Studies in Applied Mathematics最新文献

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Nonlinear Systems of PDEs Admitting Infinite-Dimensional Lie Algebras and Their Connection With Ricci Flows. II: The Two-Dimensional Space Case 含无限维李代数的偏微分方程非线性系统及其与Ricci流的关系。二：二维空间案例

IF 2.3 2区数学 Q1 MATHEMATICS, APPLIED

Studies in Applied Mathematics

Pub Date : 2025-10-03 DOI: 10.1111/sapm.70120

Roman Cherniha, John R. King

Motivated by previous results in special cases associated with Ricci flows, all possible two-components evolutions systems of (1+2)-dimensional second-order partial differential equations (PDEs) admitting an infinite-dimensional Lie algebra are constructed. It is shown that a natural generalization of this Lie algebra to the higher-dimensional case does not lead to a more general result because the infinite-dimensional symmetry is broken. The recently derived system, which is related to Ricci flows, is identified as a very particular case among the evolution systems obtained. All possible radially symmetric stationary solutions of the Ricci-flow-associated special case are then constructed using the surprisingly rich Lie algebra of the resulting reduced system of ordinary differential equations (ODEs), exemplifying the exceptional status of such systems. Moreover, it is proved that this Lie algebra is reducible to the fifteen-dimensional algebra of the simplest system of two second-order ODEs. Several time-dependent exact solutions in the radially symmetric case are constructed as well. It is shown that the solutions obtained are bounded and smooth provided arbitrary parameters are correctly specified. By their nature, geometric PDEs typically enjoy rich symmetry properties; our analysis illustrates how those properties may be extrapolated to broader classes of models that are of independent interest.

在前人关于Ricci流的研究结果的启发下，构造了所有允许无限维李代数的（1+2）维二阶偏微分方程（PDEs）的双分量演化系统。结果表明，将该李代数自然推广到高维情况并不能得到更一般的结果，因为无限维对称性被打破了。最近导出的与里奇流有关的系统被认为是所得到的演化系统中的一个非常特殊的例子。然后利用所得到的常微分方程简化系统（ode）的惊人丰富的李代数构造了里奇流相关特殊情况的所有可能的径向对称稳态解，举例说明了此类系统的特殊地位。并且证明了该李代数可约为最简单的两个二阶ode系统的十五维代数。在径向对称情况下，构造了几个随时间变化的精确解。结果表明，在正确指定任意参数的情况下，得到的解是有界的、光滑的。就其性质而言，几何偏微分方程通常具有丰富的对称性；我们的分析说明了如何将这些特性外推到更广泛的模型类别中，这些模型具有独立的兴趣。

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引用次数: 0

Spatiotemporal Dynamics of a Delayed Diffusive Single-Species Model in Closed Advective Environments 封闭平流环境中延迟扩散单物种模型的时空动力学

IF 2.3 2区数学 Q1 MATHEMATICS, APPLIED

Studies in Applied Mathematics

Pub Date : 2025-10-01 DOI: 10.1111/sapm.70122

Shixia Xin, Hongying Shu, Hua Nie

We investigate the spatiotemporal dynamics of a single-species diffusive model incorporating maturation delay in closed advective heterogeneous environments. First, we establish the well-posedness of the system and prove the existence and uniqueness of the nonconstant positive steady state. Subsequently, we analyze the local stability of the unique nonconstant positive steady state and demonstrate the occurrence of Hopf bifurcation through the corresponding eigenvalue problem. By utilizing a weighted inner product parameterized by the advection rate, we further characterize the stability and direction of the Hopf bifurcation. Finally, we examine how advection rate and spatial length influence the first Hopf bifurcation value, revealing their effects on system dynamics. Our results demonstrate that both advection and spatial scale can either enhance or suppress the likelihood of Hopf bifurcation, depending on the spatial heterogeneity of the intrinsic growth rate.

我们研究了封闭平流异质环境中包含成熟延迟的单物种扩散模型的时空动力学。首先，我们建立了系统的适定性，证明了非常正稳态的存在唯一性。随后，我们分析了唯一非常正稳态的局部稳定性，并通过相应的特征值问题证明了Hopf分岔的存在。利用平流率参数化的加权内积，进一步刻画了Hopf分岔的稳定性和方向。最后，我们研究了平流速率和空间长度对第一Hopf分岔值的影响，揭示了它们对系统动力学的影响。我们的研究结果表明，平流和空间尺度可以增强或抑制Hopf分岔的可能性，这取决于内在增长率的空间异质性。

引用次数: 0

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IF 2.3 2区数学 Q1 MATHEMATICS, APPLIED

Studies in Applied Mathematics

Pub Date : 2025-10-01 DOI: 10.1111/sapm.70124

引用次数: 0

Microstructure-Induced Finite-Speed Heat Propagation in Fluids Through Porous Media: Analytical Results 微观结构诱导的流体通过多孔介质的有限速度热传播：分析结果

IF 2.3 2区数学 Q1 MATHEMATICS, APPLIED

Studies in Applied Mathematics

Pub Date : 2025-10-01 DOI: 10.1111/sapm.70118

Luca Bisconti, Paolo Maria Mariano

In nonisothermal setting, microstructural interactions may determine finite-speed heat propagation. We consider such an effect in the dynamics of a viscous incompressible complex fluid (i.e., one with “active” microstructure) through a porous medium. Nonlocal actions and nonlinear damping are considered as determined by the solid–fluid and microstructural interactions. After a choice of constitutive structures and the introduction of a specific truncation of some higher-order terms, we prove existence and uniqueness of global strong solutions to the balance equations. We also analyze pertinent weak solutions.

在非等温环境下，微观结构的相互作用可能决定有限速度的热传播。我们在粘性不可压缩复杂流体（即具有“活性”微观结构的流体）通过多孔介质的动力学中考虑了这种效应。非局部作用和非线性阻尼被认为是由固体-流体和微观结构相互作用决定的。通过本构结构的选择和引入一些高阶项的特定截断，证明了平衡方程整体强解的存在唯一性。并分析了相应的弱解。

引用次数: 0

Multidimensional Stability of Planar Traveling Waves for Stochastically Perturbed Reaction–Diffusion Systems 随机摄动反应扩散系统平面行波的多维稳定性

IF 2.3 2区数学 Q1 MATHEMATICS, APPLIED

Studies in Applied Mathematics

Pub Date : 2025-09-26 DOI: 10.1111/sapm.70114

M. van den Bosch, H. J. Hupkes

We consider reaction–diffusion systems with multiplicative noise on a spatial domain of dimension two or higher. The noise process is white in time, colored in space, and invariant under translations. Inspired by previous works on the real line, we establish the multidimensional stability of planar waves on a cylindrical domain on timescales that are exponentially long with respect to the noise strength. This is achieved by means of a stochastic phase-tracking mechanism that can be maintained over such long timescales. The corresponding mild formulation of our problem features stochastic integrals with respect to anticipating integrands, which hence cannot be understood within the well-established setting of Itô-integrals. To circumvent this problem, we exploit and extend recently developed theory concerning forward integrals.

我们考虑在二维或更高维度的空间域上具有乘性噪声的反应扩散系统。噪声过程在时间上是白色的，在空间上是彩色的，在平移下是不变的。受前人实线研究的启发，我们在相对于噪声强度呈指数长的时间尺度上建立了柱面域上平面波的多维稳定性。这是通过一种随机相位跟踪机制来实现的，这种机制可以在如此长的时间尺度上保持不变。我们的问题的相应温和的公式具有相对于预期积分的随机积分，因此不能在Itô-integrals的既定设置中理解。为了避免这个问题，我们利用和推广了最近发展起来的关于正积分的理论。

引用次数: 0

A Mathematical Model for Neuron Reorientation and Axonal Growth on a Cyclically Stretched Substrate 循环拉伸基底上神经元重定向和轴突生长的数学模型

IF 2.3 2区数学 Q1 MATHEMATICS, APPLIED

Studies in Applied Mathematics

Pub Date : 2025-09-23 DOI: 10.1111/sapm.70103

Annachiara Colombi, Andrea Battaglia, Chiara Giverso

Experiments have shown that mechanical cues play a central role in determining the direction and rate of axonal growth. In particular, neurons seeded on planar substrates undergoing periodic stretching have been shown to reorient and reach a stable equilibrium orientation corresponding to angles within the interval $� � (� �^{60 � \circ �} �, � �^{90 � \circ �} �) � �$ with respect to the main stretching direction. In this work, we present a new model that considers both the reorientation and growth of neurons in response to cyclic stretching. Specifically, a linear viscoelastic model for the growth cone reorientation with the addition of a stochastic term is merged with a moving-boundary model for tubulin-driven neurite growth to simulate the axonal pathfinding process. Various combinations of stretching frequencies and strain amplitudes have been tested by numerical simulation of the proposed model. The simulations show that neurons tend to reorient toward an equilibrium angle that falls in the experimentally observed range. Moreover, the model captures the relation between the stretching condition and the speed of reorientation. Indeed, numerical results show that neurons tend to reorient faster as the frequency and amplitude of oscillation increase.

实验表明，机械线索在决定轴突生长的方向和速度方面起着核心作用。特别是，在平面基底上播撒的神经元经过周期性拉伸后，可以重新定向，并在60°范围内达到稳定的平衡方向。90°$左[60^{circ}，90^{circ}右]$相对于主要拉伸方向。在这项工作中，我们提出了一个新的模型，该模型考虑了神经元在响应循环拉伸时的重新定向和生长。具体地说，将生长锥重定向的线性粘弹性模型与小管蛋白驱动的神经突生长的移动边界模型相结合，模拟轴突寻径过程。对所提出的模型进行了数值模拟，测试了拉伸频率和应变幅值的各种组合。模拟结果表明，神经元倾向于重新定向到一个在实验观察范围内的平衡角度。此外，该模型还捕获了拉伸条件与重定向速度之间的关系。事实上，数值结果表明，随着振荡频率和振幅的增加，神经元倾向于更快地重新定向。

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引用次数: 0

Exact Periodic Solutions of the Generalized Constantin–Lax–Majda Equation With Dissipation 具有耗散的广义Constantin-Lax-Majda方程的精确周期解

IF 2.3 2区数学 Q1 MATHEMATICS, APPLIED

Studies in Applied Mathematics

Pub Date : 2025-09-19 DOI: 10.1111/sapm.70115

Denis A. Silantyev, Pavel M. Lushnikov, Michael Siegel, David M. Ambrose

<div> We present exact pole dynamics solutions to the generalized Constantin–Lax–Majda (gCLM) equation in a periodic geometry with dissipation <math> <semantics> <mrow> <mo>−</mo> <msup> <mi>Λ</mi> <mi>σ</mi> </msup> </mrow> <annotation>$-Lambda ^sigma$</annotation> </semantics></math>, where its spatial Fourier transform is <math> <semantics> <mrow> <mover> <msup> <mi>Λ</mi> <mi>σ</mi> </msup> <mo>̂</mo> </mover> <mo>=</mo> <msup> <mrow> <mo>|</mo> <mi>k</mi> <mo>|</mo> </mrow> <mi>σ</mi> </msup> </mrow> <annotation>$widehat{Lambda ^sigma }=|k|^sigma$</annotation> </semantics></math>. The gCLM equation is a simplified model for singularity formation in the 3D incompressible Euler equations. It includes an advection term with parameter <math> <semantics> <mi>a</mi> <annotation>$a$</annotation> </semantics></math>, which allows different relative weights for advection and vortex stretching. There has been intense interest in the gCLM equation, and it has served as a proving ground for the development of methods to study singularity formation in the 3D Euler equations. Several exact solutions for the problem on the real line have been previously found by the method of pole dynamics, but only one such solution has been reported for the periodic geometry. We derive new periodic solutions for <math> <semantics> <mrow> <mi>a</mi> <mo>=</mo> <mn>0</mn> </mrow> <annotation>$a=0$</annotation> </semantics></math> and <math> <semantics> <mrow> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> <annotation>$1/2$</annotation> </semantics></math> and <math> <semantics> <mrow> <mi>σ</mi> <mo>=</mo> <mn>0</mn> </mrow> <annotation>$sigma =0$</annotation> </semantics></math> and 1, for which a closed collection of (periodically repeated) poles evolve in the complex plane. Self-similar finite-time blowup of the solutions is analyzed and compared for the different values of <math>

本文给出了具有耗散−Λ σ $-Lambda ^sigma$的周期几何广义Constantin-Lax-Majda （gCLM）方程的精确极点动力学解。它的空间傅里叶变换是Λ σ σ = | k | σ $widehat{Lambda ^sigma }=|k|^sigma$。gCLM方程是三维不可压缩欧拉方程中奇点形成的简化模型。它包括一个参数为a $a$的平流项，它允许平流和涡旋拉伸的相对权重不同。人们对gCLM方程有着浓厚的兴趣，它已经成为研究三维欧拉方程中奇点形成方法的试验场。以前用极动力学方法已经找到了实线上问题的几个精确解，但周期几何只有一个这样的解。我们得到了a = 0 $a=0$和1 / 2 $1/2$和σ = 0 $sigma =0$和1的新的周期解，在复平面上有一个（周期性重复的）极点的闭合集合。对不同σ $sigma$值下解的自相似有限时间爆破进行了分析和比较，并与作者先前的一篇论文中关于小数据解的全局时间适定性理论进行了比较。在精确解的激励下，将适定性理论推广到a = 0 $a=0$, σ≥0 $sigma ge 0$的情况。讨论了解决方案的几个有趣的特性。

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引用次数: 0

The Korteweg-de Vries Equation With an Interface 具有界面的Korteweg-de Vries方程

IF 2.3 2区数学 Q1 MATHEMATICS, APPLIED

Studies in Applied Mathematics

Pub Date : 2025-09-17 DOI: 10.1111/sapm.70117

Hsin-Yuan Huang, Cheng-Pu Lin

In this paper, we consider the Korteweg–de Vries (KdV) equation on the real line with an interface. Using Fokas's unified transform method, the explicit solution formulas for the linear forced KdV equation with an interface are derived. Building on these solution formulas, we establish standard estimates for the linear solution and a bilinear estimate for the nonlinear term in a suitable Sobolev space. Using these estimates and a contraction mapping argument, we prove the local well-posedness for the KdV equation with an interface.

本文考虑带界面实线上的Korteweg-de Vries （KdV）方程。利用Fokas的统一变换方法，导出了带界面的线性强迫KdV方程的显式解公式。在这些解公式的基础上，我们建立了适当Sobolev空间中线性解的标准估计和非线性项的双线性估计。利用这些估计和一个收缩映射论证，我们证明了具有界面的KdV方程的局部适定性。

引用次数: 0

Integrable Boundary Conditions for the Nonlinear Schrödinger Hierarchy Via the Fokas Method 基于Fokas方法的非线性Schrödinger层次的可积边界条件

IF 2.3 2区数学 Q1 MATHEMATICS, APPLIED

Studies in Applied Mathematics

Pub Date : 2025-09-16 DOI: 10.1111/sapm.70116

Baoqiang Xia

We study integrable boundary conditions for the whole hierarchy of nonlinear Schrödinger (NLS) equations defined on the half-line. We find that the even-order and odd-order NLS equations admit rather different integrable boundary conditions. In particular, the odd-order NLS equations admit a new class of integrable boundary conditions that involves time reversal. We establish the integrability of the NLS hierarchy with our new boundary conditions by demonstrating the existence of infinitely many integrals of motion in involution. Moreover, we develop the boundary dressing technique to construct soliton solutions satisfying these new boundary conditions.

研究了半线上定义的非线性Schrödinger （NLS）方程全层次的可积边界条件。我们发现偶阶和奇阶NLS方程具有不同的可积边界条件。特别地，奇阶NLS方程承认了一类新的涉及时间反转的可积边界条件。通过证明无穷多个运动积分的对合性，用新的边界条件建立了NLS层次的可积性。此外，我们还发展了边界修饰技术来构造满足这些新边界条件的孤子解。

引用次数: 0

Surprising Symmetry Properties and Exact Solutions of Kolmogorov Backward Equations With Power Diffusivity 具有幂扩散系数的Kolmogorov倒向方程的惊人对称性和精确解

IF 2.3 2区数学 Q1 MATHEMATICS, APPLIED

Studies in Applied Mathematics

Pub Date : 2025-09-15 DOI: 10.1111/sapm.70105

Serhii D. Koval, Elsa Dos Santos Cardoso-Bihlo, Roman O. Popovych

Using the original advanced version of the direct method, we efficiently compute the equivalence groupoids and equivalence groups of two peculiar classes of Kolmogorov backward equations with power diffusivity and solve the problems of their complete group classifications. The results on the equivalence groups are double-checked with the algebraic method. Within these classes, the remarkable Fokker–Planck and the fine Kolmogorov backward equations are distinguished by their exceptional symmetry properties. We extend the known results on these two equations to their counterparts with respect to a nontrivial discrete equivalence transformation. Additionally, we carry out Lie reductions of the equations under consideration up to the point equivalence, exhaustively study their hidden Lie symmetries, and generate wider families of their new exact solutions via acting by their recursion operators on constructed Lie-invariant solutions. This analysis reveals eight powers of the space variable with exponents $� � � - � 1 � � �$ , 0, 1, 2, 3, 4, 5, and 6 as values of the diffusion coefficient that are prominent due to symmetry properties of the corresponding equations.

利用直接法的原始高级版本，我们有效地计算了两类特殊的幂扩散Kolmogorov后向方程的等价群和等价群，并解决了它们的完全群分类问题。用代数方法对等价群上的结果进行了复核。在这些类别中，引人注目的福克-普朗克方程和精细的柯尔莫哥洛夫后向方程以其特殊的对称性而闻名。我们将这两个方程的已知结果推广到关于非平凡离散等价变换的对应方程。此外，我们对所考虑的方程进行了李约简直到点等价，详尽地研究了它们的隐李对称性，并通过它们的递归算子作用于构造的李不变解产生了更广泛的新精确解族。该分析揭示了空间变量的8次幂，其指数为−1$ -1$,0,1,2,3,4,5和6，作为扩散系数的值，由于相应方程的对称性而突出。

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