Applied Mathematics Letters最新文献

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On the oscillation of second-order functional differential equations with a delayed damping term

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters

Pub Date : 2025-01-17 DOI: 10.1016/j.aml.2025.109464

Osama Moaaz , Higinio Ramos

In this work, we derive some criteria for studying the asymptotic and oscillatory behavior of solutions of functional differential equations with a delayed damping term. Our results extend and improve upon the limited prior research on this type of equations. The primary goal is to derive criteria applicable to both ordinary and non-damped cases, while accounting for the effects of delay functions. Additionally, unlike previous studies, we provide criteria that ensure the oscillation of all solutions. The significance of these results is illustrated through remarks and examples.

在这项工作中，我们推导出了一些标准，用于研究带有延迟阻尼项的函数微分方程解的渐近和振荡行为。我们的结果扩展并改进了之前对这类方程的有限研究。我们的主要目标是推导出适用于普通和非阻尼情况的标准，同时考虑延迟函数的影响。此外，与之前的研究不同，我们提供的标准能确保所有解的振荡。我们将通过注释和示例来说明这些结果的意义。

引用次数: 0

Leighton–Wintner-type oscillation theorem for the discrete p(k)-Laplacian 离散[公式省略]-拉普拉斯方程的leighton - wintner型振荡定理

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters

Pub Date : 2025-01-16 DOI: 10.1016/j.aml.2025.109465

Kōdai Fujimoto , Kazuki Ishibashi , Masakazu Onitsuka

This paper addresses oscillation problems for difference equations with a discrete

p (k)

-Laplacian. In general, applying the Riccati technique to discrete oscillations is difficult. However, this study established a Leighton–Wintner-type oscillation theorem using the Riccati technique. Three examples are provided to illustrate the results. In particular, we examined the oscillatory problem for a certain nonlinear difference equation, including the Harper model, and demonstrated that the solutions are oscillatory even when

p (k)

diverges to infinity.

本文探讨了具有离散 p(k)-Laplacian 的差分方程的振荡问题。一般来说，将里卡提技术应用于离散振荡是很困难的。然而，本研究利用 Riccati 技术建立了 Leighton-Wintner 型振荡定理。我们提供了三个例子来说明结果。其中，我们研究了包括 Harper 模型在内的某个非线性差分方程的振荡问题，并证明了即使 p(k) 发散到无穷大，解也是振荡的。

引用次数: 0

On the relation between the exponential of real matrices and that of dual matrices 实矩阵指数与对偶矩阵指数的关系

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters

Pub Date : 2025-01-16 DOI: 10.1016/j.aml.2025.109466

Chengdong Liu , Yimin Wei , Pengpeng Xie

Dual number matrices play a significant role in engineering applications such as kinematics and dynamics. The matrix exponential is ubiquitous in screw-based kinematics. In this paper, we develop an explicit formula for the dual matrix exponential. The result is closely related to the Fréchet derivative, which can be formed by the standard part and dual part of the original matrix. We only need to compute the exponential of a real matrix. Then, we give a formula of computing the dual quaternion matrix exponential. Our results are illustrated through a practical example from robotic kinematics.

双数矩阵在运动学和动力学等工程应用中发挥着重要作用。矩阵指数在基于螺杆的运动学中无处不在。在本文中，我们为对偶矩阵指数建立了一个明确的公式。其结果与弗雷谢特导数密切相关，后者可由原始矩阵的标准部分和对偶部分构成。我们只需计算实矩阵的指数。然后，我们给出了计算对偶四元数矩阵指数的公式。我们将通过一个机器人运动学的实际例子来说明我们的结果。

引用次数: 0

Geometric programming for multilinear systems with nonsingular M-tensors 具有非奇异张量的多线性系统的几何规划

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters

Pub Date : 2025-01-15 DOI: 10.1016/j.aml.2025.109462

Haibin Chen , Guanglu Zhou , Hong Yan

We consider multilinear systems which arise in various applications, such as data mining and numerical differential equations. In this paper, we show that the multilinear system with a nonsingular

M

-tensor can be formulated equivalently into a geometric programming (GP) problem which can be solved by the barrier-based interior point method with a worst-case polynomial-time complexity. To the best of our knowledge, there is not a complexity analysis for the existing algorithms of the multilinear systems. Numerical results are reported to show the efficiency of the proposed GP method.

我们考虑了在数据挖掘和数值微分方程等各种应用中出现的多线性系统。在本文中，我们展示了具有非正弦 M 张量的多线性系统可以等价地表述为一个几何程序设计（GP）问题，该问题可以通过基于障碍的内点法求解，并具有最坏情况下的多项式时间复杂度。据我们所知，现有的多线性系统算法还没有复杂度分析。报告的数值结果表明了所提出的 GP 方法的效率。

引用次数: 0

Optimal decay rate to the contact discontinuity for Navier–Stokes equations under generic perturbations 一般摄动下Navier-Stokes方程接触不连续的最优衰减率

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters

Pub Date : 2025-01-14 DOI: 10.1016/j.aml.2025.109461

Lingjun Liu , Guiqin Qiu , Shu Wang , Lingda Xu

This paper investigates the large-time asymptotic behavior of contact waves in 1-D compressible Navier–Stokes equations. We derive the optimal decay rate for generic initial perturbations, meaning the perturbation’s integral does not need to be zero. It is well-known that generic perturbations in Navier–Stokes equations generate diffusion waves, implying that the optimal decay rate for contact waves in the

L^{\infty}

-norm is

{(1 + t)}^{- 1 / 2}

. However, the presence of diffusion waves introduces error terms, leading to energy growth in the anti-derivatives of the perturbations. Furthermore, studying contact waves depends on certain structural conditions, which hold for the original system but not for its derivative systems. This makes it challenging to obtain accurate estimates for the energy of the derivatives.

In this paper, we refine the estimates for both anti-derivatives and the original perturbations. We then introduce an innovative transformation to ensure that the structural conditions continue to hold for the system of derivatives. With this approach, we achieve better estimates for the derivatives, leading to the optimal decay rates. This result improves upon the well-known findings of Huang et al. (2008), and the method has the potential for application in more general systems.

本文研究了一维可压缩纳维-斯托克斯方程中接触波的大时间渐近行为。我们推导了一般初始扰动的最佳衰减率，这意味着扰动的积分不一定为零。众所周知，纳维-斯托克斯方程中的一般扰动会产生扩散波，这意味着L∞正态下接触波的最佳衰减率为(1+t)-1/2。然而，扩散波的存在引入了误差项，导致扰动的反衍生物能量增长。此外，研究接触波取决于某些结构条件，这些条件对原始系统成立，但对其导数系统却不成立。这就使得获得导数能量的精确估计具有挑战性。

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引用次数: 0

Stability analysis of a conservative reaction–diffusion system with rate controls 具有速率控制的保守反应扩散系统的稳定性分析

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters

Pub Date : 2025-01-14 DOI: 10.1016/j.aml.2025.109457

Jie Ding , Fei Xu , Zhi Ling

This paper demonstrates the fundamental properties of a conservative reaction–diffusion system. The solution of the system exists globally and is unique, as well as uniformly converges to its constant equilibrium as time tends to infinity. In addition, the steady-state system only has a constant solution under a mass conservation condition.

本文证明了一类保守反应扩散系统的基本性质。系统的解全局存在且唯一，并在时间趋于无穷时一致收敛于其常平衡态。此外，稳态系统只有在质量守恒条件下才有常数解。

引用次数: 0

Energy-equidistributed moving mesh strategies for simulating Hamiltonian partial differential equations 模拟哈密顿偏微分方程的能量等分布移动网格策略

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters

Pub Date : 2025-01-13 DOI: 10.1016/j.aml.2025.109460

Qinjiao Gao , Zhengjie Sun , Zongmin Wu

This paper presents an innovative energy-equidistributed moving mesh strategy for simulating Hamiltonian partial differential equations (PDEs) characterized by solitons and rapid temporal variations. A novel framework, named the Energy Equidistribution Principles (EEPs), is introduced, highlighting the critical role of energy conservation in achieving accurate simulations. Building on EEPs, three kinds of energy-equidistributed moving mesh PDEs (EMMPDEs) are proposed, each grounded in different methodologies. These strategies are rigorously examined in terms of their convergence conditions and rates. Both theoretical analysis and numerical experiments demonstrate that the proposed EMMPDEs offer superior robustness and effectiveness in long-term simulations, compared to traditional arc-length-equidistributed MMPDEs.

本文提出了一种新颖的能量等分布移动网格策略，用于模拟以孤子和快速时间变化为特征的哈密顿偏微分方程。介绍了一种新的框架，称为能量均分原则（EEPs），强调了节能在实现精确模拟中的关键作用。在此基础上，提出了三种能量等分布移动网格偏微分方程（EMMPDEs），每一种基于不同的方法。这些策略在其收敛条件和速率方面进行了严格的检查。理论分析和数值实验都表明，与传统的弧长等分布MMPDEs相比，所提出的EMMPDEs在长期模拟中具有更好的鲁棒性和有效性。

引用次数: 0

W2,δ estimates for fully nonlinear parabolic inequalities on C1,α domains [公式省略]域上完全非线性抛物不等式的估计

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters

Pub Date : 2025-01-13 DOI: 10.1016/j.aml.2025.109459

Xuemei Li

In this paper, we study boundary

W^{2, δ}

estimates for solution sets of fully nonlinear parabolic inequalities

u_{t} - M^{+} (D^{2} u, λ, Λ) \leq f (x, t) \leq u_{t} - M^{-} (D^{2} u, λ, Λ)

C^{1, α}

domains, which generalize results for elliptic equations in Li and Li (2023).

本文研究了全非线性抛物不等式 ut-M+(D2u,λ,Λ)≤f(x,t)≤ut-M-(D2u,λ,Λ) 在 C1,α 域上的解集的边界 W2,δ 估计，它概括了 Li 和 Li (2023) 中关于椭圆方程的结果。

引用次数: 0

A novel time-domain SCT-BEM for transient heat conduction analysis 一种用于瞬态热传导分析的新型时域SCT-BEM

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters

Pub Date : 2025-01-11 DOI: 10.1016/j.aml.2025.109463

Xiaotong Gao , Yan Gu , Bo Yu

Accurate and efficient treatment of domain integrals is critical for obtaining reliable and precise boundary element method (BEM) solutions in dynamic or time-dependent problems. Despite the success of existing techniques for handling domain integrals, significant challenges still remain, especially in time-dependent BEM analyses where time-dependent fundamental solutions often result in integrands with oscillations or near-singularities, particularly when small time steps are used. To address these issues, this study introduces an improved scaled coordinate transformation BEM (SCT-BEM), combined with a non-linear coordinate transformation, to enhance the robustness of domain integral evaluations in transient time-domain BEM. The proposed method is straightforward to implement, requiring minimal modifications to existing BEM frameworks, and significantly improves both the robustness and accuracy of domain integral evaluations in transient time-domain BEM.

要在动态或时间相关问题中获得可靠而精确的边界元法（BEM）解，准确而高效地处理域积分至关重要。尽管现有的域积分处理技术取得了成功，但仍然存在重大挑战，特别是在时变 BEM 分析中，时变基本解往往会导致积分出现振荡或接近奇异值，尤其是在使用小时间步长时。为解决这些问题，本研究引入了改进的比例坐标变换 BEM（SCT-BEM），并结合非线性坐标变换，以增强瞬态时域 BEM 中域积分评估的鲁棒性。所提出的方法简单易行，只需对现有的 BEM 框架进行最小限度的修改，就能显著提高瞬态时域 BEM 中域积分评估的稳健性和准确性。

引用次数: 0

Propagation direction of traveling waves for a class of nonlocal dispersal bistable epidemic models 一类非局部扩散双稳态流行病模型的行波传播方向

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters

Pub Date : 2025-01-11 DOI: 10.1016/j.aml.2025.109458

Yu-Xia Hao, Guo-Bao Zhang

This work is devoted to studying the propagation direction of the following nonlocal dispersal epidemic model (0.1)

(\begin{matrix} \frac{\partial u}{\partial t} & = d_{1} (\int_{R} J (y - x) u (y, t) d y - u) - u + α v, & x \in R, t > 0, \\ \frac{\partial v}{\partial t} & = d_{2} (\int_{R} J (y - x) v (y, t) d y - v) - β v + g (u), & x \in R, t > 0, \end{matrix})

where

d_{1}, d_{2}, α, β > 0

. By discussing the case

c = 0

and using the monotone dependence of the wave speed of traveling wave solutions on parameters, we state the sufficient conditions for the speed

c > 0

and

c < 0

under some calculations and analysis. Compared to the known works for classical diffusive epidemic models, we have to overcome difficulties due to the appearance of nonlocal dispersal operators in the current paper.

这项工作致力于研究以下非局部扩散流行病模型的传播方向（0.1)∂u∂t=d1∫RJ(y-x)u(y,t)dy-u-u+αv,x∈R,t>0,∂v∂t=d2∫RJ(y-x)v(y,t)dy-v-βv+g(u),x∈R,t>0,其中d1,d2,α,β>0。通过讨论 c=0 的情况，并利用行波解的波速对参数的单调依赖性，在一定的计算和分析下，阐述了速度 c>0 和 c<0 的充分条件。与经典扩散流行病模型的已知工作相比，本文必须克服由于非局部分散算子的出现所带来的困难。

引用次数: 0

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