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31.
Abstract

This article treats of adaptive finite difference methods for the Dirichlet boundary value problems of Poisson-type equations on a sector or a disk. It is assumed that the exact solutions have singular derivatives on a part or the whole of the boundary. Some stretching functions are used to generate nonuniform grid points. It is then shown that, under some assumptions, the adaptive finite difference solutions are convergent and the convergence can be accelerated by varying parameters in the stretching functions. Numerical examples are given to illustrate how the accuracy of numerical solutions depends on the parameters.  相似文献   
32.
H. Minkowski proved C= convext C whenever C is a compact convex subset of a finite-dimensional linear space. If C is bounded but not closed, this representation does not hold anymore. In this case, we introduce the set of so-called γ-extreme points extγC of C and show C = convext γ C = raco extγ C, where raco M denotes the rational convex hull of M.  相似文献   
33.
34.
We prove a refined version of the classical Lucas' theorem: if p is a polynomial with zeros a 1,…,a n+1 all having modulus one and φis the Blaschke product whose zeros are those of the derivative p 1, then the compression of the shift S(φ) has its numerical range circumscribed about by the (n+ l)-gon a 1a n+1 with tangent points the midpoints of then+ l sides of the polygon. This is proved via a special matrix representation of S(φ) and is a generalization of the known case for n= 2.  相似文献   
35.
An asymptotic expansion of Schilder-type integrals with general phase function on abstract Wiener spaces is given and good control on remainders is obtained. For Ornstein –Uhlenbeck semigroups perturbed by potentials on Banach spaces the asymptotic expansion is given in terms of explicitly discussed “classical orbits”, in the case of finitely many non-degenerate maxima of the phase function. A representation of the leading term by a solution of an infinite dimensional Sturm-Liouville problem is also provided  相似文献   
36.
In this paper, we are interested in the solution of a viscous scalar conservation law. We remark that its first order spatial derivatives solve a system of partial differential equations presenting a nonlocal nonlinearity. We associate a nonlinear martingale problem with this system. After proving existence and uniqueness for the martingale problem, we obtain a propagation of chaos result for a system of interacting diffusion processes. We deduce that it is possible to approximate the solution of the viscous scalar conservation law thanks to the interacting diffusions  相似文献   
37.
A class of Hilbert space-valued Markov processes which can be expressed as the mild solution of a linear abstract evolution equation is studied. Sufficient conditions for the generator of the Markov process to be well-defined are given and Kolmogorov's equation and an equation for the characteristic function of the process are derived. The theory is illustrated by examples of parabolic, hyperbolic and delay stochastic differential equations.  相似文献   
38.
In the present paper, a framework for parametric estimation in nonlinear time series is developed. Strong consistency and asymptotic normality of minimum Hellinger distance estimates for a determined class of nonlinear models are investigated. The main Interest for these estimates is motivated by their robustness under perturbations as it has been emphazized in Beran [2]. The first part of the paper is devoted to the study of some probabilistic properties which ensure the existence and the optimal properties of the estimates  相似文献   
39.
《偏微分方程通讯》2013,38(7-8):1117-1132
Barrier type boundary conditions are modeled for describing the substance diffusion in a medium when obstacles in the medium are considered. The existence of solutions of parabolic and elliptic differential equations with barrier boundary condition is presented in this paper.  相似文献   
40.
《偏微分方程通讯》2013,38(7-8):1265-1301
Abstract

We present sharp decay rates as time tends to infinity for solutions to linear Kleinc-Gordon and wave equations in domains with infinite boundaries like infinite waveguides, as well as the global well-posedness and the asymptotics for small data for the solutions to the associated nonlinear initial-boundary value problems.  相似文献   
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