Nonlinear Analysis-Real World Applications最新文献

英文中文

The matching of two Markus-Yamabe piecewise smooth systems in the plane 平面内两个马库斯-山边片断平稳系统的匹配

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications

Pub Date : 2024-11-09 DOI: 10.1016/j.nonrwa.2024.104254

Denis de Carvalho Braga , Fabio Scalco Dias , Jaume Llibre , Luis Fernando Mello

A Markus-Yamabe vector field is a smooth vector field in

R^{n}

having only one equilibrium point and such that the spectrum of its Jacobian matrix at any point of

R^{n}

is on the left of the imaginary axis in the complex plane. A vector field is globally asymptotically stable if it has a globally asymptotically stable equilibrium point

p

: all the orbits tend to

p

in forward time. One of the great results of the Qualitative Theory of Differential Equations establishes that a planar Markus-Yamabe vector field is globally asymptotically stable, but a Markus-Yamabe vector field defined in

R^{n}

n ⩾ 3

, does not have in general this property. We prove that planar crossing piecewise smooth vector fields defined in two zones formed by two Markus-Yamabe vector fields sharing the same equilibrium point located on the separation straight line are not necessarily globally asymptotically stable.

马库斯-山边矢量场是 Rn 中只有一个平衡点的光滑矢量场，其在 Rn 任意一点的雅各布矩阵谱位于复平面虚轴的左边。如果一个向量场有一个全局渐近稳定的平衡点 p，那么它就是全局渐近稳定的：在向前的时间里，所有轨道都趋向于 p。微分方程定性理论的伟大成果之一确定了平面马库斯-雅马贝向量场是全局渐近稳定的，但定义在 Rn, n⩾3 中的马库斯-雅马贝向量场一般不具有这一性质。我们证明，在两个马库斯-雅马贝向量场形成的两个区域中定义的平面交叉片断光滑向量场，共享位于分离直线上的同一个平衡点，并不一定是全局渐近稳定的。

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引用次数: 0

A general theory for the (s,p)-superposition of nonlinear fractional operators 非线性分数算子（s,p）叠加的一般理论

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications

Pub Date : 2024-11-07 DOI: 10.1016/j.nonrwa.2024.104251

Serena Dipierro, Edoardo Proietti Lippi, Caterina Sportelli, Enrico Valdinoci

We consider the continuous superposition of operators of the form

\iint_{[0, 1] \times (1, N)} {(- Δ)}_{p}^{s} u d μ (s, p),

where

μ

denotes a signed measure over the set

[0, 1] \times (1, N)

, joined to a nonlinearity satisfying a proper subcritical growth. The novelty of the paper relies in the fact that, differently from the existing literature, the superposition occurs in both

s

and

p

Here we introduce a new framework which is so broad to include, for example, the scenarios of the finite sum of different (in both

s

and

p

) Laplacians, or of a fractional

p

-Laplacian plus a

p

-Laplacian, or even combinations involving some fractional Laplacians with the “wrong” sign.

The development of this new setting comes with two applications, which are related to the Weierstrass Theorem and a Mountain Pass technique. The results obtained contribute to the existing literature with several specific cases of interest.

我们考虑的是形式为 Δ[0,1]×(1,N)(-Δ)psudμ(s,p) 的算子的连续叠加，其中 μ 表示集合 [0,1]×(1,N) 上的有符号度量，并与满足适当次临界增长的非线性连接。本文的新颖之处在于，与现有文献不同的是，叠加同时发生在 s 和 p 中。在此，我们引入了一个新的框架，该框架非常宽泛，可以包括不同（同时发生在 s 和 p 中）拉普拉斯的有限和，或分数 p 拉普拉斯加 p 拉普拉斯，甚至是涉及一些带有 "错误 "符号的分数拉普拉斯的组合。所获得的结果为现有文献提供了几个值得关注的具体案例。

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引用次数: 0

Global bounded solution in an attraction repulsion Chemotaxis-Navier-Stokes system with Neumann and Dirichlet boundary conditions 具有新曼和迪里夏特边界条件的吸引排斥趋化-纳维尔-斯托克斯系统中的全局有界解

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications

Pub Date : 2024-11-06 DOI: 10.1016/j.nonrwa.2024.104247

Luli Xu, Chunlai Mu, Minghua Zhang, Jing Zhang

This paper deals with an attraction–repulsion Chemotaxis-Navier–Stokes system with Dirichlet boundary for the attraction signal and Neumann boundary for the repulsion signal. Based on the work of Winkler (2020) and Wang et al. (2022), by using a series estimates, it is shown that in two dimension the classical solution of the system is globally bounded, under the condition of small initial values

{‖ n_{0} ‖}_{L^{1} (Ω)}

in the explicit expressions for

{‖ c_{0} ‖}_{L^{\infty} (Ω)}

and attraction–repulsion coefficients.

本文讨论了一个吸引-排斥趋化-纳维尔-斯托克斯系统，该系统的吸引信号和排斥信号分别具有迪里夏特边界和诺伊曼边界。在 Winkler (2020) 和 Wang 等人 (2022) 的研究基础上，通过系列估计，证明了在二维中，在‖c0‖L∞(Ω) 和吸引-排斥系数的显式中初始值‖n0‖L1(Ω) 较小的条件下，系统的经典解是全局有界的。

引用次数: 0

Threshold value for a quasilinear Keller–Segel chemotaxis system with the intermediate exponent in a bounded domain 在有界域中具有中间指数的准线性凯勒-西格尔趋化系统的阈值

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications

Pub Date : 2024-11-06 DOI: 10.1016/j.nonrwa.2024.104253

Hua Zhong

<div><div>We consider a quasilinear chemotaxis model <span><span><span><math><mfenced><mrow><mtable><mtr><mtd><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><mo>∇</mo><mi>⋅</mi><mrow><mo>(</mo><mi>D</mi><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow><mo>∇</mo><mi>u</mi><mo>)</mo></mrow><mo>−</mo><mo>∇</mo><mi>⋅</mi><mrow><mo>(</mo><mi>S</mi><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow><mo>∇</mo><mi>v</mi><mo>)</mo></mrow><mo>,</mo><mi>τ</mi><msub><mrow><mi>v</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><mi>Δ</mi><mi>v</mi><mo>−</mo><mi>v</mi><mo>+</mo><mi>u</mi><mo>,</mo><mspace></mspace></mtd></mtr></mtable></mrow></mfenced></math></span></span></span> with nonlinear diffusion function <span><math><mrow><mi>D</mi><mo>∈</mo><msup><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mi>∞</mi><mo>)</mo></mrow><mo>)</mo></mrow></mrow></math></span> and chemotactic sensitivity <span><math><mrow><mi>S</mi><mo>∈</mo><msup><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mi>∞</mi><mo>)</mo></mrow><mo>)</mo></mrow></mrow></math></span> in a bounded domain <span><math><mrow><mi>Ω</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></mrow></math></span> <span><math><mrow><mo>(</mo><mi>d</mi><mo>≥</mo><mn>3</mn><mo>)</mo></mrow></math></span>. Here the rate <span><math><mrow><mi>D</mi><mrow><mo>(</mo><mi>s</mi><mo>)</mo></mrow><mo>/</mo><mi>S</mi><mrow><mo>(</mo><mi>s</mi><mo>)</mo></mrow></mrow></math></span> grows like <span><math><msup><mrow><mi>s</mi></mrow><mrow><mn>2</mn><mo>−</mo><mi>m</mi></mrow></msup></math></span> with <span><math><mrow><mn>2</mn><mi>d</mi><mo>/</mo><mrow><mo>(</mo><mi>d</mi><mo>+</mo><mn>2</mn><mo>)</mo></mrow><mo><</mo><mi>m</mi><mo><</mo><mn>2</mn><mo>−</mo><mn>2</mn><mo>/</mo><mi>d</mi></mrow></math></span> as <span><math><mrow><mi>s</mi><mo>→</mo><mi>∞</mi></mrow></math></span>, and <span><math><mrow><mi>τ</mi><mo>=</mo><mn>0</mn><mo>,</mo><mn>1</mn></mrow></math></span>.</div><div>It is first shown that there exists a <span><math><mrow><msub><mrow><mi>M</mi></mrow><mrow><mo>∗</mo></mrow></msub><mo>></mo><mn>0</mn></mrow></math></span> such that if free energy with initial data is suitably small and <span><math><mrow><msubsup><mrow><mo>‖</mo><msub><mrow><mi>u</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>‖</mo></mrow><mrow><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup><mrow><mo>(</mo><mi>Ω</mi><mo>)</mo></mrow></mrow><mrow><mi>α</mi></mrow></msubsup><msubsup><mrow><mo>‖</mo><msub><mrow><mi>u</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>‖</mo></mrow><mrow><msup><mrow><mi>L</mi></mrow><mrow><mi>m</mi></mrow></msup><mrow><mo>(</mo><mi>Ω</mi><mo>)</mo></mrow></mrow><mrow><mi>β</mi></mrow></msubsup><mo><</mo><msub><mrow><mi>M</mi></mrow><mrow><mo>∗</mo></mrow></msub></mrow></math></span> with <span><math><mrow><mi>α</mi><mo>=</mo><mn>2</mn><mo>/</mo><mrow>

我们考虑一个准线性趋化模型 ut=∇⋅(D(u)∇u)-∇⋅(S(u)∇v),τvt=Δv-v+u, 非线性扩散函数 D∈C2([0,∞)) 和趋化敏感性 S∈C2([0,∞)) 在有界域 Ω⊂Rd (d≥3) 中。这里的速率 D(s)/S(s) 以 s→∞ 为 2d/(d+2)<m<2-2/d，像 s2-m 一样增长，且 τ=0,1 。首先证明存在一个 M∗>0，如果初始数据的自由能适当小且‖u0‖L1(Ω)α‖u0‖Lm(Ω)β<；M∗，α=2/(2-m)-d/m>0，β=d-2/(2-m)>0，则上述系统的经典解是时间均匀有界的。其次，在径向对称的情况下，我们可以找到 M∗>0，使得‖u0‖L1(Ω)α‖u0‖Lm(Ω)β>M∗，相应的解一定是无界的。这些结果表明，当 2d/(d+2)<m<2-2/d 时，经典解的全局行为由初始数据的规范组合来划分。

引用次数: 0

The Poincaré bifurcation by perturbing a class of cubic Hamiltonian systems 通过扰动一类立方哈密顿系统的波恩卡列分岔

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications

Pub Date : 2024-11-05 DOI: 10.1016/j.nonrwa.2024.104246

Yuan Chang, Liqin Zhao, Qiuyi Wang

This paper studies the Poincaré bifurcation of the planar vector fields

\dot{x} = H_{y} (x, y) + ɛ f (x, y)

\dot{y} = - H_{x} (x, y) + ɛ g (x, y)

, where

0 < | ɛ | ≪ 1

H (x, y) = α x^{2} + β y^{2} + a x^{4} + b x^{2} y^{2} + c y^{4}, (α, β, a, b, c) \in R^{5}, α β < 0

with

a^{2} + b^{2} + c^{2} \neq 0

, and

f (x, y)

and

g (x, y)

are polynomials in

(x, y)

of the degree

n

. The phase portraits of the unperturbed systems with at least one center can be divided into 10 classes by their phase portraits. For general

n

, we obtain the upper bound of the number of limit cycles bifurcating from period annuli if the first order Melnikov function is not identically zero. The results are new and some of the results in the literatures are improved.

本文研究了平面向量场ẋ=Hy(x,y)+ɛf(x,y)，ẏ=-Hx(x,y)+ɛg(x,y)的泊恩卡分岔，其中 0<；|ɛ|≪1，H(x,y)=αx2+βy2+ax4+bx2y2+cy4，(α,β,a,b,c)∈R5,αβ<0，a2+b2+c2≠0，f(x,y)和g(x,y)是(x,y)的 n 阶多项式。至少有一个中心的无扰动系统的相位肖像可按其相位肖像分为 10 类。对于一般 n，如果一阶梅利尼科夫函数不为同零，我们得到了从周期环分岔出的极限周期数的上限。这些结果是新的，并且改进了文献中的一些结果。

引用次数: 0

Boundedness and stabilization in an indirect pursuit-evasion model with nonlinear signal-dependent diffusion and sensitivity 具有非线性信号扩散和敏感性的间接追逐-逃避模型中的边界性和稳定性

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications

Pub Date : 2024-11-05 DOI: 10.1016/j.nonrwa.2024.104234

Chuanjia Wan, Pan Zheng

<div><div>This paper deals with an indirect pursuit-evasion model with signal-dependent diffusion and sensitivity <span><span><span><math><mfenced><mrow><mtable><mtr><mtd></mtd><mtd><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><mo>∇</mo><mi>⋅</mi><mfenced><mrow><msub><mrow><mi>D</mi></mrow><mrow><mn>1</mn></mrow></msub><mrow><mo>(</mo><mi>z</mi><mo>)</mo></mrow><mo>∇</mo><mi>u</mi></mrow></mfenced><mo>−</mo><mi>χ</mi><mo>∇</mo><mi>⋅</mi><mfenced><mrow><msub><mrow><mi>S</mi></mrow><mrow><mn>1</mn></mrow></msub><mrow><mo>(</mo><mi>z</mi><mo>)</mo></mrow><mi>u</mi><mo>∇</mo><mi>z</mi></mrow></mfenced><mo>+</mo><mi>u</mi><mfenced><mrow><mi>α</mi><mi>v</mi><mo>−</mo><msub><mrow><mi>a</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>−</mo><msub><mrow><mi>b</mi></mrow><mrow><mn>1</mn></mrow></msub><mi>u</mi></mrow></mfenced><mo>,</mo></mtd><mtd><mi>x</mi><mo>∈</mo><mi>Ω</mi><mo>,</mo><mi>t</mi><mo>></mo><mn>0</mn><mo>,</mo></mtd></mtr><mtr><mtd></mtd><mtd><msub><mrow><mi>v</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><mo>∇</mo><mi>⋅</mi><mfenced><mrow><msub><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msub><mrow><mo>(</mo><mi>w</mi><mo>)</mo></mrow><mo>∇</mo><mi>v</mi></mrow></mfenced><mo>+</mo><mi>ξ</mi><mo>∇</mo><mi>⋅</mi><mfenced><mrow><msub><mrow><mi>S</mi></mrow><mrow><mn>2</mn></mrow></msub><mrow><mo>(</mo><mi>w</mi><mo>)</mo></mrow><mi>v</mi><mo>∇</mo><mi>w</mi></mrow></mfenced><mo>+</mo><mi>v</mi><mfenced><mrow><msub><mrow><mi>a</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>−</mo><msub><mrow><mi>b</mi></mrow><mrow><mn>2</mn></mrow></msub><mi>v</mi><mo>−</mo><mi>u</mi></mrow></mfenced><mo>,</mo></mtd><mtd><mi>x</mi><mo>∈</mo><mi>Ω</mi><mo>,</mo><mi>t</mi><mo>></mo><mn>0</mn><mo>,</mo></mtd></mtr><mtr><mtd></mtd><mtd><msub><mrow><mi>w</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><mi>Δ</mi><mi>w</mi><mo>+</mo><mi>β</mi><mi>u</mi><mo>−</mo><mi>γ</mi><mi>w</mi><mo>,</mo></mtd><mtd><mi>x</mi><mo>∈</mo><mi>Ω</mi><mo>,</mo><mi>t</mi><mo>></mo><mn>0</mn><mo>,</mo></mtd></mtr><mtr><mtd></mtd><mtd><msub><mrow><mi>z</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><mi>Δ</mi><mi>z</mi><mo>+</mo><mi>δ</mi><mi>v</mi><mo>−</mo><mi>ρ</mi><mi>z</mi><mo>,</mo></mtd><mtd><mi>x</mi><mo>∈</mo><mi>Ω</mi><mo>,</mo><mi>t</mi><mo>></mo><mn>0</mn><mo>,</mo></mtd></mtr></mtable></mrow></mfenced></math></span></span></span>under homogeneous Neumann boundary conditions in a smoothly bounded domain <span><math><mrow><mi>Ω</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math></span>, where the parameters <span><math><mrow><mi>χ</mi><mo>,</mo><mi>ξ</mi><mo>,</mo><mi>α</mi><mo>,</mo><mi>β</mi><mo>,</mo><mi>γ</mi><mo>,</mo><mi>δ</mi><mo>,</mo><mi>ρ</mi><mo>,</mo><msub><mrow><mi>a</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>a</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><msub><mrow><mi>b</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>b</mi></mrow><mrow

本文论述了一个间接追逐-逃避模型，该模型具有信号依赖性扩散和灵敏度 ut=∇⋅D1(z)∇u-χ∇⋅S1(z)u∇z+uαv-a1-b1u,x∈Ω,t>；0,vt=∇⋅D2(w)∇v+ξ∇⋅S2(w)v∇w+va2-b2v-u,x∈Ω,t>0,wt=Δw+βu-γw,x∈Ω,t>；0,zt=Δz+δv-ρz,x∈Ω,t>；其中参数 χ、ξ、α、β、γ、δ、ρ、a1、a2、b1、b2 为正值，D1(z)、D2(w) 为与信号相关的扩散系数，S1(z)、S2(w) 为非线性灵敏度函数。首先，利用能量估计和莫瑟迭代，我们证明了系统存在唯一的全局有界经典解。此外，我们还研究了全局有界解的渐近稳定问题。最后，我们通过数值模拟验证了我们的理论发现。

引用次数: 0

Higher order asymptotic expansions for the convection–diffusion equation in the Fujita-subcritical case 富士达次临界情况下对流扩散方程的高阶渐近展开式

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications

Pub Date : 2024-11-05 DOI: 10.1016/j.nonrwa.2024.104249

Ryunosuke Kusaba

This paper is devoted to the asymptotic behavior of global solutions to the convection–diffusion equation in the Fujita-subcritical case. We improve the result by Zuazua (1993) and establish higher order asymptotic expansions with decay estimates of the remainders. We also discuss the optimality for the decay rates of the remainders.

本文致力于研究藤田亚临界情况下对流扩散方程全局解的渐近行为。我们改进了 Zuazua (1993) 的结果，建立了带有余数衰减估计的高阶渐近展开。我们还讨论了余数衰减率的最优性。

引用次数: 0

On the spectral stability of periodic waves of the dispersive systems of modified KdV equations 论修正 KdV 方程分散系统周期波的频谱稳定性

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications

Pub Date : 2024-11-04 DOI: 10.1016/j.nonrwa.2024.104250

Sevdzhan Hakkaev , Kadir Şamdanlı

This paper concerns the stability of periodic traveling waves of cnoidal type for the nonlinear dispersive systems. The main objective of the paper is to study their stability with respect to co-periodic perturbations.

本文涉及非线性色散系统的周期行波的稳定性。本文的主要目的是研究它们在共周期扰动下的稳定性。

引用次数: 0

Large-time behavior of solutions to outflow problem of full compressible Navier–Stokes–Korteweg equations 全可压缩 Navier-Stokes-Korteweg 方程流出问题解的大时间行为

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications

Pub Date : 2024-10-30 DOI: 10.1016/j.nonrwa.2024.104248

Yeping Li, Heyu Liu, Rong Yin

In this article, we investigate the large-time behavior of the solution to outflow problem for full compressible Navier–Stokes–Korteweg equations in the one-dimensional half space. The full compressible Navier–Stokes–Korteweg equations model compressible fluids with viscosity, heat-conductivity and internal capillarity, and include the Korteweg stress effects into the dissipative structure of the hyperbolic–parabolic system and turn out to be more complicated than that in the simpler full compressible Navier–Stokes equations. Under some suitable assumptions of the far fields and the boundary values of the density, the velocity and the absolute temperature, the asymptotic stability of the boundary layer, the 3-rarefaction wave, and the superposition of the boundary layer and the 3-rarefaction wave are shown provided that the initial perturbation and the strength of the nonlinear wave are small. The proof is mainly based on

L^{2}

-energy method, some time-decay estimates of the smoothed rarefaction wave and the space-decay estimates of the boundary layer. This can be viewed as the first result about the stability of basic wave patterns for the outflow problem of the full compressible Navier–Stokes–Korteweg equations.

本文研究了一维半空间中全可压缩 Navier-Stokes-Korteweg 方程流出问题解的大时间行为。全可压缩 Navier-Stokes-Korteweg 方程模拟了具有粘性、导热性和内毛细管性的可压缩流体，并在双曲-抛物线系统的耗散结构中包含了 Korteweg 应力效应，因此比简单的全可压缩 Navier-Stokes 方程更为复杂。在远场以及密度、速度和绝对温度的边界值的一些适当假设下，只要初始扰动和非线性波的强度很小，就能证明边界层、3-反褶波以及边界层和 3-反褶波叠加的渐近稳定性。证明主要基于 L2 能量法、平滑稀释波的一些时间衰减估计和边界层的空间衰减估计。这可以看作是关于全可压缩 Navier-Stokes-Korteweg 方程流出问题基本波型稳定性的第一个结果。

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引用次数: 0

Some fixed point results on interpolative metric spaces 关于插值度量空间的一些定点结果

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications

Pub Date : 2024-10-28 DOI: 10.1016/j.nonrwa.2024.104244

Erdal Karapınar , Ravi P. Agarwal

This paper aims to introduce some basic fixed point theorems on interpolative metric space that is a natural extension of standard metric space.

本文旨在介绍插值度量空间的一些基本定点定理，插值度量空间是标准度量空间的自然扩展。

引用次数: 0

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