共查询到20条相似文献,搜索用时 712 毫秒
1.
A. M. Vinogradov 《Acta Appl Math》1984,2(1):21-78
Starting with Lie's classical theory, we carefully explain the basic notions of the higher symmetries theory for arbitrary systems of partial differential equations as well as the necessary calculation procedures. Roughly speaking, we explain what analogs of higher KdV equations are for an arbitrary system of partial differential equations and also how one can find and use them. The cohomological nature of conservation laws is shown and some basic results are exposed which allow one to calculate, in principle, all conservation laws for a given system of partial differential equations. In particular, it is shown that symmetry and conservation law are, in some sense, the dual conceptions which coincides in the self-dual case, namely, for Euler-Lagrange equations. Training examples are also given.Translated from the Russian by B. A. Kuperschmidt. 相似文献
2.
The theory of coverings over differential equations is exposed which is an adequate language for describing various nonlocal phenomena: nonlocal symmetries and conservation laws, Bäcklund transformations, prolongation structures, etc. A notion of a nonlocal cobweb is introduced which seems quite useful for dealing with nonlocal objects. 相似文献
3.
For a systemY of partial differential equations, the notion of a covering
Y
is introduced whereY
is infinite prolongation ofY. Then nonlocal symmetries ofY are defined as transformations of
which conserve the underlying contact structure. It turns out that generating functions of nonlocal symmetries are integro-differential-type operators. 相似文献
4.
5.
A method for computing symmetries and conservation laws of integro-differential equations is proposed. It resides in reducing an integro-differential equation to a system of boundary differential equations and in computing symmetries and conservation laws of this system. A geometry of boundary differential equations is constructed like the differential case. Results of the computation for the Smoluchowski's coagulation equation are given. 相似文献
6.
In this paper, we study the Cauchy problem of a weakly dissipative μ-Hunter–Saxton equation. We first establish the local well-posedness for the weakly dissipative μ-Hunter–Saxton equation by Kato's semigroup theory. Then, we derive the precise blow-up scenario for strong solutions to the equation. Moreover, we present some blow-up results for strong solutions to the equation. Finally, we give two global existence results to the equation. 相似文献
7.
Ph. Delanoë 《Differential Geometry and its Applications》2008,26(3):327-338
Given a couple of smooth positive measures of same total mass on a compact Riemannian manifold, the associated optimal transport equation admits a symplectic Monge-Ampère structure, hence Lie solutions (in a restricted sense, though, still expressing measure-transport). Properties of such solutions are recorded; a structure result is obtained for regular ones (each consisting of a closed 1-form composed with a diffeomorphism) and a quadratic cost-functional proposed for them. 相似文献
8.
We propose the construction of a spectral sequence converging to Spencer cohomologies. By using symmetry groups of differential equations systems, we manage to unify computations by reduction to the invariant systems over a homogeneous space. The conditions of coincidence of Spencer cohomologies with the cohomologies of an invariant Spencer complex we obtain from the arithmetic of a -characteristic manifold with respect to fundamental weights of the homogeneous space. 相似文献
9.
Gerson Petronilho 《Indagationes Mathematicae》2005,16(1):67-90
In this paper we consider the problem of global Gevrey solvability for a class of sublaplacians on a toruswith coefficients in the Gevrey class Gs(TN). For this class of operators we show that global Gevrey solvability and global Gevrey hypoellipticity are both equivalent to the condition that the coefficients satisfy a Diophantine condition. 相似文献
10.
Conformal deformations on a noncompact Riemannian manifold 总被引:3,自引:0,他引:3
Ma Li 《Mathematische Annalen》1993,295(1):75-80
11.
Alexey V. Samokhin 《Acta Appl Math》1995,41(1-3):299-309
Quantities which are conserved in nondissipative media decay in the presence of dissipation. The velocity of such a decay (or the balance law) may be found explicitly using the generating function of the conservation law. The general approach is illustrated with a system of MHD equations for incompressible magnetofluids. 相似文献
12.
Laura Tonel 《Annali dell'Universita di Ferrara》1998,44(1):63-80
Following tecniques proposed by A. V. Khazikhov and V. A. Weigant in 1995, we prove the global, with respect to time, existence
and uniqueness of the solution to the Navier-Stokes equations for a compressible, viscous and barotropic fluid which moves
on the surface of a sphere. In obtaining the main estimates we make use of the Hodge decomposition and the generalized potential
theory due to K. Kodaira.
Sunto Seguendo le tecniche proposte da A. V. Khazikhov and V. A. Weigant nel 1995, si prova l'esistenza ed unicità della soluzione per le equazioni di Navier-Stokes per un fluido comprimibile, viscoso e barotropico che si muova sulla superficie di una sfera. Nell'ottenere le principali stime si utilizzano la decomposizione di Hodge e la teoria del potenziale generalizzato, dovuta a K. Kodaira.相似文献
13.
Patrick J. Rabier 《Archiv der Mathematik》2007,88(2):143-152
We prove the existence of bounded Palais-Smale sequences for abstract functionals with a mountain pass geometry under hypotheses
weaker than those commonly used in the literature. This is obtained via a generalization of a generic result of Jeanjean,
combined with a rescaling argument. Applications to the existence of nontrivial solutions to semilinear elliptic problems
are given.
Received: 17 November 2005 相似文献
14.
Werner M. Seiler 《Acta Appl Math》1995,41(1-3):311-322
The computation of a number of arbitrary functions in the general solution is briefly reviewed. The results are used to study normal systems and their symmetry reduction. We discuss the treatment of gauge systems, especially the analysis of gauge fixing conditions. As examples, the Yang-Mills equations with the Lorentz gauge and Einstein's vacuum field equations with harmonic coordinates are considered. 相似文献
15.
Graded differential equations and their deformations: A computational theory for recursion operators
An algebraic model for nonlinear partial differential equations (PDE) in the category ofn-graded modules is constructed. Based on the notion of the graded Frölicher-Nijenhuis bracket, cohomological invariants H
*
(A) are related to each object (A, ) of the theory. Within this framework, H
0
(A) generalizes the Lie algebra of symmetries for PDE's, while H
1
(A) are identified with equivalence classes of infinitesimal deformations. It is shown that elements of a certain part of H
1
(A) can be interpreted as recursion operators for the object (A, ), i.e. operators giving rise to infinite series of symmetries. Explicit formulas for computing recursion operators are deduced. The general theory is illustrated by a particular example of a graded differential equation, i.e. the Super KdV equation.Tverskoy-Yamskoy per. 14, Apt. 45, 125047 Moscow, Russia. 相似文献
16.
N. Lohoué 《Geometric And Functional Analysis》1992,2(4):394-420
Résumé On prouve des inégalités de type Sobolev pour les opérateurs (L-) oùL est un sous-Laplacien sur un groupe de Lie non moyenmable et le bout de son spectre.
We prove Sobolev inequalities for (L-) whereL is a sub-Laplacian on a non-amenable group and is the bottom of its spectrum.相似文献
17.
Shibo Liu 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(3):788-592
Existence and multiplicity results are obtained for superlinear p-Laplacian equations without the Ambrosetti and Rabinowitz condition. To overcome the difficulty that the Palais-Smale sequences of the Euler-Lagrange functional may be unbounded, we consider the Cerami sequences. Our results extend the recent results of Miyagaki and Souto [O. Miyagaki, M. Souto, Superlinear problems without Ambrosetti and Rabinowitz growth condition, J. Differential Equations 245 (2008) 3628-3638]. 相似文献
18.
Mohammad A. Rammaha Sawanya Sakuntasathien 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(5):2658-2683
We focus on the global well-posedness of the system of nonlinear wave equations
19.
Volker Priebe 《manuscripta mathematica》1994,83(1):145-159
This paper deals with the solvability of the Navier-Stokes equations on manifolds with boundary. In particular, we concentrate
on the inhomogeneous slip boundary condition. Our formulation of the equations takes into account a curvature term which results
from a proper derivation of the Navier-Stokes equations. This term has not been considered in prior work.
During the work on this version, the author received technical support through a fellowship of the DFG 相似文献
20.
Chunxia Guan 《Journal of Differential Equations》2010,248(8):2003-2159
This paper is concerned with global existence and blow-up phenomena for an integrable two-component Camassa-Holm shallow water system. A new global existence result and several new blow-up results of strong solutions to the system are presented. Our obtained results for the system are sharp and improve considerably earlier results. 相似文献