipativity condition we prove that the translation of the mean square bounded solution is periodic or almost periodic. Similar results hold in the affine case under mean square stability of the linear part of the equation.  相似文献   

3.
4.
A three-point difference scheme recently proposed in Ref. 1 for the numerical solution of a class of linear, singularly perturbed, two-point boundary-value problems is investigated. The scheme is derived from a first-order approximation to the original problem with a small deviating argument. It is shown here that, in the limit, as the deviating argument tends to zero, the difference scheme converges to a one-sided approximation to the original singularly perturbed equation in conservation form. The limiting scheme is shown to be stable on any uniform grid. Therefore, no advantage arises from using the deviating argument, and the most accurate and efficient results are obtained with the deviation at its zero limit.  相似文献   

5.
In this work we obtain some new results concerning the existence of solutions to an impulsive first-order, nonlinear ordinary differential equation with periodic boundary conditions. The ideas involve differential inequalities and Schaefer's fixed-point theorem.  相似文献   

6.
It is known that the energy of a weak solution to the Euler equation is conserved if it is slightly more regular than the Besov space . When the singular set of the solution is (or belongs to) a smooth manifold, we derive various Lp-space regularity criteria dimensionally equivalent to the critical one. In particular, if the singular set is a hypersurface the energy of u is conserved provided the one-sided non-tangential limits to the surface exist and the non-tangential maximal function is L3 integrable, while the maximal function of the pressure is L3/2 integrable. The results directly apply to prove energy conservation of the classical vortex sheets in both 2D and 3D at least in those cases where the energy is finite.  相似文献   

7.
This paper deals with the spectrum of a linear, weighted eigenvalue problem associated with a singular, second order, elliptic operator in a bounded domain, with Dirichlet boundary data. In particular, we analyze the existence and uniqueness of principal eigenvalues. As an application, we extend the usual concepts of linearization and Frechet derivability, and the method of sub and supersolutions to some semilinear, singular elliptic problems.  相似文献   

8.
Problems related to perturbation theory of smooth invariant tori of dynamical systems in an-dimensional Euclidean spaceR n are considered. The clarification of these problems plays an important role for perturbation theory suggested by the author in [1] and extends the scope of its application.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 12, pp. 1665–1699, December, 1994.  相似文献   

9.
This paper deals with the smoothness of the transition map between two sections transverse to the fast flow of a singularly perturbed vector field (one fast, multiple slow directions). Orbits connecting both sections are canard orbits, i.e. they first move rapidly towards the attracting part of a critical surface, then travel a distance near this critical surface, even beyond the point where the orbit enters the repelling part of the critical surface, and finally repel away from the surface. We prove that the transition map is smooth. In a transcritical situation however, where orbits from an attracting part of one critical manifold follow the repelling part of another critical manifold, the smoothness of the transition map may be limited, due to resonance phenomena that are revealed by blowing up the turning point! We present a polynomial example in R3.  相似文献   

10.
11.
Let X and Y be Hilbert spaces, and let T : XY be a bounded linear operator with closed range. In this paper, we present an optimal perturbation result on the least squares solutions to the operator equation Tx = y under the most general condition.  相似文献   

12.
This paper investigates the existence of solutions for nonlinear systems of second order, singular boundary value problems (BVPs) with Bohr boundary conditions. A key application that arises from this theory is the famous Thomas–Fermi equations for the model of the atom when it is in a neutral state. The methodology in this paper uses an alternative and equivalent BVP, which is in the class of resonant singular BVPs, and thus this paper obtains novel results by implementing an innovative differential inequality, Lyapunov functions and topological techniques. This approach furnishes new results in the area of singular BVPs for a priori bounds and existence of solutions, where the BVP has unrestricted growth conditions and subject to the Bohr boundary conditions. In addition, the results can be relaxed and hold for the non-singular case too.  相似文献   

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14.
In singular optimal control problems, the functional form of the optimal control function is usually determined by solving the algebraic equation which results by successively differentiating the switching function until the control appears explicitly. This process defines the order of the singular problem. Order-related results are developed for singular linear-quadratic problems and for a bilinear example which gives new insights into the relationship between singular problem order and singular are order.Dedicated to R. BellmanThis work was supported by the National Science Foundation under Grant No. ENG-77-16660.  相似文献   

15.
We study a quadratic parabolic control problem with pointwise final state constraints. As the set of admissible states has an empty interior, the existence of Lagrange multipliers cannot be proved directly. We obtain, however some optimality conditions by expressing the fact that among a space of regular perturbations of the optimal control, the null perturbation is optimal. We show that the qualification hypothesis can be effectively checked in some examples and that the information given by the optimality conditions is useful because it allows to get some regularity results for the optimal control.  相似文献   

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We investigate spectrum and asymptotic distribution of the eigenvalues of certain singular Sturm-Liouville eigenvalue problems on the half-line having a weight function that changes sign.  相似文献   

18.
We show the main features of the MATLAB code HOFiD_UP for solving second order singular perturbation problems. The code is based on high order finite differences, in particular on the generalized upwind method. Within its simplicity, it uses order variation and continuation for solving any difficult nonlinear scalar problem. Several numerical tests on linear and nonlinear problems are considered. The best performances are reported on problems with perturbation parameters near the machine precision, where most of the codes for two-point BVPs fail.  相似文献   

19.
魏广生  王侃民 《数学研究》1999,32(2):166-172
考 虑具中间亏指数 的非负系数对 称微分算式 ,在 Krein 空间 L2r [a,∞) 内生 成的自伴 算子,本文证明此算 子是可定化算 子,从而得到其非 实谱仅由有限 个成共轭对的特 征值构成  相似文献   

20.
Necessary and sufficient conditions are obtained for the existence of symmetric positive solutions to the boundary value problem
  相似文献   

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