共查询到20条相似文献,搜索用时 93 毫秒
1.
Serguei A. Nazarov 《Mathematical Methods in the Applied Sciences》1997,20(3):219-243
The dependence on the small parameter ε of constants in Korn's inequalities is investigated for domains which are obtained by joining thin rods to an elastic spatial body. The external ends of the rods are clamped. The asymptotic accuracy of the derived inequalities is achieved by certain distribution of weight multipliers and powers of ε in L2-norms of displacements and their derivatives while the introduced weights differ for longitudinal and transversal components of displacement fields in the rods. © 1997 by B.G. Teubner Stuttgart-John Wiley & Sons, Ltd. 相似文献
2.
《代数通讯》2013,41(7):2723-2732
Abstract Let L be a line bundle on a smooth curve C, which defines a birational morphism onto Φ(C) ? P r . We prove that, under suitable assumptions on L, which are satisfied by Castelnuovo's curves, a generic section in H 0(C, L 2) can be written as α2 + β2 + γ2, with α, β, γ ∈ H 0(C, L). If there are no quadrics of rank 3 containing Φ(C), this is true for any section. For canonical curves, this gives a non linear version of Noether's Theorem. 相似文献
3.
Eun‐Jae Park 《Numerical Methods for Partial Differential Equations》2005,21(2):213-228
Mixed finite element methods are analyzed for the approximation of the solution of the system of equations that describes the flow of a single‐phase fluid in a porous medium in ?d, d ≤ 3, subject to Forchhheimer's law—a nonlinear form of Darcy's law. Existence and uniqueness of the approximation are proved, and optimal order error estimates in L∞(J; L2(Ω)) and in L∞(J; H(div; Ω)) are demonstrated for the pressure and momentum, respectively. Error estimates are also derived in L∞(J; L∞(Ω)) for the pressure. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005 相似文献
4.
Monique Sablé Tougeron 《偏微分方程通讯》2013,38(9-10):1449-1479
We Confirm two conjectures of Lax about Glimm's weak solutions for initial boundary value problem whose data have compact support; asmptotic decay as t-1/2 of the total variation in the genuinely nonlinear case and L1 -approximation by N-waves or travelling-waves in general case; it is boundary's version of Liu's results [Li2]. 相似文献
5.
6.
Paolo Boggiatto Giuseppe De Donno Alessandro Oliaro 《Mathematische Nachrichten》2009,282(12):1656-1663
We study boundedness and compactness properties for the Weyl quantization with symbols in Lq (?2d ) acting on Lp (?d ). This is shown to be equivalent, in suitable Banach space setting, to that of the Wigner transform. We give a short proof by interpolation of Lieb's sufficient conditions for the boundedness of the Wigner transform, proving furthermore that these conditions are also necessary. This yields a complete characterization of boundedness for Weyl operators in Lp setting; compactness follows by approximation. We extend these results defining two scales of spaces, namely L*q (?2d ) and L?q (R2d ), respectively smaller and larger than the Lq (?2d ),and showing that the Weyl correspondence is bounded on L*q (R2d ) (and yields compact operators), whereas it is not on L?q (R2d ). We conclude with a remark on weak‐type Lp boundedness (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
7.
Robin Young 《纯数学与应用数学通讯》1993,46(6):903-948
We consider the Cauchy problem for a general N × N system of conservation laws. Existence of solutions was proved by Glimm using his celebrated random choice scheme. In this paper, we obtain a third-order interaction estimate analagous to that obtained by Glimm for 2×2 systems. By using this estimate, and identifying a global cancellation effect, we obtain L∞-stability for solutions generated by Glimm's scheme. As an immediate consequence we have L1-stability and L∞-decay, obtained by Temple for 2×2 systems. © 1993 John Wiley & Sons, Inc. 相似文献
8.
R. Fehlberg Jr. 《代数通讯》2013,41(6):2501-2512
Makar–Limanov's conjecture states that, if a division ring D is finitely generated and infinite dimensional over its center k, then D contains a free k-subalgebra of rank 2. In this work, we will investigate the existence of such structures in D, the division ring of fractions of the skew polynomial ring L[t; σ], where t is a variable and σ is a k-automorphism of L. For instance, we prove Makar-Limanov's conjecture when either L is the function field of an abelian variety or the function field of the n-dimensional projective space. 相似文献
9.
Jinghong Liu Gui Hu Qiding Zhu 《Numerical Methods for Partial Differential Equations》2013,29(3):1043-1055
For a variable coefficient elliptic boundary value problem in three dimensions, using the properties of the bubble function and the element cancelation technique, we derive the weak estimate of the first type for tetrahedral quadratic elements. In addition, the estimate for the W1,1‐seminorm of the discrete derivative Green's function is also given. Finally, we show that the derivatives of the finite element solution uh and the corresponding interpolant Π2u are superclose in the pointwise sense of the L∞‐norm. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013 相似文献
10.
For several decades, much attention has been paid to the two-sample Behrens-Fisher (BF) problem which tests the equality of
the means or mean vectors of two normal populations with unequal variance/covariance structures. Little work, however, has
been done for the k-sample BF problem for high dimensional data which tests the equality of the mean vectors of several high-dimensional normal
populations with unequal covariance structures. In this paper we study this challenging problem via extending the famous Scheffe’s
transformation method, which reduces the k-sample BF problem to a one-sample problem. The induced one-sample problem can be easily tested by the classical Hotelling’s
T
2 test when the size of the resulting sample is very large relative to its dimensionality. For high dimensional data, however,
the dimensionality of the resulting sample is often very large, and even much larger than its sample size, which makes the
classical Hotelling’s T
2 test not powerful or not even well defined. To overcome this difficulty, we propose and study an L
2-norm based test. The asymptotic powers of the proposed L
2-norm based test and Hotelling’s T
2 test are derived and theoretically compared. Methods for implementing the L
2-norm based test are described. Simulation studies are conducted to compare the L
2-norm based test and Hotelling’s T
2 test when the latter can be well defined, and to compare the proposed implementation methods for the L
2-norm based test otherwise. The methodologies are motivated and illustrated by a real data example.
The work was supported by the National University of Singapore Academic Research Grant (Grant No. R-155-000-085-112) 相似文献
11.
Abderrazek Karoui Hichem Ben Aouicha Adel Jawahdou 《Numerical Functional Analysis & Optimization》2013,34(6):691-714
The first goal of this article is to discuss the existence of solutions of nonlinear quadratic integral equations. These equations are considered in the Banach space L p (?+). The arguments used in the existence proofs are based on Schauder's and Darbo's fixed point theorems. In particular, to apply Schauder's fixed point theorem based method, a special care is devoted to the proof of the L p -compactness of the operators associated with our nonlinear quadratic integral equations. The second goal of this work is to study a numerical method for solving nonlinear Volterra integral equations of a fairly general type. Finally, we provide the reader with some examples that illustrate the different results of this work. 相似文献
12.
This paper is concerned with boundary control of one-dimensional vibrating media whose motion is governed by a wave equation with a 2n-order spatial self-adjoint and positive-definite linear differential operator with respect to 2n boundary conditions. Control is applied to one of the boundary conditions and the control function is allowed to vary in the Sobolev space W, p for p∈[2, ∞] With the aid of Banach space theory of trigonometric moment problems, necessary and sufficient conditions for null-controllability are derived and applied to vibrating strings and Euler beams. For vibrating strings also, null-controllability by Lp-controls on the boundary is shown by a direct method which makes use of d'Alembert's solution formula for the wave equation. 相似文献
13.
Eunjung Lee Wonjoon Choi Heonkyu Ha 《Numerical Methods for Partial Differential Equations》2020,36(6):1389-1404
This paper utilizes the Picard method and Newton's method to linearize the stationary incompressible Navier–Stokes equations and then uses an LL* approach, which is a least-squares finite element method applied to the dual problem of the corresponding linear system. The LL* approach provides an L2-approximation to a given problem, which is not typically available with conventional finite element methods for nonlinear second-order partial differential equations. We first show that the proposed combination of linearization scheme and LL* approach provides an L2-approximation to the stationary incompressible Navier–Stokes equations. The validity of L2-approximation is proven through the analysis of the weak problem corresponding to the linearized Navier–Stokes equations. Then, the convergence is analyzed, and numerical results are presented. 相似文献
14.
Ming‐Jun Lai Chun Liu Paul Wenston 《Numerical Methods for Partial Differential Equations》2003,19(6):776-827
We use a bivariate spline method to solve the time evolution Navier‐Stokes equations numerically. The bivariate splines we use in this article are in the spline space of smoothness r and degree 3r over triangulated quadrangulations. The stream function formulation for the Navier‐Stokes equations is employed. Galerkin's method is applied to discretize the space variables of the nonlinear fourth‐order equation, Crank‐Nicholson's method is applied to discretize the time variable, and Newton's iterative method is then used to solve the resulting nonlinear system. We show the existence and uniqueness of the weak solution in L2(0, T; H2(Ω)) ∩ L∞(0, T; H1(Ω)) of the 2D nonlinear fourth‐order problem and give an estimate of how fast the numerical solution converges to the weak solution. The C1 cubic splines are implemented in MATLAB for solving the Navier‐Stokes equations numerically. Our numerical experiments show that the method is effective and efficient. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 776–827, 2003. 相似文献
15.
Christian G. Simader 《Mathematische Nachrichten》2006,279(4):415-430
For boundary data ? ∈ W 1,2(G ) (where G ? ?N is a bounded domain) it is an easy exercise to prove the existence of weak L 2‐solutions to the Dirichlet problem “Δu = 0 in G, u |?G = ? |?G ”. By means of Weyl's Lemma it is readily seen that there is ? ∈ C ∞(G ), Δ? = 0 and ? = u a.e. in G . On the contrary it seems to be a complicated task even for this simple equation to prove continuity of ? up to the boundary in a suitable domain if ? ∈ W 1,2(G ) ∩ C 0( ). The purpose of this paper is to present an elementary proof of that fact in (classical) Dirichlet domains. Here the method of weak solutions (resp. Dirichlet's principle) is equivalent to the classical approaches (Poincaré's “sweeping‐out method”, Perron's method). (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
16.
Peter Howard 《纯数学与应用数学通讯》1999,52(10):1295-1313
We study the pointwise behavior of perturbations from a viscous shock solution to a scalar conservation law, obtaining an estimate independent of shock strength. We find that for a perturbation with initial data decaying algebraically or slower, the perturbation decays in time at the rate of decay of the integrated initial data in any Lp norm, p ≥ 1. Stability in any Lp norm is a direct consequence. The approach taken is that of obtaining pointwise estimates on the perturbation through a Duhamel's principle argument that employs recently developed pointwise estimates on the Green's function for the linearized equation. © 1999 John Wiley & Sons, Inc. 相似文献
17.
Norbert Weck 《Mathematical Methods in the Applied Sciences》2004,27(5):603-621
By a general argument, it is shown that Maxwell–Herglotz‐fields are dense (with respect to the C∞(Ω)‐topology) in the space of all solutions to Maxwell's equations in Ω. This is used to provide corresponding approximation results in global spaces (e.g. in L2‐Sobolev‐spaces Hm(Ω)) and for boundary data. Proofs are given within the framework of generalized Maxwell's equations using differential forms. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
18.
In this paper we prove the optimal pointwise Hölder estimates for the Kohn's Laplacian □ b for CR manifolds of class C 2. We first derive optimal L 2 theory for solutions of □ b directly without using pseudo-differential operators. Then we use the scaling method to obtain pointwise estimates in non-istotropic Campanato spaces based on the maximal L 2 theory. 相似文献
19.
J.‐Y. Chemin 《纯数学与应用数学通讯》2011,64(12):1587-1598
This article studies the problem of L2 stability and weak‐strong uniqueness of solutions of the incompressible Navier‐Stokes on the whole space \input amssym ${\Bbb S}^3$ constructed by Kato's approach in spaces coming from Littlewood‐Paley theory and using the L1 smoothing effect for the heat flow. © 2011 Wiley Periodicals, Inc. 相似文献
20.
In this article, the existence of a global strong solution for all finite time is derived for the Kirchhoff's model of parabolic type. Based on exponential weight function, some new regularity results which reflect the exponential decay property are obtained for the exact solution. For the related dynamics, the existence of a global attractor is shown to hold for the problem when the non-homogeneous forcing function is either independent of time or in L∞(L2). With the finite element Galerkin method applied in spatial direction keeping time variable continuous, a semidiscrete scheme is analyzed, and it is also established that the semidiscrete system has a global discrete attractor. Optimal error estimates in L∞(H1) norm are derived which are valid uniformly in time. Further, based on a backward Euler method, a completely discrete scheme is analyzed and error estimates are derived. It is also further, observed that in cases where f = 0 or f = O(e?γ0t) with γ0 > 0, the discrete solutions and error estimates decay exponentially in time. Finally, some numerical experiments are discussed which confirm our theoretical findings. 相似文献