Nonlinear Analysis-Real World Applications最新文献

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Global bifurcation for a predator-prey system with nonlinear boundary-mediated dispersal 一类具有非线性边界介导扩散的捕食-食饵系统的全局分岔

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications

Pub Date : 2025-11-15 DOI: 10.1016/j.nonrwa.2025.104547

Kaikai Liu , Shangjiang Guo

This paper presents a complete bifurcation analysis of steady-state solutions for a predator-prey reaction-diffusion-advection system featuring density-dependent boundary conditions. By developing a novel synthesis of local and global bifurcation theories, we characterize the full solution structure emerging from semi-trivial states, revealing how nonlinear boundary terms qualitatively alter system dynamics. Our main results establish: (i) precise conditions for coexistence state bifurcations that coincide with stability transitions of semi-trivial solutions; (ii) complete global continuation of solution branches showing either unbounded persistence or novel connection patterns; and (iii) quantitative criteria for stability thresholds governed by boundary-mediated feedback. The analysis overcomes significant technical challenges through sharp a priori estimates and careful treatment of non-self-adjoint operators arising from the nonlinear boundary conditions. These theoretical advances provide mechanistic explanations for edge effects in ecological systems while developing mathematical tools applicable to broader pattern formation problems. The work opens new directions for studying nonlinear boundary phenomena in biological systems, with natural extensions to multi-species communities and chemotaxis models.

本文给出了具有密度依赖边界条件的捕食者-猎物反应-扩散-平流系统稳态解的完全分岔分析。通过发展局部和全局分岔理论的新综合，我们描述了从半平凡状态出现的全解结构，揭示了非线性边界项如何定性地改变系统动力学。我们的主要结果建立了：(1)与半平凡解的稳定跃迁重合的共存状态分岔的精确条件；（ii）解分支的完全全局延拓，显示无界持久性或新颖的连接模式；（iii）由边界介导反馈控制的稳定性阈值的定量标准。该分析通过敏锐的先验估计和对非线性边界条件引起的非自伴随算子的仔细处理，克服了重大的技术挑战。这些理论进展为生态系统中的边缘效应提供了机制解释，同时开发了适用于更广泛格局形成问题的数学工具。这项工作为研究生物系统中的非线性边界现象开辟了新的方向，并将其自然扩展到多物种群落和趋化模型。

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引用次数: 0

Global strong solutions for 3-D immiscible and slightly compressible two-phase flow in porous media 多孔介质中三维非混相微可压缩两相流的全局强解

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications

Pub Date : 2025-11-10 DOI: 10.1016/j.nonrwa.2025.104531

Lei Xu , Mengxue Du

In this paper, we consider the flow of two-phase slightly compressible and immiscible fluids in porous media. We focus on the case where the densities of phases follow exponential laws with small compressibility factors, the absolute permeability is linked to the porosity via a Kozeny-Carman relation, and source terms account for realistic injection and production rates. Under some realistic hypotheses based on the data, we establish the local existence and uniqueness of strong solutions for the regularized three-dimensional system. We further show that the solution is global under small assumptions for the system without source terms. This is the first high-dimensional result of the strong solution without any symmetric assumptions for immiscible two-phase flow systems in porous media.

本文考虑两相微可压缩非混相流体在多孔介质中的流动。我们关注的是这样的情况：相密度遵循指数定律，压缩系数较小，绝对渗透率通过Kozeny-Carman关系与孔隙度联系起来，源项考虑了实际的注入和生产速度。在一些基于数据的现实假设下，我们建立了正则化三维系统强解的局部存在唯一性。我们进一步证明，对于没有源项的系统，在较小的假设下，解是全局的。这是对多孔介质中非混相两相流系统，在没有任何对称假设的情况下，首次得到强溶液的高维结果。

引用次数: 0

Centers and Lyapunov quantities in a cubic polynomial Kolmogorov differential system 三次多项式Kolmogorov微分系统中的中心和Lyapunov量

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications

Pub Date : 2025-11-09 DOI: 10.1016/j.nonrwa.2025.104536

Jaume Llibre , Zhilin Wang , Dongmei Xiao

In this paper we study the center-focus problem for a class of planar cubic polynomial differential system. It is shown that the system has at most two centers, and the center is elementary if the system has a center. Moreover, we characterize the center conditions and show that the maximum order of a weak focus is four if the system has a unique linear center-type equilibrium. And if the system has two linear center-type equilibria, then either the two equilibria are centers or each of them is a weak focus with order one.

本文研究了一类平面三次多项式微分系统的中心焦点问题。证明了系统最多有两个中心，如果系统有中心，则中心为初等中心。此外，我们对中心条件进行了刻画，并证明了当系统具有唯一的线性中心平衡时，弱焦点的最大阶数为4。如果系统有两个线性中心型平衡，那么这两个平衡要么是中心，要么是一个1阶的弱焦点。

引用次数: 0

On the control cost via the null controllability concept: The case of an interior set degenerate Schrödinger equation with finite delay 基于零可控性概念的控制代价：有限延迟内集退化Schrödinger方程的情况

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications

Pub Date : 2025-11-08 DOI: 10.1016/j.nonrwa.2025.104532

Mohamed Alahyane , Abderrazak Chrifi , Younes Echarroudi

In this paper, we are interested in the null controllability property of linear degenerate Schrödinger equation with a finite delay and a degeneracy that occurs in an interior subset of

(0, 1), i.e \exists W_{1} \subset \subset (0, 1), such that \forall x \in W_{1}, k (x) = 0

, where

k

stands for quantum diffusion. More precisely, we are looking for a suitable control, called the control time, which steers the studied wave to zero equilibrium in a finite time. To this end, we wield the classical procedure based on a adequate Carleman estimate involving a new weight functions and afterwards we get our observability inequality matched with the full adjoint system.

在本文中，我们对有限延迟线性退化Schrödinger方程的零可控性感兴趣，并且退化发生在（0,1），i的内部子集中。e∃W1∧(0,1)，使得∀x∈W1，k(x)=0，其中k代表量子扩散。更准确地说，我们正在寻找一种合适的控制，称为控制时间，它可以在有限的时间内将所研究的波转向零平衡。为此，我们运用经典的方法，在充分的Carleman估计的基础上，引入一个新的权函数，然后得到与全伴随系统匹配的可观察性不等式。

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引用次数: 0

Non-isentropic rotating compressible fluids under strong stratification 强分层作用下非等熵旋转可压缩流体

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications

Pub Date : 2025-11-08 DOI: 10.1016/j.nonrwa.2025.104529

Ming Lu, Chenxi Su

In this paper, we study compressible Navier-Stokes systems for non-isentropic fluids subject to rotational effects under strong gravitational stratification, focusing on the multi-scale asymptotic analysis of the problem. Key dimensionless parameters-including the Mach number, Froude number, Péclet number, and Rossby number-are scaled with specific powers of the small parameter

ϵ

. In particular, the Mach number and the Froude number are assumed to be of the same order in

ϵ

. Moreover, the Reynolds number is considered to approach infinity as

ϵ \to 0

. Our analysis shows that the limiting system corresponds to a variant of the two-dimensional incompressible Euler equations.

本文研究了在强重力分层下受旋转作用的非等熵流体的可压缩Navier-Stokes系统，重点研究了该问题的多尺度渐近分析。关键的无量纲参数——包括马赫数、弗劳德数、passclet数和罗斯比数——用小参数的特定幂来缩放。特别是，假设马赫数和弗劳德数在御柱中具有相同的阶数。此外，当λ→0时，雷诺数被认为接近无穷大。我们的分析表明，极限系统对应于二维不可压缩欧拉方程的一个变体。

引用次数: 0

A geometric analysis of the Bazykin-Berezovskaya predator-prey model with Allee effect in an economic framework 经济框架下具有Allee效应的Bazykin-Berezovskaya捕食-猎物模型的几何分析

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications

Pub Date : 2025-11-07 DOI: 10.1016/j.nonrwa.2025.104534

Jacopo Borsotti , Mattia Sensi

We study a fast-slow version of the Bazykin-Berezovskaya predator-prey model with Allee effect evolving on two timescales, through the lenses of Geometric Singular Perturbation Theory (GSPT). The system we consider is in non-standard form. We completely characterize its dynamics, providing explicit threshold quantities to distinguish between a rich variety of possible asymptotic behaviors. Moreover, we propose numerical results to illustrate our findings. Lastly, we comment on the real-world interpretation of these results, in an economic framework and in the context of predator-prey models.

本文通过几何奇异摄动理论（GSPT）的透镜，研究了两个时间尺度上具有Allee效应的Bazykin-Berezovskaya捕食-猎物模型的快-慢版本。我们考虑的系统是非标准形式的。我们完全表征其动力学，提供明确的阈值量，以区分丰富的各种可能的渐近行为。此外，我们提出了数值结果来说明我们的发现。最后，我们在经济框架和捕食者-猎物模型的背景下对这些结果的现实世界解释进行了评论。

引用次数: 0

Global existence and optimal time-decay rates of 3D non-isentropic compressible Navier-Stokes system with potential force 具有位势力的三维非等熵可压缩Navier-Stokes系统的全局存在性和最优时间衰减率

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications

Pub Date : 2025-11-06 DOI: 10.1016/j.nonrwa.2025.104535

Wenwen Huo , Chao Zhang

This paper concerns the global existence and optimal time-decay rate for the higher-order spatial derivative of classical solutions for the three-dimensional viscous and heat-conductive fluids, which is governed by the compressible Navier-Stokes (CNS) system with an external potential force. We first establish the global existence of the non-isentropic CNS system with potential force when the initial data is a small perturbation near the equilibrium state. Subsequently, we show the upper and lower bounds of the optimal decay rates for the solution and its spatial derivatives based on energy estimate and low-high frequency decomposition.

本文研究了具有外部位力的可压缩Navier-Stokes （CNS）系统控制的三维粘性导热流体经典解的高阶空间导数的全局存在性和最优时间衰减率。在初始数据为接近平衡状态的小扰动时，首先建立了具有势力的非等熵CNS系统的全局存在性。随后，我们给出了基于能量估计和低高频分解的解及其空间导数的最优衰减率的上界和下界。

引用次数: 0

Spreading speeds for a Lotva-Volterra competition system with advection in a periodic habitat 周期性栖息地中具有平流的Lotva-Volterra竞争系统的传播速度

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications

Pub Date : 2025-11-05 DOI: 10.1016/j.nonrwa.2025.104528

Hong-Jie Wu, Bang-Sheng Han, Hong-Lei Wei, Yinghui Yang

The study investigates pulsating wave speeds in an advective two-species competition-diffusion system under periodic environments. Recent studies have confirmed the existence and characterized the qualitative dynamics of pulsating waves. In this paper, we determine pulsating wave speed’s signs with identical diffusion rates and characterize invasion dynamics of competing species in heterogeneous environments by comparing the reactions and competitions. Specifically, we first establish a criterion for zero-speed waves and derive sufficient conditions for strictly positive or negative speeds. Our framework extends previous studies (e.g., Ding and Liang, Math. Ann. 385 (2023), 1–36) by considering functional representation of periodic steady-state solutions and explicit inclusion of advection effects and extends (e.g., Du et al., Z. Angew. Math. Phys. 71 (2020), 27 pp.) by further considering the sign of the pulsating wave speed, determining the long-time behavior of two strongly competing species. Crucially, the presence of the advection term indeed exerts a certain influence on the long-time behavior of two strongly competing species: From the perspective of the proof process, the appearance of the advection term increased the difficulty and complexity of proving Lemmas 2.3 and 3.1; from the result perspective, the advection term necessitates specific structural conditions for definitive speed determination. These findings advance understanding of pattern selection mechanisms in flow-driven ecological systems.

研究了周期环境下平流两种竞争扩散系统的脉动波速度。近年来的研究证实了脉动波的存在，并定性地描述了脉动波的动力学特性。本文确定了具有相同扩散速率的脉动波速符号，并通过比较反应和竞争来表征异质环境中竞争物种的入侵动力学。具体地说，我们首先建立了零速度波的判据，并推导了严格正或负速度的充分条件。我们的框架扩展了以前的研究(例如，Ding和Liang， Math。Ann. 385(2023), 1-36)通过考虑周期稳态解的函数表示和明确包含平流效应和扩展(例如，Du等人，Z. Angew。数学。物理71(2020)，27页)通过进一步考虑脉动波速度的标志，确定两个强烈竞争物种的长期行为。至关重要的是，平流项的存在确实对两个强竞争物种的长期行为产生了一定的影响：从证明过程来看，平流项的出现增加了证明引理2.3和3.1的难度和复杂性；从结果的角度来看，平流项需要特定的结构条件才能确定最终的速度。这些发现促进了对流量驱动型生态系统模式选择机制的理解。

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引用次数: 0

A generalized Richards growth model with conditional Hyers-Ulam stability 具有条件Hyers-Ulam稳定性的广义Richards增长模型

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications

Pub Date : 2025-11-02 DOI: 10.1016/j.nonrwa.2025.104530

Douglas R. Anderson , Masakazu Onitsuka

The Hyers–Ulam stability of a first-order nonlinear differential equation based on a generalized Richards growth model (also known as a Savageau growth model) is conditionally established based on the maximum size of the perturbation being not too large and the initial condition being not too small in terms of the carrying capacity and the powers involved. The Hyers–Ulam stability constants are determined explicitly and are shown to depend on the relative sizes of the power parameters in the model. Examples are provided of both stability and instability to illustrate the sharpness of our results. The main result is then applied to a tissue growth model. These results generalize known stability properties of the logistic equation and contribute to the theory of functional stability in nonlinear differential equations, with implications for population and biological models and related applications.

基于广义Richards增长模型（又称Savageau增长模型）的一阶非线性微分方程的Hyers-Ulam稳定性是有条件地建立在摄动的最大尺寸不太大，初始条件在承载能力和所涉及的幂次方面不太小的基础上。Hyers-Ulam稳定常数是明确确定的，并显示依赖于模型中功率参数的相对大小。文中还提供了稳定性和不稳定性的例子来说明我们的结果的明晰性。然后将主要结果应用于组织生长模型。这些结果推广了logistic方程已知的稳定性性质，并有助于非线性微分方程的泛函稳定性理论，对种群和生物模型及其相关应用具有重要意义。

引用次数: 0

Boundedness and large-time behavior in a two-species doubly degenerate diffusion chemotaxis system with logistic proliferation 一类具有logistic扩散的两种双退化扩散趋化系统的有界性和大时行为

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications

Pub Date : 2025-11-01 DOI: 10.1016/j.nonrwa.2025.104525

Yuting Xiang

<div><div>The two-species doubly degenerate nutrient taxis model with competitive kinetics<span><span><span><math><mtable><mtr><mtd><mrow><mo>{</mo><mtable><mtr><mtd><mrow><mrow></mrow><msub><mi>u</mi><mrow><mn>1</mn><mi>t</mi></mrow></msub></mrow></mtd><mtd><mrow><mo>=</mo><msub><mrow><mo>(</mo><msub><mi>u</mi><mn>1</mn></msub><mi>v</mi><msub><mi>u</mi><mrow><mn>1</mn><mi>x</mi></mrow></msub><mo>)</mo></mrow><mi>x</mi></msub><mo>−</mo><msub><mrow><mo>(</mo><msubsup><mi>u</mi><mn>1</mn><mn>2</mn></msubsup><mi>v</mi><msub><mi>v</mi><mi>x</mi></msub><mo>)</mo></mrow><mi>x</mi></msub><mo>+</mo><msub><mi>μ</mi><mn>1</mn></msub><msub><mi>u</mi><mn>1</mn></msub><mrow><mo>(</mo><mn>1</mn><mo>−</mo><msub><mi>u</mi><mn>1</mn></msub><mo>−</mo><msub><mi>a</mi><mn>1</mn></msub><msub><mi>u</mi><mn>2</mn></msub><mo>)</mo></mrow><mo>,</mo></mrow></mtd><mtd><mrow><mi>x</mi><mo>∈</mo><mstyle><mi>Ω</mi></mstyle><mo>,</mo><mi>t</mi><mo>></mo><mn>0</mn><mo>,</mo></mrow></mtd></mtr><mtr><mtd><msub><mi>u</mi><mrow><mn>2</mn><mi>t</mi></mrow></msub></mtd><mtd><mrow><mo>=</mo><msub><mrow><mo>(</mo><msub><mi>u</mi><mn>2</mn></msub><mi>v</mi><msub><mi>u</mi><mrow><mn>2</mn><mi>x</mi></mrow></msub><mo>)</mo></mrow><mi>x</mi></msub><mo>−</mo><msub><mrow><mo>(</mo><msubsup><mi>u</mi><mn>2</mn><mn>2</mn></msubsup><mi>v</mi><msub><mi>v</mi><mi>x</mi></msub><mo>)</mo></mrow><mi>x</mi></msub><mo>+</mo><msub><mi>μ</mi><mn>2</mn></msub><msub><mi>u</mi><mn>2</mn></msub><mrow><mo>(</mo><mn>1</mn><mo>−</mo><msub><mi>u</mi><mn>2</mn></msub><mo>−</mo><msub><mi>a</mi><mn>2</mn></msub><msub><mi>u</mi><mn>1</mn></msub><mo>)</mo></mrow><mo>,</mo></mrow></mtd><mtd><mrow><mi>x</mi><mo>∈</mo><mstyle><mi>Ω</mi></mstyle><mo>,</mo><mi>t</mi><mo>></mo><mn>0</mn><mo>,</mo></mrow></mtd></mtr><mtr><mtd><msub><mi>v</mi><mi>t</mi></msub></mtd><mtd><mrow><mo>=</mo><msub><mi>v</mi><mrow><mi>x</mi><mi>x</mi></mrow></msub><mo>−</mo><mrow><mo>(</mo><msub><mi>u</mi><mn>1</mn></msub><mo>+</mo><msub><mi>u</mi><mn>2</mn></msub><mo>)</mo></mrow><mi>v</mi><mo>,</mo></mrow></mtd><mtd><mrow><mi>x</mi><mo>∈</mo><mstyle><mi>Ω</mi></mstyle><mo>,</mo><mi>t</mi><mo>></mo><mn>0</mn><mo>,</mo></mrow></mtd></mtr></mtable></mrow></mtd></mtr></mtable></math></span></span></span>is considered under no-flux boundary conditions in an open bounded interval <span><math><mrow><mstyle><mi>Ω</mi></mstyle><mo>⊂</mo><mi>R</mi></mrow></math></span>, where <span><math><mrow><msub><mi>a</mi><mi>i</mi></msub><mo>></mo><mn>0</mn></mrow></math></span> and <span><math><mrow><msub><mi>μ</mi><mi>i</mi></msub><mo>></mo><mn>0</mn></mrow></math></span> for <span><math><mrow><mo>(</mo><mi>i</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></mrow></math></span>. It is shown that for all suitably regular nonnegative initial data <span><math><mrow><mo>(</mo><msub><mi>u</mi><mn>10</mn></msub><mo>,</mo><msub><mi>u</mi><mn>20</mn></msub><mo>,</mo><msub><mi>v</mi><mn>0</mn></msub><mo>)</mo></mrow></math></span>, where <span><math><ms

考虑具有竞争动力学的两种双退化营养趋同模型{u1t=(u1vu1x)x−(u12vvx)x+μ1u1(1−u1−a1u2),x∈Ω，t>0,u2t=(u2vu2x)x−(u22vvx)x+μ2u2(1−u2−a2u1),x∈Ω，t>0,vt=vxx−(u1+u2)v,x∈Ω，t>0，在开放有界区间Ω∧R中的无流量边界条件下，其中（i=1,2）的ai>；0和μi>；0。证明了对于所有适当正则非负初始数据（u10,u20,v0），其中u10和u20为严格正，v0为正，上述系统至少存在一个全局弱解满足以下有界性∥u1（·，t）∥Lp（Ω）+∥u2（·，t）∥Lp（Ω）+∥v（·，t）∥W1,∞（Ω）≤C。此外，通过构造合适的能量泛函，我们建立了上述系统解的大时性，并证明了以下性质：•若a1，a2∈(0,1)，则存在一个序列tk→∞，使得L2（Ω）中的全局弱解（u1,u2,v）（·，tk）→（1−a11−a1a2,1−a21−a1a2,0）为k→∞；•若a1≥1>；a2>0，则存在一个序列tk→∞，使得L2（Ω）上的整体弱解（u1,u2,v）（·，tk）→（0,1,0）为k→∞。

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