共查询到20条相似文献,搜索用时 31 毫秒
1.
A. Rozanova-Pierrat 《Applicable analysis》2013,92(3):391-408
Recalling the proprieties of the Khokhlov–Zabolotskaya–Kuznetsov (KZK) equation, we prove the controllability of moments result for the linear part of the KZK equation and its non-linear perturbation. 相似文献
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We give bounds on the first non-zero eigenvalue of the scalar Laplacian for both the Page and the Chen–LeBrun–Weber Einstein metrics. One notable feature is that these bounds are obtained without explicit knowledge of the metrics or numerical approximation to them. Our method also allows the estimation of the invariant part of the spectrum for both metrics. We go on to discuss an application of these bounds to the linear stability of the metrics. We also give numerical evidence to suggest that the bounds for both metrics are extremely close to the actual eigenvalue. 相似文献
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We study the three-dimensional Cauchy problem of the Poisson–Nernst–Planck–Navier–Stokes equations. We first show that the corresponding stationary system has a unique semi-trivial solution under a general doping profile. Under initial small perturbations around such the semi-trivial stationary solution and small doping profile, we obtain the unique global-in-time solution to the non-stationary system. Moreover, we prove the asymptotic convergence of the solution toward the semi-trivial stationary solution as time tends to infinity. 相似文献
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The spt-crank of a vector partition, or an S -partition, was introduced by Andrews, Garvan and Liang. Let NS(m,n) denote the net number of S-partitions of n with spt-crank m, that is, the number of S -partitions (π1,π2,π3) of n with spt-crank m such that the length of π1 is odd minus the number of S -partitions (π1,π2,π3) of n with spt-crank m such that the length of π1 is even. Andrews, Dyson and Rhoades conjectured that {NS(m,n)}m is unimodal for any n , and they showed that this conjecture is equivalent to an inequality between the rank and crank of ordinary partitions. They obtained an asymptotic formula for the difference between the rank and crank of ordinary partitions, which implies NS(m,n)≥NS(m+1,n) for sufficiently large n and fixed m. In this paper, we introduce a representation of an ordinary partition, called the m-Durfee rectangle symbol, which is a rectangular generalization of the Durfee symbol introduced by Andrews. We give a proof of the conjecture of Andrews, Dyson and Rhoades. We also show that this conjecture implies an inequality between the positive rank and crank moments obtained by Andrews, Chan and Kim. 相似文献
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O. Lazarev and E.H. Lieb proved that, given f1,…,fn∈L1([0,1];C), there exists a smooth function Φ that takes values on the unit circle and annihilates span{f1,…,fn}. We give an alternative proof of that fact that also shows the W1,1 norm of Φ can be bounded by 5πn+1. Answering a question raised by Lazarev and Lieb, we show that if p>1 then there is no bound for the W1,p norm of any such multiplier in terms of the norms of f1,…,fn. 相似文献
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Vyacheslav Pivovarchik 《Integral Equations and Operator Theory》2012,73(3):383-393
The method (Martynyuk and Pivovarchik, Inverse Probl. 26(3):035011, 2010) of recovering the potential of the Sturm–Liouville equation on a half of the interval by the spectrum of a boundary value problem and by the restriction of the potential onto the other half of the interval is used for treating the missing eigenvalue problem (Trans. Am. Math. Soc. 352:2765–3789, 2000, J. R. Astr. Soc. 62:41–48, 1980, J. Math. Pures Appl. 91:468–475, 2009, J. Math. Soc. Japan 38:39–65, 1986). The latter arises in the case of the half-inverse (Hochstadt–Lieberman) problem with Robin boundary conditions and lies in the fact that in many cases all the eigenvalues but one are needed to recover the potential and the Robin condition at one of the ends. 相似文献
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Min-Chun Hong 《Annals of Global Analysis and Geometry》2001,20(1):23-46
For a parameter > 0, we study a type of vortex equations, which generalize the well-known Hermitian–Einstein equation, for a connection A and a section of a holomorphic vector bundle E over a Kähler manifold X. We establish a global existence of smooth solutions to heat flow for a self-dual Yang–Mills–Higgs field on E. Assuming the -stability of (E, ), we prove the existence of the Hermitian Yang–Mills–Higgs metric on the holomorphic bundle E by studying the limiting behaviour of the gauge flow. 相似文献
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Fernando Charro Guido De Philippis Agnese Di Castro Davi Máximo 《Calculus of Variations and Partial Differential Equations》2013,48(3-4):667-693
We prove L ∞ bounds and estimates of the modulus of continuity of solutions to the Poisson problem for the normalized infinity and p-Laplacian, namely $$\begin{array}{ll} -\Delta_p^N u=f\quad{\rm for } \; n < p \leq\infty.\end{array}$$ We are able to provide a stable family of results depending continuously on the parameter p. We also prove the failure of the classical Alexandrov–Bakelman–Pucci estimate for the normalized infinity Laplacian and propose alternate estimates. 相似文献
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Cristian Lăzureanu 《Comptes Rendus Mathematique》2017,355(5):596-600
In this note, we construct integrable deformations of the three-dimensional real valued Maxwell–Bloch equations by modifying their constants of motions. We obtain two Hamilton–Poisson realizations of the new system. Moreover, we prove that the obtained system has infinitely many Hamilton–Poisson realizations. Particularly, we present a Hamilton–Poisson approach of the system obtained considering two concrete deformation functions. 相似文献
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In this article, we give a new proof of the Carey–Helton–Howe–Pincus trace formula using Kato's theory of “relatively-smooth” operators and Krein's trace formula. 相似文献
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We present a Riemann–Hilbert problem formalism for the initial value problem for the Camassa–Holm equation on the line (CH). We show that: (i) for all , the solution of this problem can be obtained in a parametric form via the solution of some associated Riemann–Hilbert problem; (ii) for large time, it develops into a train of smooth solitons; (iii) for small ω, this soliton train is close to a train of peakons, which are piecewise smooth solutions of the CH equation for . To cite this article: A. Boutet de Monvel, D. Shepelsky, C. R. Acad. Sci. Paris, Ser. I 343 (2006). 相似文献
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I. D. Kan 《Mathematical Notes》2016,99(3-4):378-381
In the present paper, the inequality inverse to the Cauchy–Bunyakovskii–Schwarz inequality and generalizing other well-known inversions of this inequality is proved. 相似文献
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A. Rashid 《Journal of Mathematical Sciences》2009,160(1):84-94
In this paper, we consider the spectral collocation method for the Ginzburg–Landau equation coupled with the Benjamin–Bona–Mahony
equation. Semidiscrete and fully discrete spectral collocation schemes are given. In the fully discrete case, a three-level
spectral collocation scheme is considered. An energy estimation method is used to obtain error estimates for the approximate
solutions.
Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 57, Suzdal
Conference–2006, Part 3, 2008. 相似文献
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In this paper we give two characterizations of the Poletsky–Stessin–Hardy spaces in the complex plane: First we completely describe functions in these spaces by having a harmonic majorant with a certain growth condition and we prove some basic results about these spaces. Second we describe these functions in terms of their boundary values as a weighted subclass of the usual $L^p$ class with respect to the arclength measure on the boundary, when the boundary is $C^2$ . In particular, we extend the classical result of Beurling which describes the invariant subspaces of the shift operator. Additionally we provide non-trivial examples. 相似文献