Nonlinear Analysis-Real World Applications最新文献

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Harmonic oscillations and their stability around surface Ekman layer 表面埃克曼层周围的谐波振荡及其稳定性

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications

Pub Date : 2025-10-29 DOI: 10.1016/j.nonrwa.2025.104527

Thi Ngoc Ha Vu, Thieu Huy Nguyen

We study the Navier-Stokes equations in a rotating framework near the surface Ekman layer and establish the existence and polynomial stability of a time-periodic solution under the action of a time-periodic external force. Furthermore, when the external forcing is almost periodic in time, we prove the existence and stability of an almost periodic solution. These results describe the nonlinear dynamics of (almost) harmonic oscillations around the surface Ekman spiral. In the absence of external forcing, the nonlinear stability of the Ekman spiral profile follows as a direct consequence.

研究了靠近表面Ekman层的旋转框架中的Navier-Stokes方程，建立了在时间周期外力作用下的时间周期解的存在性和多项式稳定性。此外，当外力在时间上几乎是周期的时候，我们证明了一个几乎周期解的存在性和稳定性。这些结果描述了围绕表面埃克曼螺旋的（几乎）谐波振荡的非线性动力学。在没有外力的情况下，直接导致了埃克曼螺旋剖面的非线性稳定性。

引用次数: 0

Spatial profiles of a diffusion-advection epidemic model with saturated incidence mechanism and birth-death effect 具有饱和发病机制和生-死效应的扩散-平流流行病模型的空间剖面

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications

Pub Date : 2025-10-28 DOI: 10.1016/j.nonrwa.2025.104524

Xiaodan Chen, Renhao Cui

In this paper, we are concerned with a diffusion-advection SIS (susceptible-infected-susceptible) epidemic model with saturated incidence mechanism and birth-death effect. The basic reproduction number

R_{0}

has been derived through a variational expression and determined the threshold dynamics. We mainly investigate spatial profiles of endemic equilibrium with respect to large advection, small dispersal of susceptible/infected individuals and large saturation. These results may offer some prospective applications on disease control and prediction.

本文研究了具有饱和发病机制和生-死效应的扩散-平流SIS（易感-感染-易感）流行病模型。通过变分表达式导出了基本繁殖数R0，并确定了阈值动态。我们主要研究了大平流、小扩散和大饱和情况下地方性平衡的空间分布。这些结果可能在疾病控制和预测方面具有一定的应用前景。

引用次数: 0

Sharp rate of accelerating propagation in a nonlocal model arising in population dynamics 种群动态中产生的非局部模型中加速繁殖的急剧速率

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications

Pub Date : 2025-10-27 DOI: 10.1016/j.nonrwa.2025.104526

Na Li

This paper is devoted to studying propagation dynamics in an age-structured population model incorporating two interacting nonlocal mechanisms. We analyze how interactions between nonlocal dispersal kernels shape propagation dynamics based on comparison arguments and the evolutionary viewpoint. By appealing to monotone dynamical system theory, we investigate the existence of spreading speed and its variational characterization. By developing a framework for establishing the fundamental solution and its refined estimates, we construct sub- and super-solutions to rigorously prove the sharp rate of accelerating propagation, which is closely related to the tail heaviness of the convolution of two nonlocal dispersal kernels. Additionally, the influence of time delay on the rate of propagation is discussed under specific conditions. Our findings reveal the crucial role of interactions between nonlocal dispersal kernels in determining the rate of propagation.

本文研究了一个包含两种相互作用的非局部机制的年龄结构种群模型中的繁殖动力学。基于比较论证和进化观点，分析了非局部扩散核之间的相互作用如何影响传播动力学。利用单调动力系统理论，研究了扩散速度的存在性及其变分性质。通过建立基本解及其精细估计的框架，我们构造了子解和超解来严格证明加速传播的急剧速率，这与两个非局部扩散核卷积的尾重密切相关。此外，还讨论了在特定条件下延时对传播速率的影响。我们的发现揭示了非局部扩散核之间的相互作用在决定繁殖速率方面的关键作用。

引用次数: 0

Dispersive blow-up for a coupled Schrödinger-fifth order KdV system 耦合Schrödinger-fifth阶KdV系统的色散爆破

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications

Pub Date : 2025-10-26 DOI: 10.1016/j.nonrwa.2025.104522

Eddye Bustamante, José Jiménez Urrea, Jorge Mejía

In this work we establish a dispersive blow-up result for the initial value problem (IVP) for the coupled Schrödinger-fifth order Korteweg-de Vries system

\begin{matrix} \begin{matrix} i u_{t} + \partial_{x}^{2} u & = α u v + {γ | u |}^{2} u, x \in R, t \in R, \\ \partial_{t} v + \partial_{x}^{5} v + \partial_{x} v^{2} & = ϵ \partial_{x} {| u |}^{2}, x \in R, t \in R, \\ u (x, 0) & = u_{0} (x), v (x, 0) = v_{0} (x) . \end{matrix}} \end{matrix}

To achieve this, we prove a local well-posedness result in Bourgain spaces of the type

X^{s + β, b} \times Y^{s, b}

, along with a regularity property for the nonlinear part of the IVP solutions. This property enables the construction of initial data that leads to the dispersive blow-up phenomenon.

在这项工作中，我们建立了耦合Schrödinger-fifth阶Korteweg-de Vries系统的初值问题（IVP）的色散爆破结果：ut+∂x2u=αuv+γ|u|2u,x∈R,t∈R,∂tv+∂x5v+∂xv2= λ∂x|u|2,x∈R,t∈R,u(x,0)=u0(x),v(x,0)=v0(x)。为了实现这一点，我们证明了x +β，b×Ys，b型Bourgain空间中的局部适定性结果，以及IVP解的非线性部分的正则性。这一特性使我们能够构造导致分散爆炸现象的初始数据。

引用次数: 0

Finite time blow-up in a quasilinear Keller-Segel system with indirect signal production 具有间接信号产生的拟线性Keller-Segel系统的有限时间爆破

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications

Pub Date : 2025-10-24 DOI: 10.1016/j.nonrwa.2025.104523

Taian Jin, Yuxiang Li

<div><div>We study the Neumann initial-boundary value problem for the following quasilinear chemotaxis system with indirect signal production<math><mi>★</mi></math><math><mtable><mtr><mtd><mrow><mo>{</mo><mtable><mtr><mtd><mrow><msub><mi>u</mi><mi>t</mi></msub><mo>=</mo><mi>∇</mi><mo>·</mo><mrow><mo>(</mo><mi>D</mi><mo>(</mo><mi>u</mi><mo>)</mo><mi>∇</mi><mi>u</mi><mo>)</mo></mrow><mo>−</mo><mi>∇</mi><mo>·</mo><mrow><mo>(</mo><mi>S</mi><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow><mi>∇</mi><mi>v</mi><mo>)</mo></mrow><mo>,</mo></mrow></mtd></mtr><mtr><mtd><mrow><mn>0</mn><mo>=</mo><mstyle><mi>Δ</mi></mstyle><mi>v</mi><mo>−</mo><mi>μ</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>+</mo><mi>w</mi><mo>,</mo></mrow></mtd></mtr><mtr><mtd><mrow><msub><mi>w</mi><mi>t</mi></msub><mo>+</mo><mi>w</mi><mo>=</mo><mi>u</mi></mrow></mtd></mtr></mtable></mrow></mtd></mtr></mtable></math>in <math><mrow><mstyle><mi>Ω</mi></mstyle><mo>⊂</mo><mi>R</mi><msup><mrow></mrow><mi>n</mi></msup></mrow></math> with <math><mrow><mi>n</mi><mo>≥</mo><mn>1</mn></mrow></math>. Here <math><mrow><mi>μ</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>:</mo><mo>=</mo><msub><mi>⨏</mi><mstyle><mi>Ω</mi></mstyle></msub><mi>w</mi><mrow><mo>(</mo><mo>·</mo><mo>,</mo><mi>t</mi><mo>)</mo></mrow></mrow></math>, <math><mrow><mi>D</mi><mo>∈</mo><mi>C</mi><msup><mrow></mrow><mn>2</mn></msup><mrow><mo>(</mo><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mi>∞</mi><mo>)</mo></mrow><mo>)</mo></mrow><mspace></mspace><mtext>is</mtext><mspace></mspace><mtext>positive</mtext><mspace></mspace><mtext>on</mtext><mspace></mspace><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mi>∞</mi><mo>)</mo></mrow></mrow></math> and <math><mrow><mi>S</mi><mo>∈</mo><mi>C</mi><msup><mrow></mrow><mn>2</mn></msup><mrow><mo>(</mo><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mi>∞</mi><mo>)</mo></mrow><mo>)</mo></mrow><mspace></mspace><mtext>is</mtext><mspace></mspace><mtext>nonnegative</mtext></mrow></math>. We prove the following:<ul><li>•<div>If <math><mrow><mstyle><mi>Ω</mi></mstyle><mo>=</mo><msub><mi>B</mi><mi>R</mi></msub><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow></mrow></math> with some <math><mrow><mi>R</mi><mo>></mo><mn>0</mn></mrow></math>, <math><mrow><mi>D</mi><mrow><mo>(</mo><mi>s</mi><mo>)</mo></mrow><mo>≤</mo><msub><mi>k</mi><mn>1</mn></msub><mi>s</mi><msup><mrow></mrow><mi>q</mi></msup></mrow></math> and <math><mrow><mi>S</mi><mrow><mo>(</mo><mi>s</mi><mo>)</mo></mrow><mo>≥</mo><msub><mi>k</mi><mn>2</mn></msub><mi>s</mi><msup><mrow></mrow><mi>p</mi></msup></mrow></math> for all <math><mrow><mi>s</mi><mo>≥</mo><mn>1</mn></mrow></math>, where <math><mrow><msub><mi>k</mi><mn>1</mn></msub><mo>,</mo><msub><mi>k</mi><mn>2</mn></msub><mo>,</mo><mi>p</mi><mo>></mo><mn>0</mn></mrow></math> and <math><mrow><mi>p</mi><mo>

我们研究了以下具有间接信号产生的拟线性趋化系统的Neumann初边值问题★{ut=∇·(D(u)∇u) -∇·（S(u)∇v），0=Δv−μ(t)+w,wt+w= Ω∧Rn，其中n≥1。这里μ(t): =⨏Ωw(·t), D∈C2([0,∞))ispositiveon[0,∞)和S∈isnonnegative C2([0,∞))。•如果Ω=BR(0)且R>；0，且对于所有s≥1，其中k1，k2,p>；0和p>；q+2n， D(s)≤k1sq和s (s)≥k2sp，则存在一些径向对称初始数据，使得对应的解在有限时间内对任意质量水平m:=∫Ωu0dx>；0爆破。•如果D和S满足S(S)D(S)≤ksp，对于所有的s>；0和某些k>；0和p<；2n， D从上到下都是代数有界的，那么对于任何适当正则的初始数据，对应的解全局存在并且保持有界。我们研究了（★）的有限时间爆破现象，补充了Fuest et al.（2023）的结果。

引用次数: 0

A note on the logistic damping effect to ensure the global solvability of the chemotaxis system with degenerate signal-dependent motility 关于保证具有退化信号依赖运动的趋化系统全局可解性的logistic阻尼效应的注释

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications

Pub Date : 2025-10-21 DOI: 10.1016/j.nonrwa.2025.104520

Quanyong Zhao, Jinrong Wang

<div><div>This paper is devoted to investigating the logistic source damping effect of the following model<math><mtable><mtr><mtd><mrow><mo>{</mo><mtable><mtr><mtd><mrow><msub><mi>u</mi><mi>t</mi></msub><mo>=</mo><mi>∇</mi><mo>·</mo><mrow><mo>(</mo><mi>φ</mi><mrow><mo>(</mo><mi>v</mi><mo>)</mo></mrow><mi>∇</mi><mi>u</mi><mo>)</mo></mrow><mo>−</mo><mi>∇</mi><mo>·</mo><mrow><mo>(</mo><mi>u</mi><mi>χ</mi><mrow><mo>(</mo><mi>v</mi><mo>)</mo></mrow><mi>∇</mi><mi>v</mi><mo>)</mo></mrow><mo>+</mo><mi>r</mi><mi>u</mi><mo>−</mo><mi>μ</mi><msup><mi>u</mi><mi>α</mi></msup><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><mrow><msub><mi>v</mi><mi>t</mi></msub><mo>=</mo><mstyle><mi>Δ</mi></mstyle><mi>v</mi><mo>−</mo><mi>v</mi><mo>+</mo><mi>u</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>under homogeneous Neumann boundary conditions in a smooth bounded domain <math><mrow><mstyle><mi>Ω</mi></mstyle><mo>⊂</mo><msup><mi>R</mi><mi>n</mi></msup></mrow></math>, where <math><mrow><mi>r</mi><mo>∈</mo><mi>R</mi><mo>,</mo><mi>μ</mi><mo>≥</mo><mn>0</mn></mrow></math> and <math><mrow><mi>α</mi><mo>></mo><mn>1</mn></mrow></math> are constants. For the case <math><mrow><mrow><mo>(</mo><mi>φ</mi><mo>,</mo><mi>χ</mi><mo>)</mo></mrow><mo>∈</mo><msup><mrow><mo>[</mo><msup><mi>C</mi><mn>2</mn></msup><mrow><mo>(</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mi>∞</mi><mo>)</mo></mrow><mo>)</mo></mrow><mo>]</mo></mrow><mn>2</mn></msup><mo>,</mo><mi>φ</mi><mrow><mo>(</mo><mi>v</mi><mo>)</mo></mrow><mo>></mo><mn>0</mn><mspace></mspace><mtext>and</mtext><mspace></mspace><mfrac><msup><mrow><mo>|</mo><mi>χ</mi><mrow><mo>(</mo><mi>v</mi><mo>)</mo></mrow><mo>|</mo></mrow><mn>2</mn></msup><mrow><mi>φ</mi><mo>(</mo><mi>v</mi><mo>)</mo></mrow></mfrac></mrow></math> is bounded on <math><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mi>∞</mi><mo>)</mo></mrow></math>, generating the prototypical choice given by <math><mrow><mi>φ</mi><mrow><mo>(</mo><mi>v</mi><mo>)</mo></mrow><mo>=</mo><msup><mi>v</mi><mrow><mo>−</mo><mi>k</mi></mrow></msup></mrow></math> and <math><mrow><mi>χ</mi><mrow><mo>(</mo><mi>v</mi><mo>)</mo></mrow><mo>=</mo><mi>k</mi><msup><mi>v</mi><mrow><mo>−</mo><mi>k</mi><mo>−</mo><mn>1</mn></mrow></msup></mrow></math> with <math><mrow><mi>k</mi><mo>></mo><mn>0</mn></mrow></math>, it is shown that even with large initial data, the existence of the global classical solution to the above problem can be achieved when <math><mrow><mi>α</mi><mo>></mo><mn>3</mn><mo>−</mo><mfrac><mn>6</mn><mrow><mi>n</mi><mo>+</mo><mn>4</mn></mrow></mfrac></mrow></math> with <math><mrow

本文研究了光滑有界区域Ω∧Rn中齐次诺伊曼边界条件下模型{ut=∇·(φ(v)∇u) -∇·(uχ(v)∇v)+ru−μuα,x∈Ω，t>0,vt=Δv−v+u,x∈Ω，t>；0的logistic源阻尼效应，其中r∈r，μ≥0和α>；1是常数。对于(φ,χ)∈[C2((0,∞))]2,φ(v)>；0和|χ(v)|2φ(v)在（0,∞）上有界的情况，生成了φ(v)=v−k和χ(v)=kv−k−1在k>；0时给出的原型选择，证明了即使有较大的初始数据，α>；3−6n+4在μ>；0时也能得到上述问题的全局经典解的存在性，这优化了Lv和Wang （Proc. Roy）著作中使用的条件。Soc。爱丁堡教派151(2021)821-841)，刘和高（苹果）。数学。左163(2025)109470)。对于奇异原型φ(v)=vk和χ(v)=−kvk−1，也研究了保证经典解全局存在的logistic阻尼强度。

引用次数: 0

Time-delayed generalized Korteweg–de Vries-Burgers equation: Well-posedness and exponential decay 时滞广义Korteweg-de Vries-Burgers方程：适定性和指数衰减

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications

Pub Date : 2025-10-21 DOI: 10.1016/j.nonrwa.2025.104519

Ibtissam Issa, Cristina Pignotti

This study explores the generalized Korteweg-de Vries-Burgers equation incorporating delay feedback and a damping term. Using semigroup arguments and Lyapunov functional techniques, we establish the existence of a global solution when the exponent of the nonlinear term satisfies some growth conditions. Furthermore, we prove exponential stability estimates under suitable assumptions: first in the case of a positive damping coefficient, then within a more comprehensive framework, accommodating sign changes in both coefficients, i.e. for the damping and the delay feedback. In both cases, we adopt refined conditions on the delay feedback’s coefficient, extending and enhancing existing results in the literature. In particular, our conditions are independent of the time delay size.

本文研究了包含延迟反馈和阻尼项的广义Korteweg-de Vries-Burgers方程。利用半群参数和Lyapunov泛函技术，建立了当非线性项的指数满足某些增长条件时全局解的存在性。此外，我们在适当的假设下证明了指数稳定性估计：首先在正阻尼系数的情况下，然后在更全面的框架内，容纳两个系数的符号变化，即对于阻尼和延迟反馈。在这两种情况下，我们对延迟反馈系数采用了改进的条件，扩展和增强了文献中已有的结果。特别是，我们的条件与时间延迟大小无关。

引用次数: 0

Global existence of weak solutions to a cell migration and (de)differentiation model with double haptotaxis in the context of tissue regeneration 在组织再生的背景下，具有双重趋向性的细胞迁移和（去）分化模型的弱解的全局存在

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications

Pub Date : 2025-10-15 DOI: 10.1016/j.nonrwa.2025.104516

Nishith Mohan, Christina Surulescu

We study a model for the spread and (de)differentiation of mesenchymal stem cells and chondrocytes in a scaffold whose fibers are coated with hyaluron. The chondrocytes produce new extracellular matrix, which, together with hyaluron, serves as a haptotactic cue for the stem cell migration. We prove global existence of weak solutions of the corresponding cross-diffusion system with double haptotaxis.

我们研究了间充质干细胞和软骨细胞在纤维被透明质包裹的支架中的扩散和（去）分化模型。软骨细胞产生新的细胞外基质，其与透明质一起作为干细胞迁移的触致性线索。证明了具有双趋向性的交叉扩散系统弱解的整体存在性。

引用次数: 0

Singularities of solutions to the non-Newtonian polytropic filtration 非牛顿多向过滤解的奇异性

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications

Pub Date : 2025-10-14 DOI: 10.1016/j.nonrwa.2025.104518

Meiling Zhou, Liangwei Wang, Jingxue Yin, Can Lu

In this paper, we study the non-Newtonian polytropic filtration equation

u_{t} - div ({| \nabla u^{m} |}^{p - 2} \nabla u^{m}) = 0

with a positive initial data on a smooth bounded domain

Ω \subset R^{n}

for

n \geq 3

, where

0 < m < 1

2 < p < 1 + \frac{1}{m}

, and in particular

p < \frac{n (m + 1)}{1 + m n}

. To investigate the regularity of solutions to the Dirichlet problem for this equation when the initial data exhibit a singularity of the form

u_{0} (x) \sim A {| x |}^{- γ}

for

x \in Ω ∖ {0}

with

A > 0

and

γ > 0

, we introduce a linear diffusion term in the regularization process. This addition ensures that the equation remains uniformly parabolic, thereby satisfying both the maximum principle and the comparison principle. The desired results are obtained provided that the coefficient of this regularization term converges to zero in the norm of the appropriate function space. This paper shows that the behavior of the solution depends critically on the value of the exponent

γ

in the initial data, leading to the following distinct cases: finite-time boundedness, infinite-time boundedness, singular stabilization, and infinite-time blow-up.

本文研究了光滑有界域Ω∧Rn上具有正初始数据的非牛顿多向滤波方程ut−div(|∇um|p−2∇um)=0，其中n≥3,0<m< 1,2 <p<1+1m，特别是p<；n(m+1)1+mn。为了研究该方程的Dirichlet问题解的正则性，当初始数据表现为形式为u0(x) ~ a |x|−γ的奇点时，对于x∈Ω∈{0}，具有a >；0和γ>；0，我们在正则化过程中引入线性扩散项。这一补充保证了方程保持一致抛物，从而同时满足极大值原理和比较原理。当正则化项的系数在适当的函数空间范数内收敛于零时，得到了期望的结果。本文证明了解的行为严重依赖于初始数据中指数γ的值，从而导致以下不同的情况：有限时间有界性，无限时间有界性，奇异稳定和无限时间爆破。

引用次数: 0

Large-time behavior of large solutions to the 2D compressible Navier–Stokes equations with slip boundary conditions 具有滑移边界条件的二维可压缩Navier-Stokes方程大解的大时间行为

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications

Pub Date : 2025-10-10 DOI: 10.1016/j.nonrwa.2025.104517

Ying Dai , Ying Sun , Hao Xu

This paper is concerned with an initial-boundary value problem of 2D barotropic compressible Navier–Stokes equations subject to slip boundary conditions. Under the assumption that the density is uniformly bounded from above, we study the convergence of the solutions to its associated equilibrium with an exponential decay rate. The analysis is based on the elementary energy methods, the techniques from blow-up criterion and some new estimates for the gradient of velocity.

研究二维正压可压缩Navier-Stokes方程在滑移边界条件下的初边值问题。在密度从上到下均匀有界的假设下，我们研究了其相关平衡解的收敛性和指数衰减率。分析是基于初等能量法、爆破判据技术和一些新的速度梯度估计。

引用次数: 0

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Nonlinear Analysis-Real World Applications

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