Journal de Mathematiques Pures et Appliquees最新文献

英文中文

Asymptotic and global analysis of principal eigenvalues for linear time-periodic parabolic systems 线性时间周期抛物型系统主特征值的渐近与全局分析

IF 2.3 1区数学 Q1 MATHEMATICS

Journal de Mathematiques Pures et Appliquees

Pub Date : 2025-11-01 Epub Date: 2025-08-28 DOI: 10.1016/j.matpur.2025.103781

Shuang Liu

The paper is concerned with the effects of the spatio-temporal heterogeneity on the principal eigenvalues of some linear time-periodic parabolic systems. Various asymptotic behaviors of the principal eigenvalue and its monotonicity, as a function of the diffusion rate and frequency, are derived. In particular, some singular behaviors of the principal eigenvalues are characterized when both the diffusion rate and frequency approach zero, with some scalar time-periodic Hamilton-Jacobi equation as the limiting equation. Furthermore, we completely classify the topological structures of the level sets for the principal eigenvalues in the plane of the diffusion rate and frequency. Our results not only generalize the findings in [28] for scalar periodic-parabolic operators, but also reveal more rich global information, for time-periodic parabolic systems, on the dependence of the principal eigenvalues upon the spatio-temporal heterogeneity.

本文研究了一类线性时间周期抛物型系统的时空异质性对其主特征值的影响。导出了主特征值及其单调性作为扩散速率和频率的函数的各种渐近性质。特别地，当扩散速率和频率都趋近于零时，用标量时间周期Hamilton-Jacobi方程作为极限方程，刻画了主特征值的奇异行为。进一步，我们对扩散速率和频率平面上主特征值的水平集的拓扑结构进行了完全分类。我们的结果不仅推广了[28]中关于标量周期抛物算子的发现，而且还揭示了更多关于时间周期抛物系统的主特征值对时空异质性的依赖的丰富的全局信息。

引用次数: 0

Spreading properties and forced traveling waves of reaction-diffusion equations in a time-heterogeneous shifting environment 反应扩散方程在时非均质位移环境下的传播特性和强迫行波

IF 2.1 1区数学 Q1 MATHEMATICS

Journal de Mathematiques Pures et Appliquees

Pub Date : 2025-11-01 Epub Date: 2025-06-13 DOI: 10.1016/j.matpur.2025.103759

Lei Zhang , Xiao-Qiang Zhao

In this paper, we study the propagation dynamics for a large class of time and space heterogeneous reaction-diffusion equations

u_{t} = u_{x x} + u g (x - ω (t), t, u)

, where

ω (t)

represents the shifting distance, and the nonlinearity

u g (ξ, t, u)

is asymptotically of KPP type as

ξ \to - \infty

and is negative as

ξ \to + \infty

. Let

c^{⁎}

be the spreading speed of the limiting equation

u_{t} = u_{x x} + u g (- \infty, t, u)

. Under the assumption that the shifting speed

ω^{'} (t)

admits a uniform mean c, we show that the solutions with compactly supported initial data go to zero eventually when

c \leq - c^{⁎}

, the leftward spreading speed is

- c^{⁎}

when

c > - c^{⁎}

, and the rightward spreading speed is c and

c^{⁎}

when

c \in (- c^{⁎}, c^{⁎})

and

c \geq c^{⁎}

, respectively. We also establish the existence, uniqueness and nonexistence of the forced traveling wave in terms of the sign of

c - c^{⁎}

本文研究了一大类时空非均相反应扩散方程ut=uxx+ug（x - ω(t),t,u）的传播动力学，其中ω(t)表示移动距离，非线性ug（ξ,t,u）在ξ→−∞时渐近为KPP型，在ξ→+∞时为负值。设c _为极限方程ut=uxx+ug（−∞,t,u）的扩展速度。在移动速度ω ' (t)允许一个均匀均值c的假设下，我们证明当c≤−c oc oc时，具有紧支持初始数据的解最终趋于零，当c>；−c oc oc时，左向扩展速度为−c oc oc，当c∈(−c oc oc,c oc)和c≥c oc时，右向扩展速度分别为c和c oc。我们还利用c−c的符号证明了强迫行波的存在性、唯一性和不存在性。

引用次数: 0

Parabolic Lusztig varieties and chromatic symmetric functions 抛物型Lusztig变异体与色对称函数

IF 2.1 1区数学 Q1 MATHEMATICS

Journal de Mathematiques Pures et Appliquees

Pub Date : 2025-11-01 Epub Date: 2025-07-21 DOI: 10.1016/j.matpur.2025.103771

Alex Abreu , Antonio Nigro

The characters of Kazhdan–Lusztig elements of the Hecke algebra over

S_{n}

(and in particular, the chromatic symmetric function of indifference graphs) are completely encoded in the (intersection) cohomology of Lusztig varieties. Considering the forgetful map to some partial flag variety, the decomposition theorem tells us that this cohomology splits as a sum of intersection cohomology groups with coefficients in some local systems of subvarieties of the partial flag variety. We prove that these local systems correspond to representations of subgroups of

S_{n}

. An explicit characterization of such representations would provide a recursive formula for the computation of such characters/chromatic symmetric functions, which could settle Haiman's conjecture about the positivity of the monomial characters of Kazhdan–Lusztig elements and Stanley–Stembridge conjecture about e-positivity of chromatic symmetric function of indifference graphs. We also find a connection between the character of certain homology groups of subvarieties of the partial flag varieties and the Grojnowski–Haiman hybrid basis of the Hecke algebra.

Sn上的Hecke代数的Kazhdan-Lusztig元的性质（特别是无差异图的色对称函数）完全编码在Lusztig变元的（交）上同调中。考虑到某些部分标志变体的遗忘映射，分解定理告诉我们，该上同调在部分标志变体的子变体的某些局部系统中分裂为带系数的交上同调群的和。我们证明了这些局部系统对应于Sn的子群的表示。对这类表征的明确刻画，将为这类特征/色对称函数的计算提供一个递推公式，从而解决Haiman关于Kazhdan-Lusztig元单项式特征的正性猜想和Stanley-Stembridge关于无差异图色对称函数e-正性的猜想。我们还发现了部分旗变体的某些子变体的同调群的性质与Hecke代数的Grojnowski-Haiman杂交基之间的联系。

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引用次数: 0

On isomorphism of the space of continuous functions with finite p-th variation along a partition sequence 分配序列上有限p次变分的连续函数空间的同构性

IF 2.1 1区数学 Q1 MATHEMATICS

Journal de Mathematiques Pures et Appliquees

Pub Date : 2025-11-01 Epub Date: 2025-06-16 DOI: 10.1016/j.matpur.2025.103753

Purba Das , Donghan Kim

We study the concept of (generalized) p-th variation of a real-valued continuous function along a general class of refining sequence of partitions. We show that the finiteness of the p-th variation of a given function is closely related to the finiteness of

ℓ^{p}

-norm of the coefficients along a Schauder basis, similar to the fact that Hölder coefficient of the function is connected to

ℓ^{\infty}

-norm of the Schauder coefficients. This result provides an isomorphism between the space of α-Hölder continuous functions with finite (generalized) p-th variation along a given partition sequence and a subclass of infinite-dimensional matrices equipped with an appropriate norm, in the spirit of Ciesielski.

我们研究了一个实值连续函数沿一般划分精炼序列的（广义）p次变分的概念。我们证明了给定函数的p次变分的有限性与沿Schauder基的系数的r∞范数的有限性密切相关，类似于函数的Hölder系数与Schauder系数的r∞范数相连的事实。根据Ciesielski的精神，给出了沿给定配分序列具有有限（广义）p次变分的α-Hölder连续函数空间与具有适当范数的无限维矩阵子类之间的同构。

引用次数: 0

Hidden asymptotics for the weak solutions of the strongly stratified Boussinesq system without rotation 无旋转强分层Boussinesq系统弱解的隐渐近性

IF 2.1 1区数学 Q1 MATHEMATICS

Journal de Mathematiques Pures et Appliquees

Pub Date : 2025-10-01 Epub Date: 2025-06-16 DOI: 10.1016/j.matpur.2025.103750

Frédéric Charve

The asymptotics of the strongly stratified Boussinesq system when the Froude number goes to zero have been previously investigated, but the resulting limit system surprisingly did not depend on the thermal diffusivity

ν^{'}

. In this article we obtain richer asymptotics (depending on

ν^{'}

) for more general ill-prepared initial data.

As for the rotating fluids system, the only way to reach this limit consists in finding suitable non-conventional initial data: here, to a function classically depending on the full space variable, we add a second one only depending on the vertical coordinate.

Thanks to a refined study of the structure of the limit system and to new adapted Strichartz estimates, we obtain convergence in the context of weak Leray-type solutions providing explicit convergence rates when possible. In the usually simpler case

ν = ν^{'}

we are able to improve the Strichartz estimates and the convergence rates. The last part of the appendix is devoted to the proof of a new and crucial dispersion estimate, as classical methods fail.

Finally, our theorems can also be rewritten as a global existence result and asymptotic expansion for the classical Boussinesq system near an explicit stationary solution and for large non-conventional vertically stratified initial data.

以前已经研究了强分层Boussinesq系统在弗劳德数趋于零时的渐近性，但令人惊讶的是，所得到的极限系统并不依赖于热扩散率ν '。在本文中，我们对更一般的准备不足的初始数据获得了更丰富的渐近性（取决于ν '）。对于旋转流体系统，达到这个极限的唯一方法是找到合适的非常规初始数据：在这里，对于一个经典地依赖于全空间变量的函数，我们添加第二个仅依赖于垂直坐标的函数。由于对极限系统结构的精细研究和新的适应的Strichartz估计，我们在弱leray型解的情况下获得了收敛性，在可能的情况下提供了显式的收敛率。在通常更简单的情况下，ν=ν '，我们能够改进Strichartz估计和收敛速率。附录的最后一部分致力于证明一个新的和关键的色散估计，因为经典方法失败了。最后，我们的定理也可以改写为经典Boussinesq系统在显式平稳解附近和大型非常规垂直分层初始数据的全局存在性结果和渐近展开式。

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引用次数: 0

Positive temperature in nonlinear thermoviscoelasticity and the derivation of linearized models 非线性热粘弹性中的正温度及线性化模型的推导

IF 2.1 1区数学 Q1 MATHEMATICS

Journal de Mathematiques Pures et Appliquees

Pub Date : 2025-10-01 Epub Date: 2025-06-16 DOI: 10.1016/j.matpur.2025.103751

Rufat Badal , Manuel Friedrich , Martin Kružík , Lennart Machill

According to the Nernst theorem or, equivalently, the third law of thermodynamics, the absolute zero temperature is not attainable. Starting with an initial positive temperature, we show that there exist solutions to a Kelvin-Voigt model for quasi-static nonlinear thermoviscoelasticity at a finite-strain setting [45], obeying an exponential-in-time lower bound on the temperature. Afterwards, we focus on the case of deformations near the identity and temperatures near a critical positive temperature, and we show that weak solutions of the nonlinear system converge in a suitable sense to solutions of a system in linearized thermoviscoelasticity. Our result extends the recent linearization result in [4], as it allows the critical temperature to be positive.

根据能斯特定理，或者说热力学第三定律，绝对零度是不可能达到的。从初始正温度开始，我们证明了在有限应变设置[45]下准静态非线性热粘弹性Kelvin-Voigt模型存在解，服从温度的指数时间下界。然后，我们重点讨论了在恒等附近的变形和温度接近临界正温度的情况，并证明了非线性系统的弱解在适当意义上收敛于线性化热粘弹性系统的解。我们的结果扩展了[4]中最近的线性化结果，因为它允许临界温度为正。

引用次数: 0

‘t Hooft bundles on the complete flag threefold and moduli spaces of instantons t Hooft束上的完全标志三倍和模空间的实例

IF 2.1 1区数学 Q1 MATHEMATICS

Journal de Mathematiques Pures et Appliquees

Pub Date : 2025-10-01 Epub Date: 2025-06-13 DOI: 10.1016/j.matpur.2025.103763

Vincenzo Antonelli , Francesco Malaspina , Simone Marchesi , Joan Pons-Llopis

In this work we study the moduli spaces of instanton bundles on the flag twistor space

F : = F (0, 1, 2)

. We stratify them in terms of the minimal twist supporting global sections and we introduce the notion of (special) ‘t Hooft bundle on F. In particular we prove that there exist μ-stable ‘t Hooft bundles for each admissible charge k. We completely describe the geometric structure of the moduli space of (special) ‘t Hooft bundles for arbitrary charge k. Along the way to reach these goals, we describe the possible structures of multiple curves supported on some rational curves in F as well as the family of del Pezzo surfaces realized as hyperplane sections of F. Finally we investigate the splitting behavior of ‘t Hooft bundles when restricted to conics.

本文研究了旗扭空间F:=F（0,1,2）上的瞬子束的模空间。我们根据支持全局截面的最小扭转对它们进行了分层，并在f上引入了（特殊）t Hooft束的概念，特别证明了对于每一个可允许的电荷k都存在μ稳定的t Hooft束。我们完整地描述了任意电荷k的（特殊）t Hooft束的模空间的几何结构。我们描述了F中若干有理曲线支撑的多重曲线的可能结构，以及作为F的超平面截面实现的del Pezzo曲面族，最后研究了F的Hooft束在限制于二次曲线时的分裂行为。

引用次数: 0

A Le Potier-type isomorphism twisted with multiplier submodule sheaves 带乘子模束的Le potier型同构

IF 2.1 1区数学 Q1 MATHEMATICS

Journal de Mathematiques Pures et Appliquees

Pub Date : 2025-10-01 Epub Date: 2025-06-13 DOI: 10.1016/j.matpur.2025.103760

Yaxiong Liu , Zhuo Liu , Hui Yang , Xiangyu Zhou

In this paper, we obtain a Le Potier-type isomorphism theorem twisted with multiplier submodule sheaves, which relates a holomorphic vector bundle endowed with a strongly Nakano semi-positive singular Hermitian metric to the tautological line bundle with the induced metric. As applications, we obtain a Kollár-type injectivity theorem, a Nadel-type vanishing theorem, and a singular holomorphic Morse inequality for holomorphic vector bundles and so on.

本文得到了一个带乘子模束扭曲的Le potier型同构定理，该定理将赋有强Nakano半正奇异hermite度规的全纯向量束与带诱导度规的同构线束联系起来。作为应用，我们得到了一个Kollár-type注入定理，一个nadell型消失定理，一个全纯向量束的奇异全纯Morse不等式等。

引用次数: 0

Large-time asymptotics for hyperbolic systems with non-symmetric relaxation: An algorithmic approach 非对称松弛双曲型系统的大时渐近性：一种算法方法

IF 2.1 1区数学 Q1 MATHEMATICS

Journal de Mathematiques Pures et Appliquees

Pub Date : 2025-10-01 Epub Date: 2025-06-16 DOI: 10.1016/j.matpur.2025.103757

Timothée Crin-Barat , Lorenzo Liverani , Ling-Yun Shou , Enrique Zuazua

We study the stability of one-dimensional linear hyperbolic systems with non-symmetric relaxation. Introducing a new frequency-dependent Kalman stability condition, we prove an abstract decay result underpinning a form of inhomogeneous hypocoercivity. In contrast with the homogeneous setting, the decay rates depend on how the Kalman condition is fulfilled and, in most cases, a loss of derivative occurs: one must require an additional regularity assumption on the initial data to ensure the decay.

Under structural assumptions, we refine our abstract result by providing an algorithm, of wide applicability, for the construction of Lyapunov functionals. This allows us to systematically establish decay estimates for a given system and uncover algebraic cancellations (beyond the reach of the Kalman-based approach) reducing the loss of derivatives in high frequencies. To demonstrate the applicability of our method, we derive new stability results for the Sugimoto model, which describes the propagation of nonlinear acoustic waves, and for a beam model of Timoshenko type with memory.

研究了具有非对称弛豫的一维线性双曲型系统的稳定性。引入一个新的频率相关卡尔曼稳定性条件，证明了支持非齐次次矫顽力形式的抽象衰减结果。与齐次设置相反，衰减率取决于如何满足卡尔曼条件，并且在大多数情况下，会发生导数损失：必须要求对初始数据进行额外的规则性假设以确保衰减。在结构假设下，我们通过提供一个广泛适用的Lyapunov泛函构造算法来完善我们的抽象结果。这使我们能够系统地建立给定系统的衰减估计，并揭示代数消去（超出了基于卡尔曼的方法的范围），减少高频导数的损失。为了证明我们的方法的适用性，我们得到了描述非线性声波传播的杉本模型和具有记忆的Timoshenko型波束模型的新的稳定性结果。

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引用次数: 0

Long time behaviour of the solution of Maxwell's equations in dissipative generalized Lorentz materials (II) A modal approach 耗散广义洛伦兹材料中麦克斯韦方程组解的长时间行为（II）一个模态方法

IF 2.1 1区数学 Q1 MATHEMATICS

Journal de Mathematiques Pures et Appliquees

Pub Date : 2025-09-01 Epub Date: 2025-04-28 DOI: 10.1016/j.matpur.2025.103720

Maxence Cassier , Patrick Joly , Luis Alejandro Rosas Martínez

This work concerns the analysis of electromagnetic dispersive media modelled by generalized Lorentz models. More precisely, this paper is the second of two articles dedicated to the long time behaviour of solutions of Maxwell's equations in dissipative Lorentz media, via the decay rate of the electromagnetic energy for the corresponding Cauchy problem. In opposition to the frequency dependent Lyapunov functions approach used in [4], we develop a method based on the spectral analysis of the underlying non selfadjoint operator of the model. Although more involved, this approach is closer to physics, as it uses the dispersion relation of the model, and has the advantage to provide more precise and more optimal results, leading to distinguish the notion of weak and strong dissipation.

这项工作涉及用广义洛伦兹模型模拟的电磁色散介质的分析。更准确地说，这篇论文是两篇文章中的第二篇，专门讨论麦克斯韦方程组解在耗散洛伦兹介质中的长时间行为，通过相应的柯西问题的电磁能量衰减率。与[4]中使用的频率相关Lyapunov函数方法相反，我们开发了一种基于模型底层非自伴随算子的频谱分析的方法。这种方法虽然比较复杂，但更接近物理，因为它利用了模型的色散关系，并且具有提供更精确和更优结果的优势，从而区分了弱耗散和强耗散的概念。

引用次数: 0

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全部 ACS Publications Elsevier ieeexplore Springer The Royal Society of Chemistry Wiley

期刊

Journal de Mathematiques Pures et Appliquees

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