Nonlinear Analysis-Real World Applications最新文献

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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

Rescaling invariance exponents for the Lane-Emden heat flow system Lane-Emden热流系统不变性指数的重标化

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.2025.104515

Haochuan Huang , Rui Huang , Gege Liu , Jingxue Yin

This paper is concerned with the existence and asymptotic behavior of solutions for the Lane-Emden heat flow system. Our arguments are based on the upper and lower solutions method, which is different from the semigroup techniques and a fixed point theorem in previous works [3, 11]. It is worthy of mentioning that our results do not impose the integrability restrictions on initial values and thus the decay rate exponents of the initial values can be selected as the rescaling invariance exponents for the Lane-Emden heat flow system.

本文研究了Lane-Emden热流系统解的存在性和渐近性。我们的论证是基于上下解的方法，不同于以往作品[3,11]中的半群技术和不动点定理。值得一提的是，我们的结果没有对初值施加可积性限制，因此可以选择初值的衰减率指数作为Lane-Emden热流系统的重标化不变性指数。

引用次数: 0

Local existence and blow-up of solutions for the higher-order viscoelastic equation with general source term and variable exponents: Theoretical and numerical results 具有一般源项和变指数的高阶粘弹性方程解的局部存在性和爆破性：理论和数值结果

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications

Pub Date : 2025-10-07 DOI: 10.1016/j.nonrwa.2025.104512

Nebi Yılmaz , Muhteşem Demir , Erhan Pişkin

This study explores a higher-order viscoelastic equation characterized by variable exponents. We demonstrate the local existence of weak solutions by imposing appropriate conditions on these variable exponents. Furthermore, we investigate the phenomenon of finite-time blow-up for solutions that begin with positive initial energy. Finally, we give a 2D numerical example for the blow up.

研究了一种以变指数为特征的高阶粘弹性方程。通过对这些变指数施加适当的条件，证明了弱解的局部存在性。进一步研究了初始能量为正的解的有限时间爆破现象。最后，给出了爆破的二维数值算例。

引用次数: 0

Hierarchical null controllability of a degenerate parabolic equation with nonlocal coefficient 一类具有非局部系数的退化抛物方程的层次零可控性

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications

Pub Date : 2025-10-04 DOI: 10.1016/j.nonrwa.2025.104513

Juan Límaco, João Carlos Barreira, Suerlan Silva, Luis P. Yapu

In this paper we use a Stackelberg-Nash strategy to show the local null controllability of a parabolic equation where the diffusion coefficient is the product of a degenerate function in space and a nonlocal term. We consider one control called leader and two controls called followers. To each leader we associate a Nash equilibrium corresponding to a bi-objective optimal control problem; then, we find a leader that solves the null controllability problem. The linearized degenerated system is treated adapting Carleman estimates for degenerated systems from Demarque, Límaco and Viana [31] and the local controllability of the non-linear system is obtained using Liusternik’s inverse function theorem. The nonlocal coefficient originates a multiplicative coupling in the optimality system that gives rise to interesting calculations in the applications of the inverse function theorem.

本文利用Stackelberg-Nash策略，给出了扩散系数为空间退化函数与非局部项积的抛物方程的局部零可控性。我们考虑一个称为领导者的控制和两个称为追随者的控制。对于每个领导者，我们将纳什均衡与双目标最优控制问题相关联；然后，我们找到一个解决零可控性问题的领导者。采用Demarque， Límaco和Viana[31]对退化系统的Carleman估计对线性化退化系统进行处理，并利用Liusternik反函数定理得到非线性系统的局部可控性。非局部系数在最优性系统中产生了乘法耦合，在反函数定理的应用中产生了有趣的计算。

引用次数: 0

Wave breaking and traveling waves for the quadratic-cubic Camassa–Holm equation 二次立方Camassa-Holm方程的破波和行波

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications

Pub Date : 2025-09-29 DOI: 10.1016/j.nonrwa.2025.104493

Xuanxuan Han, Shaojie Yang

This paper is concerned with the solutions of the quadratic-cubic Camassa–Holm equation which is a model that explore the change in the physical structure of the solutions from the peakons to the bell-shaped solitary wave solutions. The first type of solutions exhibits finite time singularity in the sense of wave breaking. We perform a refined analysis based on the local structure of the dynamics to provide a condition on the initial data to guarantee wave breaking. The key feature of the method is to refine the analysis on characteristics and conserved quantities to the Riccati-type differential inequality. The other type of solutions which we study is the traveling waves, we investigate nonexistence of the Camassa–Holm-type peaked traveling wave solutions. Moreover, we discover how the symmetric structure is connected to the steady structure of solutions to the quadratic-cubic Camassa–Holm equation, and prove that the classical symmetric waves must be traveling wave solutions.

本文研究了二次-三次Camassa-Holm方程的解，该方程是一个探讨从峰到钟形孤波解的物理结构变化的模型。第一类解在破波意义上表现出有限时间奇点。我们根据动力学的局部结构进行了精细的分析，以提供一个初始数据的条件来保证破波。该方法的主要特点是将特征和守恒量的分析细化到riccati型微分不等式。我们研究的另一类解是行波，我们研究了camassa - holm型峰值行波解的不存在性。此外，我们还发现了对称结构与二次三次Camassa-Holm方程解的稳定结构之间的联系，并证明了经典对称波必须是行波解。

引用次数: 0

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Nonlinear Analysis-Real World Applications

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