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951.
952.
The study of nonlinear diffusion equations produces a number of peculiar phenomena not present in the standard linear theory. Thus, in the sub-field of very fast diffusion it is known that the Cauchy problem can be ill-posed, either because of non-uniqueness, or because of non-existence of solutions with small data. The equations we consider take the general form ut=(D(u,ux)ux)x or its several-dimension analogue. Fast diffusion means that D→∞ at some values of the arguments, typically as u→0 or ux→0. Here, we describe two different types of non-existence phenomena. Some fast-diffusion equations with very singular D do not allow for solutions with sign changes, while other equations admit only monotone solutions, no oscillations being allowed. The examples we give for both types of anomaly are closely related. The most typical examples are vt=(vx/∣v∣)x and ut=uxx/∣ux∣. For these equations, we investigate what happens to the Cauchy problem when we take incompatible initial data and perform a standard regularization. It is shown that the limit gives rise to an initial layer where the data become admissible (positive or monotone, respectively), followed by a standard evolution for all t>0, once the obstruction has been removed. 相似文献
953.
Jacek Tabor 《Journal of Differential Equations》2002,180(1):171-197
954.
955.
956.
Muhammad Aslam NoorThemistocles M. Rassias 《Journal of Mathematical Analysis and Applications》2002,268(1):334-343
In this paper, we consider and analyze a new class of projection methods for solving pseudomonotone general variational inequalities using the Wiener-Hopf equations technique. The modified methods converge for pseudomonotone operators. Our proof of convergence is very simple as compared with other methods. The proposed methods include several known methods as special cases. 相似文献
957.
V. A. Yumaguzhin 《Acta Appl Math》2002,72(1-2):155-181
It is known that a linear ordinary differential equation of order n3 can be transformed to the Laguerre–Forsyth form y
(n)=
i=3
n
a
n–i
(x)y
(n–i) by a point transformation of variables. The classification of equations of this form in a neighborhood of a regular point up to a contact transformation is given. 相似文献
958.
S. P. Sidorov 《Journal of Approximation Theory》2002,118(2):188-201
In this paper, we will show that Lagrange interpolatory polynomials are optimal for solving some approximation theory problems concerning the finding of linear widths.In particular, we will show that
, where
n is a set of the linear operators with finite rank n+1 defined on
−1,1], and where
n+1 denotes the set of polynomials p=∑i=0n+1aixi of degreen+1 such that an+11. The infimum is achieved for Lagrange interpolatory polynomial for nodes
. 相似文献
Full-size image
959.
960.
A finitely generated group is called representation rigid (briefly, rigid) if for every n, has only finitely many classes of simple representations in dimension n. Examples include higher rank S-arithmetic groups. By Margulis super rigidity, the latter have a stronger property: they are representation super rigid; i.e., their proalgebraic completion is finite dimensional. We construct examples of nonlinear rigid groups which are not super rigid, and which exhibit every possible type of infinite dimensionality. Whether linear representation rigid groups are super rigid remains an open question. 相似文献