Journal of Differential Equations最新文献

英文中文

Mathematical analysis of subwavelength resonant acoustic scattering in multi-layered high-contrast structures 多层高对比度结构中亚波长共振声散射的数学分析

IF 2.3 2区数学 Q1 MATHEMATICS

Journal of Differential Equations

Pub Date : 2026-01-23 DOI: 10.1016/j.jde.2026.114133

Youjun Deng , Lingzheng Kong , Yongjian Liu , Liyan Zhu

Multi-layered structures are widely used in the construction of metamaterial devices to realize various cutting-edge waveguide applications. This paper makes several contributions to the mathematical analysis of subwavelength resonances in a structure of N-layer nested resonators. Firstly, based on the Dirichlet-to-Neumann approach, we reduce the solution of the acoustic scattering problem to an N-dimensional linear system, and derive the optimal asymptotic characterization of subwavelength resonant frequencies in terms of the eigenvalues of an

N \times N

tridiagonal matrix, which we refer to as the generalized capacitance matrix. Moreover, we provide a modal decomposition formula for the scattered field, as well as a monopole approximation for the far-field pattern of the acoustic wave scattered by the N-layer nested resonators. Finally, some numerical results are presented to corroborate the theoretical findings.

多层结构被广泛应用于超材料器件的构建，以实现各种尖端波导应用。本文对n层嵌套谐振器结构中亚波长共振的数学分析做出了一些贡献。首先，基于Dirichlet-to-Neumann方法，我们将声散射问题的解简化为n维线性系统，并根据N×N三对角矩阵的特征值推导出亚波长谐振频率的最优渐近表征，我们将其称为广义电容矩阵。此外，我们还提供了散射场的模态分解公式，以及n层嵌套谐振器散射声波远场图形的单极子近似。最后，给出了一些数值结果来证实理论结果。

引用次数: 0

On sesquilinear forms for lower semibounded (singular) Sturm–Liouville operators 下半有界（奇异）Sturm-Liouville算子的半线性形式

IF 2.3 2区数学 Q1 MATHEMATICS

Journal of Differential Equations

Pub Date : 2026-01-23 DOI: 10.1016/j.jde.2026.114131

Jussi Behrndt , Fritz Gesztesy , Seppo Hassi , Roger Nichols , Henk de Snoo

Any self-adjoint extension of a (singular) Sturm–Liouville operator bounded from below uniquely leads to an associated sesquilinear form. This form is characterized in terms of principal and nonprincipal solutions of the Sturm–Liouville operator by using generalized boundary values. We provide these forms in detail in all possible cases (explicitly, when both endpoints are limit circle, when one endpoint is limit circle, and when both endpoints are limit point).

从下有界的（奇异）Sturm-Liouville算子的任何自伴随扩展唯一地导致一个相关的半线性形式。用广义边值表示Sturm-Liouville算子的主解和非主解。我们在所有可能的情况下（明确地，当两个端点都是极限环时，当一个端点是极限环时，以及当两个端点都是极限点时）详细地提供了这些形式。

引用次数: 0

Corrigendum to “Spectral optimization for weighted anisotropic problems with Robin conditions” [J. Differ. Equ. 378 (2024) 303–338] “具有Robin条件的加权各向异性问题的谱优化”[J]。是不同的。第378(2024)303-338条]

IF 2.3 2区数学 Q1 MATHEMATICS

Journal of Differential Equations

Pub Date : 2026-01-23 DOI: 10.1016/j.jde.2026.114130

Benedetta Pellacci , Giovanni Pisante , Delia Schiera

引用次数: 0

Variational construction of asymptotic orbits in contact Hamiltonian systems 接触哈密顿系统渐近轨道的变分构造

IF 2.3 2区数学 Q1 MATHEMATICS

Journal of Differential Equations

Pub Date : 2026-01-23 DOI: 10.1016/j.jde.2026.114141

Liang Jin , Jun Yan , Kai Zhao

For contact Hamiltonian systems without monotonicity assumption, there is a family of invariant sets

{{\tilde{N}}_{u}}

naturally stratified by the solutions u to the corresponding Hamilton-Jacobi equation. Under convergence assumptions of the solution semigroup, we establish the existence of semi-infinite orbits asymptotic to some

{\tilde{N}}_{u}

and heteroclinic orbits between

{\tilde{N}}_{u}

and

{\tilde{N}}_{v}

for different solutions u and v by variational methods. We also give verifiable criteria to ensure the convergence assumptions. As a corollary, we give a description of action minimizing orbits of the model system studied in [26].

对于无单调性假设的接触哈密顿系统，存在一类由相应哈密顿-雅可比方程解自然分层的不变集{N ~ u}。在解半群的收敛假设下，用变分方法证明了不同解u和v的半无限轨道渐近于某些N ~ u和N ~ u与N ~ v之间的异斜轨道的存在性。并给出了收敛性假设的可验证准则。作为推论，我们给出了[26]中所研究的模型系统的作用最小轨道的描述。

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引用次数: 0

The spatially inhomogeneous Vlasov-Nordström-Fokker-Planck system in the intrinsic weak diffusion regime 本征弱扩散区空间非均匀Vlasov-Nordström-Fokker-Planck体系

IF 2.3 2区数学 Q1 MATHEMATICS

Journal of Differential Equations

Pub Date : 2026-01-23 DOI: 10.1016/j.jde.2026.114137

Shengchuang Chang , Shuangqian Liu , Tong Yang

The spatially homogeneous Vlasov-Nordström-Fokker-Planck system is known to exhibit nontrivial large time behavior, naturally leading to weak diffusion of the Fokker-Planck operator. This weak diffusion, combined with the singularity of relativistic velocity, presents a significant challenge in analysis for the spatially inhomogeneous counterpart.

In this paper, we demonstrate that the Cauchy problem for the spatially inhomogeneous Vlasov-Nordström-Fokker-Planck system, without friction, maintains dynamically stable relative to the corresponding spatially homogeneous system. Our results are twofold: (1) we establish the existence of a unique global classical solution and characterize the asymptotic behavior of the spatially inhomogeneous system using a refined weighted energy method; (2) we directly verify the dynamic stability of the spatially inhomogeneous system in the framework of rescaled solutions.

已知空间均匀Vlasov-Nordström-Fokker-Planck系统表现出非平凡的大时间行为，自然导致福克-普朗克算子的弱扩散。这种弱扩散与相对论速度的奇异性相结合，对空间非均匀对应物的分析提出了重大挑战。本文证明了无摩擦的空间非齐次Vlasov-Nordström-Fokker-Planck系统相对于相应的空间齐次系统保持动态稳定的柯西问题。我们的研究结果有两个方面：(1)我们建立了一个唯一的全局经典解的存在性，并利用一种改进的加权能量方法刻画了空间非齐次系统的渐近行为；(2)在重标解的框架下直接验证了空间非齐次系统的动态稳定性。

引用次数: 0

Uniform robustness of strong attractors for non-autonomous dynamical systems: Theoretical results and applications 非自治动力系统强吸引子的一致鲁棒性：理论结果和应用

IF 2.3 2区数学 Q1 MATHEMATICS

Journal of Differential Equations

Pub Date : 2026-01-22 DOI: 10.1016/j.jde.2026.114134

Qiangheng Zhang , Tomás Caraballo , Shuang Yang

This paper is concerned with the uniform upper semi-continuity of strong pullback attractors for non-autonomous dynamical systems with delay parameter generated by retarded partial differential equations. In the theoretical section, we establish two theoretical results: one is the existence and uniqueness of strong pullback attractors, the other is the uniform upper semi-continuity of strong pullback attractors. The second result strengthens the findings of Carvalho et al. (2009) [5] and Zhang et al. (2024) [34]. In the application section, we consider the non-autonomous reaction-diffusion equations with delays defined on

R^{n}

. We not only establish the tail-estimates of solutions (The idea comes from Wang (1999) [24]), but also the tail-ends estimates of solutions in the regular space, which together with the truncated estimate technique and spectrum decomposition method of solutions proves the asymptotic compactness of the solutions in the regular space.

研究了由时滞偏微分方程产生时滞参数的非自治动力系统强回拉吸引子的一致上半连续性问题。在理论部分，我们建立了两个理论结果：一个是强回拉吸引子的存在唯一性，另一个是强回拉吸引子的均匀上半连续性。第二个结果强化了Carvalho et al.(2009)[5]和Zhang et al.(2024)[34]的发现。在应用部分，我们考虑在Rn上定义时滞的非自治反应扩散方程。我们不仅建立了解的尾部估计（思想来源于Wang(1999)[24]），而且还建立了正则空间中解的尾部估计，并结合截断估计技术和解的谱分解方法证明了正则空间中解的渐近紧性。

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引用次数: 0

Averaging theory and catastrophes 平均理论和灾难

IF 2.3 2区数学 Q1 MATHEMATICS

Journal of Differential Equations

Pub Date : 2026-01-21 DOI: 10.1016/j.jde.2026.114126

Pedro C.C.R. Pereira , Mike R. Jeffrey , Douglas D. Novaes

When a dynamical system is subject to a periodic perturbation, the averaging method can be applied to obtain an autonomous leading order ‘guiding system’, placing the time dependence at higher orders. Recent research focused on investigating invariant structures in non-autonomous differential systems arising from hyperbolic structures in the guiding system, such as periodic orbits and invariant tori. Complementarily, the effect that bifurcations in the guiding system have on the original non-autonomous one has also been recently explored, albeit less frequently. This paper extends this study by providing a broader description of the dynamics that can emerge from non-hyperbolic structures of the guiding system. Specifically, we prove here that

K

-universal bifurcations in the guiding system ‘persist’ in the original non-autonomous one, while non-versal bifurcations, such as the transcritical and pitchfork, do not. We illustrate the results on examples of a fold, a transcritical, a pitchfork, and a saddle-focus.

当动力系统受到周期性扰动时，可以应用平均方法获得一个自主的超前阶“导向系统”，将时间依赖置于更高阶。近年来的研究主要集中在研究由导向系统中的双曲结构引起的非自治微分系统中的不变量结构，如周期轨道和不变量环面。与此相辅相成的是，指导系统的分叉对原来的非自治系统的影响最近也进行了探讨，尽管频率较低。本文通过提供从导向系统的非双曲结构中可能出现的动力学的更广泛的描述来扩展这一研究。具体地说，我们在这里证明了引导系统中的k -通用分岔“坚持”在原始的非自治分岔中，而非通用分岔，如跨临界和干草叉，则不会。我们举例说明了一个折叠，一个跨临界，一个干草叉，和一个鞍焦点的结果。

引用次数: 0

Regularity theory for the space homogeneous polyatomic Boltzmann flow 空间均匀多原子玻尔兹曼流的正则性理论

IF 2.3 2区数学 Q1 MATHEMATICS

Journal of Differential Equations

Pub Date : 2026-01-21 DOI: 10.1016/j.jde.2026.114128

Ricardo Alonso , Milana Čolić

In this paper, we study the polyatomic Boltzmann equation based on continuous internal energy, focusing on physically relevant collision kernels of the hard potentials type with integrable angular part. We establish three main results: smoothing effects of the gain collision operator, propagation of velocity and internal energy first-order derivatives of solutions, and exponential decay estimates for singularities of the initial data. These results ultimately lead to a decomposition theorem, showing that any solution splits into a smooth part and a rapidly decaying rough component.

本文研究了基于连续内能的多原子玻尔兹曼方程，重点研究了具有角部可积的硬势型的物理相关碰撞核。我们建立了三个主要结果：增益碰撞算子的平滑效应，速度和内能的一阶导数的传播，以及初始数据奇点的指数衰减估计。这些结果最终导致分解定理，表明任何解都分裂成光滑部分和快速衰减的粗糙部分。

引用次数: 0

The Lp-boundedness of wave operators for nonhomogeneous fourth-order Schrödinger operators in high dimensions 高维非齐次四阶Schrödinger算子的波算子的lp有界性

IF 2.3 2区数学 Q1 MATHEMATICS

Journal of Differential Equations

Pub Date : 2026-01-21 DOI: 10.1016/j.jde.2026.114132

Zijun Wan , Xiaohua Yao

<div><div>This paper investigates the <math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math>-boundedness of wave operators associated with the following nonhomogeneous fourth-order Schrödinger operator on <math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math>:<math><mi>H</mi><mo>=</mo><msub><mrow><mi>H</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>+</mo><mi>V</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>,</mo><mspace></mspace><msub><mrow><mi>H</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>=</mo><msup><mrow><mi>Δ</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>−</mo><mi>Δ</mi><mo>.</mo></math> Assuming the real-valued potential V exhibits sufficient decay and regularity, we prove that for all dimensions <math><mi>n</mi><mo>≥</mo><mn>5</mn></math>, the wave operators <math><msub><mrow><mi>W</mi></mrow><mrow><mo>±</mo></mrow></msub><mo>(</mo><mi>H</mi><mo>,</mo><msub><mrow><mi>H</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>)</mo></math> are bounded on <math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>)</mo></math> for all <math><mn>1</mn><mo>≤</mo><mi>p</mi><mo>≤</mo><mo>∞</mo></math>, provided that zero is a regular threshold of H.</div><div>As applications, we derive the sharp <math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math>-<math><msup><mrow><mi>L</mi></mrow><mrow><msup><mrow><mi>p</mi></mrow><mrow><mo>′</mo></mrow></msup></mrow></msup></math> dispersive estimates for Schrödinger group <math><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo><mi>i</mi><mi>t</mi><mi>H</mi></mrow></msup></math>, as well as for the solutions operators <math><mi>cos</mi><mo>⁡</mo><mo>(</mo><mi>t</mi><msqrt><mrow><mi>H</mi></mrow></msqrt><mo>)</mo></math> and <math><mfrac><mrow><mi>sin</mi><mo>⁡</mo><mo>(</mo><mi>t</mi><msqrt><mrow><mi>H</mi></mrow></msqrt><mo>)</mo></mrow><mrow><msqrt><mrow><mi>H</mi></mrow></msqrt></mrow></mfrac></math> associated with the following beam equations with potentials:<math><mrow><mo>{</mo><mtable><mtr><mtd><msubsup><mrow><mo>∂</mo></mrow><mrow><mi>t</mi></mrow><mrow><mn>2</mn></mrow></msubsup><mi>u</mi><mo>+</mo><mrow><mo>(</mo><msup><mrow><mi>Δ</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>−</mo><mi>Δ</mi><mo>+</mo><mi>V</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>)</mo></mrow><mi>u</mi><mo>=</mo><mn>0</mn><mo>,</mo></mtd><mtd></mtd></mtr><mtr><mtd><mi>u</mi><mo>(</mo><mn>0</mn><mo>,</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>,</mo><mspace></mspace><msub><mrow><mo>∂</mo></mrow><mrow><mi>t</mi></mrow></msub><mi>u</mi><mo>(</mo><mn>0</mn><mo>,</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>,</mo></mtd><mtd><mo>(</mo><mi>t</mi><mo>,</mo><m

本文研究了下列Rn上非齐次四阶Schrödinger算子的波算子的lp有界性：H=H0+V(x),H0=Δ2−Δ。假设实值势V具有足够的衰减和规律性，我们证明了对于所有维度n≥5，对于所有1≤p≤∞，波算子W±（H,H0）在Lp（Rn）上有界，假设0是H的规则阈值。以及解算子cos （tH）和sin (tH)H与以下具有势的束方程相关：{∂t2u+（Δ2−Δ+V(x)）u=0,u(0,x)=f(x),∂tu(0,x)=g(x),(t,x)∈R×Rn,n≥5，其中p '表示p的Hölder共轭，1≤p≤2。此外，我们注意到，对于带有参数ϵ>；0的算子ϵΔ2−Δ+V也有相同的结果，这为相关方程的分析提供了更大的灵活性。

引用次数: 0

High multiplicity and global structure of coexistence states in a predator-prey model with saturation 饱和捕食-食饵模型中共存状态的高多样性和全局结构

IF 2.3 2区数学 Q1 MATHEMATICS

Journal of Differential Equations

Pub Date : 2026-01-20 DOI: 10.1016/j.jde.2026.114116

Kousuke Kuto , Julián López-Gómez , Eduardo Muñoz-Hernández

This paper establishes that, under the appropriate range of values of the parameters involved in the formulation of the model, a diffusive predator-prey system with saturation can have an arbitrarily large number of coexistence states for sufficiently large saturation rates. Moreover, it ascertains the global structure of the set of coexistence states in the limiting system as the saturation rate blows up.

本文建立了在模型公式中所涉及的参数的适当取值范围内，对于足够大的饱和率，具有饱和的扩散捕食-食饵系统可以具有任意多的共存状态。此外，还确定了饱和速率爆炸时极限系统共存状态集的全局结构。

引用次数: 0

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