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61.
Armen Shirikyan 《Journal of Functional Analysis》2007,249(2):284-306
The paper is devoted to studying the distribution of stationary solutions for 3D Navier-Stokes equations perturbed by a random force. Under a non-degeneracy assumption, we show that the support of such a distribution coincides with the entire phase space, and its finite-dimensional projections are minorised by a measure possessing an almost surely positive smooth density with respect to the Lebesgue measure. Similar assertions are true for weak solutions of the Cauchy problem with a regular initial function. The results of this paper were announced in the short note [A. Shirikyan, Controllability of three-dimensional Navier-Stokes equations and applications, in: Sémin. Équ. Dériv. Partielles, 2005-2006, École Polytech., Palaiseau, 2006]. 相似文献
62.
N.-K. Lee T.A. Vilgis 《The European Physical Journal B - Condensed Matter and Complex Systems》2002,28(4):451-465
We study the elastic properties of single A/B random copolymer chains, with a specific sequence and use them as theoretical
model for so called HP proteins. HP proteins carry hydrophilic (P) and hydrophobic (H) monomers. We predict a rich structure
in the force-extension relations which can be attributed to the information in the sequence. The variational method is used
to probe local minima on the path of stretching and releasing for the chain molecules. At a given force, we find multiple
configurations which are separated by energy barriers. A collapsed globular configuration consists of several domains which
unravel cooperatively. Upon stretching, the unfolding path shows a stepwise pattern corresponding to the unfolding of each
domain. While releasing, several cores can be created simultaneously in the middle of the chain, resulting in a different
path of collapse. The long-range interactions and stiffness of the chain simplify the potential landscape given by the disorder
in sequence.
Received 5 March 2002 / Received in final form 16 May 2002 Published online 13 August 2002 相似文献
63.
Daniel FRANCO Gennaro INFANTE Donal O'REGAN 《数学学报(英文版)》2006,22(6):1745-1750
We establish new criteria for the existence of either positive or nonzero solutions of the Urysohn integral equation. We also discuss the existence of an interval of positive eigenvalues and sufficient conditions for the existence of at least a positive eigenvalue with a nonzero or positive eigenfunction for the Urysohn integral operator. Among others, we employ techniques based on fixed point index theory for compact maps, which are new for this type of equation. 相似文献
64.
S. P. Popov 《Computational Mathematics and Mathematical Physics》2006,46(6):983-994
Numerical solutions to three systems of integrable evolutionary equations from the Toda lattice hierarchy are analyzed. These are the classical Toda lattice, the second local dispersive flow, and the second extended dispersive flow. Special attention is given to the properties of soliton solutions. For the equations of the second local flow, two types of solitons interacting in a special manner are found. Solutions corresponding to various initial data are qualitatively outlined. 相似文献
65.
66.
In this paper, we discuss the viscosity solutions of the weakly coupled systems of fully nonlinear second-order degenerate parabolic equations and their Cauchy-Dirichlet problem. We prove the existence, uniqueness and continuity of viscosity solution by combining Perron's method with the technique of coupled solutions. The results here generalize those in Proc. London Math. Soc. 63 (1991) 212-240 and Comm. Partial Differential Equations 16 (1991) 1095-1128. 相似文献
67.
This paper investigates the existence of positive solutions of a singular boundary value problem with negative exponent similar
to standard Emden-Fowler equation. A necessary and sufficient condition for the existence of C[0, 1] positive solutions as
well as C1[0, 1] positive solutions is given by means of the method of lower and upper solutions with the Schauder fixed point theorem. 相似文献
68.
Banach空间二阶周期边值问题解的存在性 总被引:2,自引:0,他引:2
利用一些比较结果,讨论了Banach空间中二阶周期边值问题解的存在性,获得了若干解的存在性与唯一性结果。 相似文献
69.
There are few techniques available to numerically solve sixth-order boundary-value problems with two-point boundary conditions. In this paper we show that the Sinc-Galerkin method is a very effective tool in numerically solving such problems. The method is then tested on examples with homogeneous and nonhomogeneous boundary conditions and a comparison with the modified decomposition method is made. It is shown that the Sinc-Galerkin method yields better results.
70.
We give an account of the appearance and first developments of the statistical model of atoms proposed by Thomas and Fermi, focusing on the main results achieved by Fermi and his group in Rome. Particular attention is addressed to the unknown contribution to this subject by Majorana, anticipating some important results reached later by leading physicists. 相似文献