共查询到20条相似文献,搜索用时 46 毫秒
1.
Answering a question left open in Métivier and Zumbrun (2005), we show for general symmetric hyperbolic boundary problems with constant coefficients, including in particular systems with characteristics of variable multiplicity, that the uniform Lopatinski condition implies strong L 2 well-posedness, with no further structural assumptions. The result applies, more generally, to any system that is strongly L 2 well-posed for at least one boundary condition. The proof is completely elementary, avoiding reference to Kreiss symmetrizers or other specific techniques. On the other hand, it is specific to the constant-coefficient case; at least, it does not translate in an obvious way to the variable-coefficient case. The result in the hyperbolic case is derived from a more general principle that can be applied, for example, to parabolic or partially parabolic problems like the Navier–Stokes or viscous MHD equations linearized about a constant state or even a viscous shock. 相似文献
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Quadratic groups, whose definitions depend on form parameters, contain the orthogonal groups, symplectic groups, classical unitary groups and all the classical groups of Dieudonné [4] as well as those of Bruhat and Tits [2]. Gauss decomposition with prescribed semisimple part in these groups is presented. As an application, the analog of a conjecture of Thompson is also studied for these groups. 相似文献
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We prove the global existence and scattering for the Hartree-type equation in H s (?3) the low regularity space s < 1. We follow the ideas in Colliander et al. (2004) to the Hartree-type nonlinearity, and also develop the theory of the classical multilinear operator modifying the L p estimate in Coifman and Meyer (1978). 相似文献
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The article considers linear elliptic equations with regular Borel measures as inhomogeneity. Such equations frequently appear in state-constrained optimal control problems. By a counter example of Serrin [18], it is known that, in the presence of non-smooth data, a standard weak formulation does not ensure uniqueness for such equations. Therefore several notions of solution have been developed that guarantee uniqueness. In this note, we compare different definitions of solutions, namely the ones of Stampacchia [19] and Boccardo-Galouët [4] and the two notions of solutions of [2, 7], and show that they are equivalent. As side results, we reformulate the solution in the sense of [19], and prove the existence of solutions in the sense of [2, 4, 7] in case of mixed boundary conditions. 相似文献
6.
Alfrederic Josse 《代数通讯》2017,45(2):606-620
The Halphen transform of a plane curve is the curve obtained by intersecting the tangent lines of the curve with the corresponding polar lines with respect to some conic. This transform was introduced by Halphen as a branch desingularization method in [5] and has also been studied in [2, 8]. We extend this notion to the Halphen transform of a space curve and study several of its properties (birationality, degree, rank, class, desingularization). 相似文献
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In this paper, based on the results in [8] we give a monomial basis for q-Schur superalgebra and then a presentation for it. The presentation is different from that in [12]. Imitating [3] and [7], we define the infinitesimal and the little q-Schur superalgebras. We give a “weight idempotent presentation” for infinitesimal q-Schur superalgebras. The BLM bases and monomial bases of little q-Schur superalgebras are obtained, and dimension formulas of infinitesimal and little q-Schur superalgebras are deduced. 相似文献
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Morton E. Harris 《代数通讯》2013,41(8):3668-3671
At some point, after publication, the author realized that the proof of [3, Theorem 5.2] is incorrect. This proof incorrectly adapts the proof of [1, Theorem 4.8] since [3, (5.5)] is incorrect. Using the same proof outline, we correct the proof of [3, Theorem 5.2]. 相似文献
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We investigate further the existence of solutions to kinetic models of chemotaxis. These are nonlinear transport-scattering equations with a quadratic nonlinearity which have been used to describe the motion of bacteria since the 80's when experimental observations have shown they move by a series of ‘run and tumble’. The existence of solutions has been obtained in several papers Chalub et al. (2004), Hwang et al. (2005a b) using direct and strong dispersive effects. Here, we use the weak dispersion estimates of Castella and Perthame (1996) to prove global existence in various situations depending on the turning kernel. In the most difficult cases, where both the velocities before and after tumbling appear, with the known methods, only Strichartz estimates can give a result, with a smallness assumption. 相似文献
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Juan C. Gutierrez Fernandez Claudia I. Garcia José Ignacio Martinez M. L. R. Montoya 《代数通讯》2013,41(10):4481-4497
Whether or not a finite-dimensional, commutative, power-associative nilalgebra is solvable is a well-known open problem. In this paper, we describe commutative, power-associative nilalgebras of dimension n ≥ 6 and nilindex n ? 1 based on the condition that n ? 4 ≤ dim 𝔄3 ≤ n ? 3. This paper is a continuation of [10], where we describe commutative power-associative nilalgebras of dimension and nilindex n. We observe that the Jordan case was obtained by L. Elgueta and A. Suazo in [2]. 相似文献
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T. Guédénon 《代数通讯》2013,41(8):2781-2793
The objective of this article is the study of localization and catenarity in strongly G-graded rings with Noetherian base ring, where G is a finitely generated, nilpotent and torsionfree group. We generalize some results of Guédénon (2000). It follows from Corollary 2.6 that if G is free Abelian of finite rank and A is a commutative strongly G-graded ring with base ring a Noetherian regular integral domain, then A is a Noetherian regular integral domain. 相似文献
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In this article, we provide a semilocal analysis for the Steffensen-type method (STTM) for solving nonlinear equations in a Banach space setting using recurrence relations. Numerical examples to validate our main results are also provided in this study to show that STTM is faster than other methods ([7, 13]) using similar convergence conditions. 相似文献
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F. Colombini 《偏微分方程通讯》2018,43(1):25-46
We consider the well-posedness of the Cauchy problem in Gevrey spaces for N×N first-order weakly hyperbolic systems. The question is to know whether the general results of Bron?tein [1] and Kajitani [9] can be improved when the coefficients depend only on time and are smooth, as it has been done for the scalar wave equation in [3]. The answer is no for general systems, and yes when the system is uniformly diagonalizable: in this case, we show that the Cauchy problem is well posed in all Gevrey classes Gs when the coefficients are C∞. Moreover, for 2×2 systems and some other special cases, we prove that the Cauchy problem is well posed in Gs for s<1+k when the coefficients are Ck, which is sharp following the counterexamples of Tarama [12]. The main new ingredient is the construction, for all hyperbolic matrix A, of a family of approximate symmetrizers, S𝜀, the coefficients of which are polynomials of 𝜀 and the coefficients of A and A*. 相似文献
15.
It was shown in [4, 14] that a bounded solution of the heat equation in a half-space which becomes zero at some time must be identically zero, even though no assumptions are made on the boundary values of the solutions. In a recent example, Luis Escauriaza showed that this statement fails if the half-space is replaced by cones with opening angle smaller than 90°. Here we show that the result remains true for cones with opening angle larger than 110°. 相似文献
16.
Raouf Ghomrasni 《随机分析与应用》2013,31(3):467-479
Given a finite collection of continuous semimartingales, a semimartingale decomposition of the corresponding ranked (order-statistics) processes was derived recently in [1]. In this paper, we obtain a more general result for semimartingales (not necessarily continuous) using a simpler approach. Furthermore, we also give a generalization of Ouknine [7, 8] and Yan's [11] formula for local times of ranked processes. 相似文献
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《代数通讯》2013,41(10):4357-4376
Let k be a field and H a Hopf k-algebra with bijective antipode, R an H-module algebra over k and A = R#H the associated smash product. The fixed subring of R under H is denoted by S. Let P be an R#H-module. Thus P is an S-module. The aim of this paper is to study the projectivity of P as a module over S. We get a generalization of some results of J.J. Garcia and Angel Del Rio [4] of Ida Doraiswamy [8] and of ours [[7], section 5]. 相似文献
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This article is a sequel of [4], where we defined supervaluations on a commutative semiring R and studied a dominance relation ? ≥ ψ between supervaluations ? and ψ on R, aiming at an enrichment of the algebraic tool box for use in tropical geometry. A supervaluation ?: R → U is a multiplicative map from R to a supertropical semiring U, cf. [4], [7], [8], [5], [9], with further properties, which mean that ? is a sort of refinement, or covering, of an m-valuation (= monoid valuation) v: R → M. In the most important case, that R is a ring, m-valuations constitute a mild generalization of valuations in the sense of Bourbaki [1], while ? ≥ ψ means that ψ: R → V is a sort of coarsening of the supervaluation ?. If ?(R) generates the semiring U, then ? ≥ ψ iff there exists a “transmission” α: U → V with ψ = α ○ ?. Transmissions are multiplicative maps with further properties, cf. [4, Section 5]. Every semiring homomorphism α: U → V is a transmission, but there are others which lack additivity, and this causes a major difficulty. In the main body of the article we study surjective transmissions via equivalence relations on supertropical semirings. We put special emphasis on homomorphic equivalence relations. Even those are often much more complicated than congruences by ideals in usual commutative algebra. 相似文献