共查询到20条相似文献,搜索用时 27 毫秒
1.
Len Meas 《Comptes Rendus Mathematique》2017,355(2):161-165
In this work, we will establish local in time dispersive estimates for solutions to the model-case Dirichlet wave equation inside a cylindrical convex domain with a smooth boundary . Let us recall that dispersive estimates are key ingredients to prove Strichartz estimates. Nonoptimal Strichartz estimates for waves inside an arbitrary domain Ω have been proved by Blair–Smith–Sogge [1], [2]. Better estimates in strictly convex domains have been obtained in [4]. Our case of cylindrical domains is an extension of the result of [4] in the case where the curvature radius ≥0 depends on the incident angle and vanishes in some directions. 相似文献
2.
In this paper we consider a diffusion system with the Belousov–Zhabotinskii (BZ for short) chemical reaction. Following Brazhnik and Tyson [4] and Pérez-Muñuzuri et al. [45], who predicted V-shaped fronts theoretically and discovered V-shaped fronts by experiments respectively, we give a rigorous mathematical proof of their results. We establish the existence of V-shaped traveling fronts in by constructing a proper supersolution and a subsolution. Furthermore, we establish the stability of the V-shaped front in . 相似文献
3.
We study solutions of the focusing energy-critical nonlinear heat equation in . We show that solutions emanating from initial data with energy and -norm below those of the stationary solution W are global and decay to zero, via the “concentration-compactness plus rigidity” strategy of Kenig–Merle [33], [34]. First, global such solutions are shown to dissipate to zero, using a refinement of the small data theory and the -dissipation relation. Finite-time blow-up is then ruled out using the backwards-uniqueness of Escauriaza–Seregin–Sverak [17], [18] in an argument similar to that of Kenig–Koch [32] for the Navier–Stokes equations. 相似文献
4.
Heayong Shin Young Wook Kim Sung-Eun Koh Hyung Yong Lee Seong-Deog Yang 《Comptes Rendus Mathematique》2018,356(3):333-339
Choe and Soret [1] constructed infinitely many compact embedded minimal surfaces in by desingularizing Clifford tori which meet each other along a great circle at the angle of the same size. We show their method works with some modifications to construct compact embedded minimal surfaces in the Berger sphere as well. 相似文献
5.
We study the realizations of certain braided vector spaces of rack type as Yetter–Drinfeld modules over a cosemisimple Hopf algebra H. We apply the strategy developed in [1] to compute their liftings and use these results to obtain the classification of finite-dimensional copointed Hopf algebras over . 相似文献
6.
Sangjib Kim 《Journal of Pure and Applied Algebra》2018,222(2):368-381
The double Pieri algebra, constructed by Howe, Lee, and the author in [10], [12], encodes information on the decomposition of Pieri type tensor products of irreducible representations for complex classical groups. In this paper we study its finite presentation in terms of generators and relations, and then prove that it admits the structure of a cluster algebra. We also study its -module structure. 相似文献
7.
We investigate blow-up properties for the initial-boundary value problem of a Keller–Segel model with consumption of chemoattractant when the spatial dimension is three. Through a kinetic reformulation of the Keller–Segel system, we first derive some higher-order estimates and obtain certain blow-up criteria for the local classical solutions. These blow-up criteria generalize the results in [4], [5] from the whole space to the case of bounded smooth domain . Lower global blow-up estimate on is also obtained based on our higher-order estimates. Moreover, we prove local non-degeneracy for blow-up points. 相似文献
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Alexander Tsymbaliuk 《Journal of Pure and Applied Algebra》2017,221(10):2633-2646
In this short article, we compute the classical limits of the quantum toroidal and affine Yangian algebras of by generalizing our arguments for from [7] (an alternative proof for is given in [10]). We also discuss some consequences of these results. 相似文献
10.
For an oriented 2-dimensional manifold Σ of genus g with n boundary components, the space carries the Goldman–Turaev Lie bialgebra structure defined in terms of intersections and self-intersections of curves. Its associated graded Lie bialgebra (under the natural filtration) is described by cyclic words in and carries the structure of a necklace Schedler Lie bialgebra. The isomorphism between these two structures in genus zero has been established in [13] using Kontsevich integrals and in [2] using solutions of the Kashiwara–Vergne problem.In this note, we give an elementary proof of this isomorphism over . It uses the Knizhnik–Zamolodchikov connection on . We show that the isomorphism naturally depends on the complex structure on the surface. The proof of the isomorphism for Lie brackets is a version of the classical result by Hitchin [9]. Surprisingly, it turns out that a similar proof applies to cobrackets.Furthermore, we show that the formality isomorphism constructed in this note coincides with the one defined in [2] if one uses the solution of the Kashiwara–Vergne problem corresponding to the Knizhnik–Zamolodchikov associator. 相似文献
11.
In this paper, we continue the study in [18]. We use the perturbation argument, modulational analysis and the energy argument in [15], [16] to show the stability of the sum of two solitary waves with weak interactions for the generalized derivative Schrödinger equation (gDNLS) in the energy space. Here (gDNLS) hasn't the Galilean transformation invariance, the pseudo-conformal invariance and the gauge transformation invariance, and the case we considered corresponds to the -supercritical case. 相似文献
12.
Sumana Hatui L.R. Vermani Manoj K. Yadav 《Journal of Pure and Applied Algebra》2018,222(10):3293-3302
Let G be a central product of two groups H and K. We study second cohomology group of G, having coefficients in a divisible abelian group D with trivial G-action, in terms of the second cohomology groups of certain quotients of H and K. In particular, for , some of our results provide a refinement of results from Wiegold (1971) [10] and Eckmann et al. (1973) [2]. 相似文献
13.
In this paper we investigate the orbital stability of solitary waves to the (generalized) Kawahara equation (gKW) which is a fifth order dispersive equation. For some values of the power of the nonlinearity, we prove the orbital stability in the energy space of two branches of even solitary waves of gKW by combining the well-known spectral method introduced by Benjamin [4] with continuity arguments. We construct the first family of even solitons by applying the implicit function theorem in the neighborhood of the explicit solitons of gKW found by Dey et al. [9]. The second family consists of even traveling waves with low speeds. They are solutions of a constraint minimization problem on the line and rescaling of perturbations of the soliton of gKdV with speed 1. 相似文献
14.
Haibo Cui Haiyan Yin Jinshun Zhang Changjiang Zhu 《Journal of Differential Equations》2018,264(7):4564-4602
In this paper, we are concerned with the asymptotic behavior of solutions to the system of Euler equations with time-depending damping, in particular, include the constant coefficient damping. We rigorously prove that the solutions time-asymptotically converge to the diffusion wave whose profile is self-similar solution to the corresponding parabolic equation, which justifies Darcy's law. Compared with previous results about Euler equations with constant coefficient damping obtained by Hsiao and Liu (1992) [2], and Nishihara (1996) [9], we obtain a general result when the initial perturbation belongs to the same space, i.e. . Our proof is based on the classical energy method. 相似文献
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A.D. Brooke-Taylor V. Fischer S.D. Friedman D.C. Montoya 《Annals of Pure and Applied Logic》2017,168(1):37-49
We provide a model where for a supercompact cardinal κ. [10] provides a sketch of how to obtain such a model by modifying the construction in [6]. We provide here a complete proof using a different modification of [6] and further study the values of other natural generalizations of classical cardinal characteristics in our model. For this purpose we generalize some standard facts that hold in the countable case as well as some classical forcing notions and their properties. 相似文献
17.
Takahiro Hashira Sachiko Ishida Tomomi Yokota 《Journal of Differential Equations》2018,264(10):6459-6485
This paper deals with the quasilinear degenerate Keller–Segel systems of parabolic–parabolic type in a ball of (). In the case of non-degenerate diffusion, Cie?lak–Stinner [3], [4] proved that if , where m denotes the intensity of diffusion and q denotes the nonlinearity, then there exist initial data such that the corresponding solution blows up in finite time. As to the case of degenerate diffusion, it is known that a solution blows up if (see Ishida–Yokota [13]); however, whether the blow-up time is finite or infinite has been unknown. This paper gives an answer to the unsolved problem. Indeed, the finite-time blow-up of energy solutions is established when . 相似文献
18.
Masoud Hassani 《Comptes Rendus Mathematique》2017,355(11):1133-1137
In this paper, we study the irreducible representation of in . This action preserves a quadratic form with signature . Thus, it acts conformally on the 3-dimensional Einstein universe . We describe the orbits induced in and its complement in . This work completes the study in [2], and is one element of the classification of cohomogeneity one actions on [5]. 相似文献
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Tamar Lando 《Annals of Pure and Applied Logic》2018,169(4):277-311
Space, as we typically represent it in mathematics and physics, is composed of dimensionless, indivisible points. On an alternative, region-based approach to space, extended regions together with the relations of ‘parthood’ and ‘contact’ are taken as primitive; points are represented as mathematical abstractions from regions.Region-based theories of space have been traditionally modeled in regular closed (or regular open) algebras, in work that goes back to [5] and [21]. Recently, logics for region-based theories of space were developed in [3] and [19]. It was shown that these logics have both a nice topological and relational semantics, and that the minimal logic for contact algebras, (defined below), is complete for both.The present paper explores the question of completeness of and its extensions for individual topological spaces of interest: the real line, Cantor space, the rationals, and the infinite binary tree. A second aim is to study a different, algebraic model of logics for region-based theories of space, based on the Lebesgue measure algebra (or algebra of Borel subsets of the real line modulo sets of Lebesgue measure zero). As a model for point-free space, the algebra was first discussed in [2]. The main results of the paper are that is weakly complete for any zero-dimensional, dense-in-itself metric space (including, e.g., Cantor space and the rationals); the extension is weakly complete for the real line and the Lebesgue measure contact algebra. We also prove that the logic is weakly complete for the infinite binary tree. 相似文献