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991.
992.
Louis Jeanjean Marco Squassina 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2009,26(5):465
For a general class of autonomous quasi-linear elliptic equations on we prove the existence of a least energy solution and show that all least energy solutions do not change sign and are radially symmetric up to a translation in . 相似文献
993.
Given any wave speed c∈R, we construct a traveling wave solution of ut=Δu+2|∇u|u in an infinitely long cylinder, which connects two locally stable and axially symmetric steady states at x3=±∞. Here u is a director field with values in S2⊂R3: |u|=1. The traveling wave has a singular point on the cylinder axis. In view of the bistable character of the potential, the result is surprising, and it is intimately related to the nonuniqueness of the harmonic map flow itself. We show that for only one wave speed the traveling wave behaves locally, near its singular point, as a symmetric harmonic map. 相似文献
994.
995.
C. S. Scherer J. F. Prolo Filho L. B. Barichello 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2009,60(1):70-115
The ADO method, an analytical version of the discrete-ordinates method, is used to solve several classical problems in the
rarefied gas dynamics field. The complete development of the solution, which is analytical in terms of the spatial variable,
is presented in a way, such that, a wide class of kinetic models are considered, in an unified approach. A series of numerical
results are showed and different simulations are used in order to establish a general comparative analysis based on this consistent
set of results provided by the same methodology.
Received: July 10, 2007; revised: October 29/December 4, 2007 相似文献
996.
Classification, reduction, group invariant solutions and conservation laws of the Gardner-KP equation 总被引:1,自引:0,他引:1
In this paper, symmetries and group invariant solutions to the Gardner-KP equation are obtained by using the direct symmetry method. At the same time, we find the corresponding Lie algebra, optimal system, classification and the similarity reductions to the equation, respectively. Our exact solutions generalize the corresponding results obtained by Wazwaz. In addition, the conservation laws of Gardner-KP equation are also given. 相似文献
997.
While connected arithmetic discrete lines are entirely characterized, only partial results exist for the more general case of arithmetic discrete hyperplanes. In the present paper, we focus on the three-dimensional case, that is on arithmetic discrete planes. Thanks to arithmetic reductions on a vector , we provide algorithms either to determine whether a given arithmetic discrete plane with as normal vector is connected, or to compute the minimal thickness for which an arithmetic discrete plane with normal vector is connected. 相似文献
998.
S.M. Myeni 《Journal of Mathematical Analysis and Applications》2009,357(1):225-231
The complete symmetry group of an 1+1 evolution equation of maximal symmetry has been demonstrated to be represented by the six-dimensional Lie algebra of point symmetries sl(2,R)s⊕W, where W is the three-dimensional Heisenberg-Weyl algebra. We construct a complete symmetry group of a 1+2 evolution equation ut=(Fy(u)ux) for some functions F using the point symmetries admitted by the equation. The 1+2 equation is not completely specifiable by point symmetries alone for some specific functions F. We make use of Ansätze already reported by Myeni and Leach [S.M. Myeni, P.G.L. Leach, Nonlocal symmetries and complete symmetry groups of evolution equations, J. Nonlinear Math. Phys. 13 (2006) 377-392] which provide a route to the determination of the required generic nonlocal symmetries necessary to supplement the point symmetries for the complete specification of these 1+2 evolution equations. Further we find that taking some suitable linear combination of Lie point symmetries helps to optimise the procedure of specifying the equation. A general result concerning the number of symmetries required to form a complete symmetry group of evolution is presented in the Conclusion. 相似文献
999.
Yasuhito Miyamoto 《Journal of Mathematical Analysis and Applications》2009,357(1):89-97
We give two sufficient conditions for a branch consisting of non-trivial solutions of an abstract equation in a Banach space not to have a (secondary) bifurcation point when the equation has a certain symmetry. When the nonlinearity f is of Allen-Cahn type (for instance f(u)=u−u3), we apply these results to an unbounded branch consisting of non-radially symmetric solutions of the Neumann problem on a disk D⊂R2
1000.
The paper deals with the study of Fredholm property and essential spectrum of general difference (or band) operators acting on the spaces l p (X) on a discrete metric space X periodic with respect to the action of a finitely generated discrete group. The Schrödinger operator on a combinatorial periodic graph is a prominent example of a band operator of this kind. 相似文献