Applied Mathematics Letters最新文献

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High asymptotic order numerical methods for highly oscillatory ODEs with large initial data 大初始数据高度振荡 ODE 的高渐近阶数值方法

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters

Pub Date : 2024-11-09 DOI: 10.1016/j.aml.2024.109365

Zhongli Liu , Hongjiong Tian

In this paper, we propose high asymptotic order numerical methods for solving highly oscillatory second order ODEs with large initial data, where the total energy of the system becomes unbounded as the oscillation frequency grows. The existing asymptotic-numerical solvers are especially designed for the classical energy bounded oscillatory equations, offering no insight into their performance with energy unbounded case. Based on the asymptotic expansion of the solution in the inverse powers of the oscillatory parameter, we propose an asymptotic numerical integrator to solve this class of highly oscillatory ODEs and discuss the computational efficiency for the case of polynomials. One numerical example is given to show the efficiency and accuracy of our proposed asymptotic-numerical solver.

在本文中，我们提出了高渐近阶数值方法，用于求解具有大量初始数据的高度振荡二阶 ODE，在这种情况下，随着振荡频率的增加，系统的总能量变得无约束。现有的渐近阶数值求解器都是专门为经典的能量受限振荡方程设计的，无法深入了解它们在能量无约束情况下的性能。基于振荡参数反幂级数求解的渐近展开，我们提出了一种渐近数值积分器来求解这类高度振荡的 ODEs，并讨论了多项式情况下的计算效率。我们给出了一个数值示例，以说明我们提出的渐近数值求解器的效率和准确性。

引用次数: 0

A note on the L1 discretization error for the Caputo derivative in Hölder spaces 关于赫尔德空间中卡普托导数的 L1 离散误差的说明

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters

Pub Date : 2024-11-09 DOI: 10.1016/j.aml.2024.109364

Félix del Teso , Łukasz Płociniczak

We establish uniform error bounds of the L1 discretization of the Caputo derivative of Hölder continuous functions. The result can be understood as: error = degree of smoothness - order of the derivative. We present an elementary proof and illustrate its optimality with numerical examples.

我们建立了赫尔德连续函数卡普托导数 L1 离散化的均匀误差边界。其结果可理解为：误差 = 平滑度 - 导数阶数。我们给出了一个基本证明，并通过数值示例说明了其最优性。

引用次数: 0

Double-pole anti-dark solitons for a Lakshmanan-Porsezian-Daniel equation in an optical fiber or a ferromagnetic spin chain 光纤或铁磁自旋链中拉克希曼-波尔舍西安-丹尼尔方程的双极反暗孤子

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters

Pub Date : 2024-11-09 DOI: 10.1016/j.aml.2024.109362

Xi-Hu Wu , Yi-Tian Gao

Under investigated in this paper is a Lakshmanan-Porsezian-Daniel equation that describes the nonlinear spin excitations in a (1+1)-dimensional isotropic biquadratic Heisenberg ferromagnetic spin chain with the octupole-dipole interaction or the propagation of the ultrashort pulses in a long-distance and high-speed optical fiber transmission system. Under certain parameter conditions, we simultaneously take the multi-pole phenomena and breather-to-soliton transitions into account, then utilize the second-order generalized Darboux transformation to derive the double-pole anti-dark solitons and graphically illustrate them. Asymptotic analysis is conducted to examine the interaction properties of double-pole anti-dark solitons, including their characteristic lines, amplitudes, phase shifts, slopes and position differences. Unlike the double-pole anti-dark solitons found in the Hirota equation, the ones in this study exhibit a distinct feature: Different soliton components share the same amplitude.

本文研究的是拉克什曼-波齐安-丹尼尔方程，该方程描述了具有八极-偶极相互作用的 (1+1)-dimensional isotropic biquadratic Heisenberg ferromagnetic spin chain 中的非线性自旋激发，或超短脉冲在长距离高速光纤传输系统中的传播。在一定的参数条件下，我们同时考虑了多极现象和呼吸到孤子的转变，然后利用二阶广义达尔布克斯变换推导出双极反暗孤子，并用图形加以说明。通过渐近分析，研究了双极反暗孤子的相互作用特性，包括其特征线、振幅、相移、斜率和位置差。与广田方程中发现的双极反暗孤子不同，本研究中的双极反暗孤子表现出一个明显的特征：不同的孤子成分具有相同的振幅。

引用次数: 0

Time-periodic mild solutions to the three-dimensional micropolar fluid equations 三维微波流体方程的时周期温和解

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters

Pub Date : 2024-11-09 DOI: 10.1016/j.aml.2024.109367

Xiaotong Mu, Jinyi Sun

The paper is concerned with the three-dimensional micropolar fluid equations. By using the successive approximation and Littlewood–Paley theory, we prove existence and uniqueness of time-periodic mild solutions of the three-dimensional micropolar fluid equations with external forces in Besov spaces.

本文关注三维微波流体方程。通过使用逐次逼近和 Littlewood-Paley 理论，我们证明了贝索夫空间中带有外力的三维微波流体方程的时间周期温和解的存在性和唯一性。

引用次数: 0

State transitions for the rational solutions of Kundu equation with non-zero boundary conditions 具有非零边界条件的昆杜方程有理解的状态转换

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters

Pub Date : 2024-11-09 DOI: 10.1016/j.aml.2024.109363

Deqin Qiu , Yongshuai Zhang , Wei Liu

Several novel rational solutions with nonzero boundary condition for the Kundu equation, which is an important physical model, are derived using the technique of generalized Darboux transformation. It is the first time that a systemic analysis has been conducted on such rational solutions for the Kundu equation. For the 1-order rational solutions with nonzero boundary conditions, our findings reveal that three parameters,

a

b

, and

β

, which are associated with the effects of self-steepening, self-phase modulation, and quintic nonlinearity in the Kundu equation, can result in four distinct states for case B and five distinct states for case C, all corresponding to rational solutions with nonzero boundary conditions.

利用广义达尔布克斯变换技术，为重要物理模型昆都方程导出了几种具有非零边界条件的新型有理解。这是首次对昆杜方程的此类有理解进行系统分析。对于具有非零边界条件的一阶有理解，我们的研究结果表明，与昆杜方程中的自膨胀、自相位调制和五次非线性效应相关的三个参数 a、b 和 β 可导致情况 B 中的四种不同状态和情况 C 中的五种不同状态，它们都对应于具有非零边界条件的有理解。

引用次数: 0

Threshold dynamics of a time-delayed dengue virus infection model incorporating vaccination failure and exposed mosquitoes 包含疫苗接种失败和暴露蚊子的延时登革热病毒感染模型的阈值动力学

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters

Pub Date : 2024-11-09 DOI: 10.1016/j.aml.2024.109366

Songbai Guo , Min He , Fuxiang Li

A time-delayed dengue virus transmission model has been developed, which takes into account vaccination failure and the presence of exposed mosquitoes. This model also incorporates the survival probability of infected individuals during the incubation period to provide a clearer understanding of how latency affects the control reproduction number

R_{c}

. Furthermore, by employing the Lyapunov functional approach, we establish the global asymptotic stability of equilibria in relation to

R_{c}

. The results indicate that the disease-free equilibrium

T^{0}

is globally asymptotically stable if and only if

R_{c} \leq 1

, whereas the endemic equilibrium

T^{*}

is globally asymptotically stable if and only if

R_{c} > 1

我们建立了一个延时登革热病毒传播模型，其中考虑到了疫苗接种失败和暴露蚊子的存在。该模型还纳入了潜伏期受感染个体的存活概率，从而更清楚地了解潜伏期如何影响控制繁殖数 Rc。此外，通过使用李亚普诺夫函数方法，我们建立了与 Rc 有关的均衡的全局渐进稳定性。结果表明，当且仅当 Rc≤1 时，无病平衡 T0 是全局渐近稳定的，而当且仅当 Rc>1 时，流行平衡 T∗ 是全局渐近稳定的。

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引用次数: 0

On the mass concentration of normalized ground state solutions for non-autonomous Kirchhoff equations 论非自治基尔霍夫方程归一化基态解的质量浓度

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters

Pub Date : 2024-11-06 DOI: 10.1016/j.aml.2024.109371

Miao Du , Xiaohan Gao

In this paper, we focus on a class of non-autonomous Kirchhoff equations, that is,

- (a + b \int_{R^{3}} {| \nabla u |}^{2} d x) Δ u - λ u = K (x) {| u |}^{p - 2} u

R^{3}

, where

a, b > 0

are constants,

λ \in R

is unknown and appears as a Lagrange multiplier,

2 < p < 6

and

K : R^{3} \to R

is a potential function. Under certain assumptions on the potential

K

, the concentration behavior of normalized ground state solutions is analyzed by using variational methods.

本文主要研究一类非自治基尔霍夫方程，即 R3 中的-(a+b∫R3|∇u|2dx)Δu-λu=K(x)|u|p-2u，其中 a、b>0 为常数，λ∈R 为未知数并作为拉格朗日乘数出现，2<p<6，K:R3→R 为势函数。在电势 K 的某些假设条件下，利用变分法分析了归一化基态解的浓度行为。

引用次数: 0

Self-interacting CBO: Existence, uniqueness, and long-time convergence 自我互动的 CBO：存在性、唯一性和长期趋同性

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters

Pub Date : 2024-11-06 DOI: 10.1016/j.aml.2024.109372

Hui Huang, Hicham Kouhkouh

A self-interacting dynamics that mimics the standard Consensus-Based Optimization (CBO) model is introduced. This single-particle dynamics is shown to converge to a unique invariant measure that approximates the global minimum of a given function. As an application, its connection to CBO with Personal Best introduced by C. Totzeck and M.-T. Wolfram (Math. Biosci. Eng., 2020) has been established.

本文介绍了一种模仿标准共识优化（CBO）模型的自相互作用动力学。研究表明，这种单粒子动力学会收敛到一个独特的不变度量，该度量近似于给定函数的全局最小值。作为应用，C. Totzeck 和 M.-T. Wolfram 介绍了它与 CBO 与 Personal Best 的联系（Math.Wolfram (Math. Biosci. Eng., 2020)提出的CBO与Personal Best的联系。

引用次数: 0

Absence of dead-core formations in chemotaxis systems with degenerate diffusion 具有退化扩散作用的趋化系统中不存在死核现象

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters

Pub Date : 2024-11-06 DOI: 10.1016/j.aml.2024.109361

Tobias Black

<div><div>In this paper we consider a chemotaxis system with signal consumption and degenerate diffusion of the form <math><mfenced><mrow><mtable><mtr><mtd></mtd><mtd><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><mo>∇</mo><mi>⋅</mi><mrow><mo>(</mo><mi>D</mi><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow><mo>∇</mo><mi>u</mi><mo>−</mo><mi>u</mi><mi>S</mi><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow><mo>∇</mo><mi>v</mi><mo>)</mo></mrow><mo>+</mo><mi>f</mi><mrow><mo>(</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>)</mo></mrow><mo>,</mo><mspace></mspace></mtd></mtr><mtr><mtd></mtd><mtd><msub><mrow><mi>v</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><mi>Δ</mi><mi>v</mi><mo>−</mo><mi>u</mi><mi>v</mi><mo>,</mo><mspace></mspace></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mfenced></math>in a bounded domain <math><mrow><mi>Ω</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></mrow></math> with smooth boundary subjected to no-flux and homogeneous Neumann boundary conditions. Herein, the diffusion coefficient <math><mrow><mi>D</mi><mo>∈</mo><msup><mrow><mi>C</mi></mrow><mrow><mn>0</mn></mrow></msup><mrow><mo>(</mo><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mi>∞</mi><mo>)</mo></mrow><mo>)</mo></mrow><mo>∩</mo><msup><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mi>∞</mi><mo>)</mo></mrow><mo>)</mo></mrow></mrow></math> is assumed to satisfy <math><mrow><mi>D</mi><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow><mo>=</mo><mn>0</mn></mrow></math>, <math><mrow><mi>D</mi><mrow><mo>(</mo><mi>s</mi><mo>)</mo></mrow><mo>></mo><mn>0</mn></mrow></math> on <math><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mi>∞</mi><mo>)</mo></mrow></math>, <math><mrow><msup><mrow><mi>D</mi></mrow><mrow><mo>′</mo></mrow></msup><mrow><mo>(</mo><mi>s</mi><mo>)</mo></mrow><mo>≥</mo><mn>0</mn></mrow></math> on <math><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mi>∞</mi><mo>)</mo></mrow></math> and that there are <math><mrow><msub><mrow><mi>s</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>></mo><mn>0</mn></mrow></math>, <math><mrow><mi>p</mi><mo>></mo><mn>1</mn></mrow></math> and <math><mrow><msub><mrow><mi>C</mi></mrow><mrow><mi>D</mi></mrow></msub><mo>></mo><mn>0</mn></mrow></math> such that <math><mrow><mi>s</mi><msup><mrow><mi>D</mi></mrow><mrow><mo>′</mo></mrow></msup><mrow><mo>(</mo><mi>s</mi><mo>)</mo></mrow><mo>≤</mo><msub><mrow><mi>C</mi></mrow><mrow><mi>D</mi></mrow></msub><mi>D</mi><mrow><mo>(</mo><mi>s</mi><mo>)</mo></mrow><mspace></mspace><mtext>and</mtext><mspace></mspace><msub><mrow><mi>C</mi></mrow><mrow><mi>D</mi></mrow></msub><msup><mrow><mi>s</mi></mrow><mrow><mi>p</mi><mo>−</mo><mn>1</mn></mrow></msup><mo>≤</mo><mi>D</mi><mrow><mo>(</mo><mi>s</mi><mo>)</mo></mrow><mspace></mspace><mtext>for</mtext><mi>s<

本文考虑了一个具有信号消耗和退化扩散的趋化系统，其形式为 ut=∇-(D(u)∇u-uS(u)∇v)+f(u,v),vt=Δv-uv，该系统在一个边界光滑的有界域 Ω⊂RN中，受无流体和同质新曼边界条件的约束。这里，假设扩散系数 D∈C0([0,∞))∩C2((0,∞)) 满足 D(0)=0, D(s)>；0 on (0,∞), D′(s)≥0 on (0,∞) and that there are s0>0, p>1 and CD>0 such that sD′(s)≤CDD(s)andCDsp-1≤D(s)fors∈[0,s0].灵敏度函数 S∈C2([0,∞)) 和源项 f∈C1([0,∞)×[0,∞)) 假定为非负。我们证明，对于所有满足 u0≥δ0>0 和 v0⁄≡0 的适当规则初始数据（u0,v0），都存在一个时域经典解，并且--尽管在 0 处存在退行性--该解满足一个扩展性准则，其形式为：Tmax=∞，或 Lim suptTmax‖u(⋅,t)‖L∞(Ω)=∞ 。此外，作为分析的一个副产品，我们证明了在Ω×(0,T)上的经典解在所有 t∈(0,T)条件下服从‖u(⋅,t)‖L∞(Ω)≤Mu，并且从上述初始数据 (u0,v0) 出发，在整个Ω×(0,T)上保持严格的正解性，也就是说，可以找到δu=δu(Ω)=∞。结果表明，在这些具有退化扩散的趋化系统中，在炸毁时间之前不可能形成死核。

引用次数: 0

Peaked Stokes waves as solutions of Babenko’s equation 作为巴边科方程解的峰值斯托克斯波

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters

Pub Date : 2024-11-04 DOI: 10.1016/j.aml.2024.109359

Spencer Locke, Dmitry E. Pelinovsky

Babenko’s equation describes traveling water waves in holomorphic coordinates. It has been used in the past to obtain properties of Stokes waves with smooth profiles analytically and numerically. We show in the deep-water limit that properties of Stokes waves with peaked profiles can also be recovered from the same Babenko’s equation. In order to develop the local analysis of singularities, we rewrite Babenko’s equation as a fixed-point problem near the maximal elevation level. As a by-product, our results rule out a corner point singularity in the holomorphic coordinates, which has been obtained in a local version of Babenko’s equation.

巴边科方程描述了全形坐标中的水波。过去，人们曾用它来分析和数值求得具有平滑剖面的斯托克斯波的特性。我们在深水极限中证明，具有峰状剖面的斯托克斯波的特性也可以从相同的巴本科方程中得到。为了对奇点进行局部分析，我们将 Babenko 方程重写为最大海拔附近的定点问题。作为副产品，我们的结果排除了全形坐标中的角点奇异性，而该奇异性是在巴本科方程的局部版本中得到的。

引用次数: 0

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