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101.
《Set-Valued Analysis》2008,16(2-3):199-227
The paper contains two groups of results. The first are criteria for calmness/subregularity for set-valued mappings between
finite-dimensional spaces. We give a new sufficient condition whose subregularity part has the same form as the coderivative
criterion for “full” metric regularity but involves a different type of coderivative which is introduced in the paper. We
also show that the condition is necessary for mappings with convex graphs. The second group of results deals with the basic
calculus rules of nonsmooth subdifferential calculus. For each of the rules we state two qualification conditions: one in
terms of calmness/subregularity of certain set-valued mappings and the other as a metric estimate (not necessarily directly
associated with aforementioned calmness/subregularity property). The conditions are shown to be weaker than the standard Mordukhovich–Rockafellar
subdifferential qualification condition; in particular they cover the cases of convex polyhedral set-valued mappings and,
more generally, mappings with semi-linear graphs. Relative strength of the conditions is thoroughly analyzed. We also show,
for each of the calculus rules, that the standard qualification conditions are equivalent to “full” metric regularity of precisely
the same mappings that are involved in the subregularity version of our calmness/subregularity condition.
The research of Jiří V. Outrata was supported by the grant A 107 5402 of the Grant Agency of the Academy of Sciences of the
Czech Republic. 相似文献
102.
Jean-Philippe Bartier 《Journal of Functional Analysis》2008,254(3):851-878
Qualitative properties of non-negative solutions to a quasilinear degenerate parabolic equation with an absorption term depending solely on the gradient are shown, providing information on the competition between the nonlinear diffusion and the nonlinear absorption. In particular, the limit as t→∞ of the L1-norm of integrable solutions is identified, together with the rate of expansion of the support for compactly supported initial data. The persistence of dead cores is also shown. The proof of these results strongly relies on gradient estimates which are first established. 相似文献
103.
This paper develops a posteriori error estimates of residual type for conforming and mixed finite element approximations of the fourth order Cahn-Hilliard equation ut + △(ε△Au-ε^-1f(u)) = 0. It is shown that the a posteriori error bounds depends on ε^-1 only in some low polynomial order, instead of exponential order. Using these a posteriori error estimates, we construct at2 adaptive algorithm for computing the solution of the Cahn- Hilliard equation and its sharp interface limit, the Hele-Shaw flow. Numerical experiments are presented to show the robustness and effectiveness of the new error estimators and the proposed adaptive algorithm. 相似文献
104.
Ajit Patel Amiya K. Pani Neela Nataraj 《Numerical Methods for Partial Differential Equations》2008,24(6):1460-1484
In this article a standard mortar finite element method and a mortar element method with Lagrange multiplier are used for spatial discretization of a class of parabolic initial‐boundary value problems. Optimal error estimates in L∞(L2) and L∞(H1)‐norms for semidiscrete methods for both the cases are established. The key feature that we have adopted here is to introduce a modified elliptic projection. In the standard mortar element method, a completely discrete scheme using backward Euler scheme is discussed and optimal error estimates are derived. The results of numerical experiments support the theoretical results obtained in this article. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2008 相似文献
105.
A model representing a coupling between a heat conducting medium and a solid structure is considered. We establish a Carleman
inequality for this model. Next we deduce a null controllability result with an internal control in the conducting medium
and there is no control in the solid part. 相似文献
106.
107.
This is a continuation of the article(Comm.Partial Differential Equations 26(2001)965).In this article,the authors consider the one-dimensional compressible isentropic Navier-Stokes equations with gravitational force,fixed boundary condition,a general pressure and the density-dependent viscosity coefficient when the viscous gas connects to vacuum state with a jump in density.Precisely,the viscosity coefficient μ is proportional to ρ^θ and 0〈θ〈1/2,where ρ is the density,and the pressure P=P(ρ)is a general pressure.The global existence and the uniqueness of weak solution are proved. 相似文献
108.
A. G. D’yakonov 《Computational Mathematics and Mathematical Physics》2008,48(5):866-876
It is shown that, in the pattern recognition problem with two nonoverlapping classes, the matrices of estimates of the object closeness are described by a metric. The transition to the algebraic closure of the model of recognizing operators of finite degree corresponds to the application of a special transformation of this metric. It is proved that the minimal degree correct algorithm can be found as a polynomial of a special form. A simple criterion for testing classification implementations is obtained. 相似文献
109.
Zhang Guangzhao Zhou Guangqun 《International Journal of Infrared and Millimeter Waves》1989,10(2):257-267
The Marple algorthm for the autoregressive spectral estimates has been applied to the SMMW Fourier transform spectrum analysis. The experimental results have shown that this method yields AR spectra with three times higher resolution than the FFT method does. The improvements obtained from the Marple algorithm over the maximum entropy algorithm include higher resolution, less bias in the spectral peak frequency estimation and absence of observed spectral line splitting. The effects of the structure of the spectral lines and the noise on the resolution are discussed.Projects supported by National Natural Science Foundation of China 相似文献
110.
In this paper, we study a second order variational problem for locally convex hypersurfaces, which is the affine invariant analogue of the classical Plateau problem for minimal surfaces. We prove existence, regularity and uniqueness results for hypersurfaces maximizing affine area under appropriate boundary conditions.