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81.
Blowup behaviors for diffusion system coupled through nonlinear boundary conditions in a half space 总被引:1,自引:0,他引:1
LIN ZhiguiSchool of Mathematical Science Yangzhou University Yangzhou China 《中国科学A辑(英文版)》2004,47(1):72-82
This paper deals with the blowup estimates near the blowup time for the system of heat equations in a half space coupled through nonlinear boundary conditions. The upper and lower bounds of blowup rate are established. The uniqueness and nonunique-ness results for the system with vanishing initial value are given. 相似文献
82.
Boundedness in Morrey spaces is studied for singular integral operators with kernels of mixed homogeneity and their commutators with multiplication by a BMO-function. The results are applied in obtaining fine (Morrey and Hölder) regularity of strong solutions to higher-order elliptic and parabolic equations with VMO coefficients. 相似文献
83.
Wlodzimierz Bryc Victor Kaftal 《Proceedings of the American Mathematical Society》2004,132(2):523-534
Bounds for non-commutative versions of two classical strong mixing coefficients for -Gaussian processes are found in terms of the angle between the underlying Hilbert spaces. As a consequence, we construct a -mixing -Gaussian stationary sequence with growth conditions on variances of partial sums. If classical processes with analogous properties were to exist, they would provide a counter-example to the Ibragimov conjecture.
84.
G. Criscuolo. 《Mathematics of Computation》2004,73(245):243-250
Recently, Mastroianni and Monegato derived error estimates for a numerical approach to evaluate the integral
where or or and is a smooth function (see G. Mastroianni and G. Monegato, Error estimates in the numerical evaluation of some BEM singular integrals, Math. Comp. 70 2001, 251-267). The error bounds for the quadrature rule approximating the inner integral given in Theorems 3, 4 of that paper are not correct according to the proof. However, following a different approach, we are able to improve the pointwise error estimates given in that paper.
where or or and is a smooth function (see G. Mastroianni and G. Monegato, Error estimates in the numerical evaluation of some BEM singular integrals, Math. Comp. 70 2001, 251-267). The error bounds for the quadrature rule approximating the inner integral given in Theorems 3, 4 of that paper are not correct according to the proof. However, following a different approach, we are able to improve the pointwise error estimates given in that paper.
85.
Yubin Yan 《BIT Numerical Mathematics》2003,43(3):647-669
We study smoothing properties and approximation of time derivatives for time discretization schemes with variable time steps for a homogeneous parabolic problem formulated as an abstract initial value problem in a Banach space. The time stepping methods are based on using rational approximations to the exponential function which are A()-stable for suitable (0,/2] with unit bounded maximum norm. First- and second-order approximations of time derivatives based on using difference quotients are considered. Smoothing properties are derived and error estimates are established under the so-called increasing quasi-quasiuniform assumption on the time steps. 相似文献
86.
Tong Yang Huijiang Zhao Changjiang Zhu 《Proceedings of the American Mathematical Society》2003,131(4):1257-1266
We give uniform BV estimates and -stability of Lax-Friedrichs' scheme for a class of systems of strictly hyperbolic conservation laws whose integral curves of the eigenvector fields are straight lines, i.e., Temple class, under the assumption of small total variation. This implies that the approximate solutions generated via the Lax-Friedrichs' scheme converge to the solution given by the method of vanishing viscosity or the Godunov scheme, and then the Glimm scheme or the wave front tracking method.
87.
D. P. Dryanov M. A. Qazi Q. I. Rahman 《Proceedings of the American Mathematical Society》2003,131(9):2741-2751
Extensions of two classical results about polynomials, one due to W. Markov and the other due to Duffin and Schaeffer, are obtained in this paper. An interesting result of S. Bernstein, which went unnoticed until it was rediscovered by P. Erdos, years later, is also generalized. Our results are especially amenable to numerical calculations, and may, therefore, be of some practical importance.
88.
For an integer n3 and any positive number , we establish the existence of smooth functions K on
n
{0} with |K–1|, such that the equation
has a smooth positive solution which blows up at the origin (i.e., u does not have slow decay near the origin). Furthermore, we show that in some situations K can be extended as a Lipschitz function on
n
. These provide counter-examples to a conjecture of C.-S. Lin when n>4, and a question of Taliaferro.
Mathematics Subject Classification (2000)Primary 35J60; Secondary 53C21 相似文献
89.
J. Colliander M. Keel G. Staffilani H. Takaoka T. Tao 《Journal of the American Mathematical Society》2003,16(3):705-749
The initial value problems for the Korteweg-de Vries (KdV) and modified KdV (mKdV) equations under periodic and decaying boundary conditions are considered. These initial value problems are shown to be globally well-posed in all -based Sobolev spaces where local well-posedness is presently known, apart from the endpoint for mKdV and the endpoint for KdV. The result for KdV relies on a new method for constructing almost conserved quantities using multilinear harmonic analysis and the available local-in-time theory. Miura's transformation is used to show that global well-posedness of modified KdV is implied by global well-posedness of the standard KdV equation.
90.
Borislav Karaivanov Pencho Petrushev Robert C. Sharpley 《Transactions of the American Mathematical Society》2003,355(7):2585-2631
In this article algorithms are developed for nonlinear -term Courant element approximation of functions in ( ) on bounded polygonal domains in . Redundant collections of Courant elements, which are generated by multilevel nested triangulations allowing arbitrarily sharp angles, are investigated. Scalable algorithms are derived for nonlinear approximation which both capture the rate of the best approximation and provide the basis for numerical implementation. Simple thresholding criteria enable approximation of a target function to optimally high asymptotic rates which are determined and automatically achieved by the inherent smoothness of . The algorithms provide direct approximation estimates and permit utilization of the general Jackson-Bernstein machinery to characterize -term Courant element approximation in terms of a scale of smoothness spaces (-spaces) which govern the approximation rates.