共查询到20条相似文献,搜索用时 15 毫秒
1.
P. J. Vassiliou 《Acta Appl Math》1987,8(2):149-163
In the first paper of this series a correspondence was established between coupled systems of two-dimensional nonlinear wave equations and the six-dimensional simply transitive Lie algebras. In the present paper we make use of this result to construct a Darboux integrable and exactly integrable nonlinear system associated with the six-parameter nilpotent Lie group G
6,1 and we give its exact general solution in terms of four arbitrary functions. The procedure is shown to be an exact linearization of the nonlinear problem. 相似文献
2.
In this paper, we study the initial-boundary value problem for a system of nonlinear wave equations, involving nonlinear damping terms, in a bounded domain Ω. The nonexistence of global solutions is discussed under some conditions on the given parameters. Estimates on the lifespan of solutions are also given. Our results extend and generalize the recent results in [K. Agre, M.A. Rammaha, System of nonlinear wave equations with damping and source terms, Differential Integral Equations 19 (2006) 1235-1270], especially, the blow-up of weak solutions in the case of non-negative energy. 相似文献
3.
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
4.
David J. Benson 《Journal of Pure and Applied Algebra》2007,211(2):497-510
We develop a rank variety for finite-dimensional modules over a certain class of finite-dimensional local k-algebras, . Included in this class are the truncated polynomial algebras , with k an algebraically closed field and arbitrary. We prove that these varieties characterise projectivity of modules (Dade’s lemma) and examine the implications for the tree class of the stable Auslander-Reiten quiver. We also extend our rank varieties to infinitely generated modules and verify Dade’s lemma in this context. 相似文献
5.
V. V. Lychagin 《Acta Appl Math》1985,3(2):135-173
The purpose of this paper is to use the geometrical theory of nonlinear partial differential equations and the theory of singularities of maps in order to obtain the general scheme for constructing shock waves from multivalued solutions, given by smooth integral manifolds. This scheme is illustrated by some examples from gas dynamics, mechanics, acoustics and thermodynamics. 相似文献
6.
7.
Bennett Chow Robert Gulliver 《Calculus of Variations and Partial Differential Equations》1996,4(3):249-264
We consider the (degenerate) parabolic equationu
t
=G(u + ug, t) on then-sphereS
n
. This corresponds to the evolution of a hypersurface in Euclidean space by a general function of the principal curvatures, whereu is the support function. Using a version of the Aleksandrov reflection method, we prove the uniform gradient estimate ¦u(·,t)¦ <C, whereC depends on the initial conditionu(·, 0) but not ont, nor on the nonlinear functionG. We also prove analogous results for the equationu
t
=G(u +cu, ¦x¦,t) on then-ballB
n
, wherec 2(B
n
). 相似文献
8.
A new class of nonassociative algebras related to integrable PDE's and ODE's is introduced. These algebras can be regarded as a noncommutative generalization of Jordan algebras. Their deformations are investigated. Relationships between such algebras and graded Lie algebras are established. 相似文献
9.
Let
be the Hecke algebra of the symmetric group
over a field K of characteristic
and
a primitive
-th root of one in K. We show that an
-module is projective if and only if its restrictions to any
-parabolic subalgebra of
is projective.
Moreover, we give a new construction of blocks of
-parabolic subalgebras, in terms of skew group algebras over local commutative
algebras.
Received: 30 June 2003 相似文献
10.
N. G. Khor'kova 《Acta Appl Math》1995,41(1-3):145-152
The groups E
1
2,n–1
(
) of Vinogradov'sC-spectral sequence for determined systems of evolution equations are considered. Presentation of these groups useful in practical computations is obtained. The group E
1
2,1
(
) is calculated for a system of Schrödinger type equations. 相似文献
11.
Francesco Calogero 《Acta Appl Math》1995,39(1-3):229-244
The investigation of nonlinear evolution equations and dynamical systems integrable in multidimensions constitutes at present our main research interest. Here we survey findings obtained recently as well as over time: solvable equations (both PDEs and ODEs) are reported, philosophical motivations and methodological approaches are outlined. For more detailed treatments, including the display and analysis of solutions, the interested reader is referred to the original papers.On leave while serving as Secretary General, Pugwash Conferences on Science and World Affairs, Geneva, London, Rome. 相似文献
12.
A. M. Verbovetsky 《Acta Appl Math》1989,15(1-2):121-136
The algebra of higher symmetries and the space of conservation laws for Zakharov's nonlinear equations of the interaction between long and short waves are completely described. The scheme of computations due to Vinogradov is used. As a result, the local nonintegrability of these equations is proved. 相似文献
13.
Moscow. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 29, No. 3, pp. 78–86, May–June, 1988. 相似文献
14.
Vyjayanthi Chari 《Advances in Mathematics》2009,220(4):1193-328
Let g be a finite-dimensional simple Lie algebra and let Sg be the locally finite part of the algebra of invariants (EndCV⊗Sg(g)) where V is the direct sum of all simple finite-dimensional modules for g and S(g) is the symmetric algebra of g. Given an integral weight ξ, let Ψ=Ψ(ξ) be the subset of roots which have maximal scalar product with ξ. Given a dominant integral weight λ and ξ such that Ψ is a subset of the positive roots we construct a finite-dimensional subalgebra of Sg and prove that the algebra is Koszul of global dimension at most the cardinality of Ψ. Using this we construct naturally an infinite-dimensional non-commutative Koszul algebra of global dimension equal to the cardinality of Ψ. The results and the methods are motivated by the study of the category of finite-dimensional representations of the affine and quantum affine algebras. 相似文献
15.
We give several equivalent characterisations of left (and hence, by duality, also of right) supported algebras. These characterisations are in terms of properties of the left and the right parts of the module category, or in terms of the classes L0 and R0 which consist respectively of the predecessors of the projective modules, and of the successors of the injective modules. 相似文献
16.
Andrea Pasquali 《Journal of Pure and Applied Algebra》2019,223(8):3537-3553
If A and B are n- and m-representation finite k-algebras, then their tensor product is not in general -representation finite. However, we prove that if A and B are acyclic and satisfy the weaker assumption of n- and m-completeness, then Λ is -complete. This mirrors the fact that taking higher Auslander algebra does not preserve d-representation finiteness in general, but it does preserve d-completeness. As a corollary, we get the necessary condition for Λ to be -representation finite which was found by Herschend and Iyama by using a certain twisted fractionally Calabi–Yau property. 相似文献
17.
Pu Zhang 《Advances in Mathematics》2004,183(1):80-126
By introducing a twisted Hopf algebra we unify several important objects of study. Skew derivations of such an algebra are defined and the corresponding skew differential operator algebras are studied. This generalizes results in the Weyl algebra. Applying this investigation to the twisted Ringel-Hall algebra we get, in particular, a natural realization of the non-positive part of a quantized generalized Kac-Moody algebra, by identifying the canonical generators with some linear, skew differential operators. This also induces some algebras which are quantum-group like. 相似文献
18.
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
19.
Wolfgang Rump 《Archiv der Mathematik》2005,84(1):11-21
Let R be a complete discrete valuation domain with quotient field K, and let be an R-order in a semisimple K-algebra. Butler, Campbell, and Kovács have shown that R-free -modules decompose into -lattices when is representation-finite. Using the theory of ladder functors, we prove the converse by constructing indecomposable R-free -modules of infinite rank if is not representation-finite.Received: 23 March 2004 相似文献
20.
Jessica Lévesque 《Journal of Pure and Applied Algebra》2008,212(5):1149-1161
We introduce a new class of algebras, the Nakayama oriented pullbacks, obtained from pullbacks of surjective morphisms of algebras A?C and B?C. We prove that such a pullback is tilted when A and B are hereditary. We also show that stably hereditary algebras respecting the clock condition are Nakayama oriented pullbacks, and we use results about these pullbacks to show when a stably hereditary algebra is tilted or iterated tilted. 相似文献