Nonlinear Analysis-Real World Applications最新文献

英文中文

Undercompressive phase transitions for the model of fluid flows in a nozzle with discontinuous cross-sectional area 具有不连续截面积的喷嘴中流体流动模型的欠压缩相变

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications

Pub Date : 2024-11-16 DOI: 10.1016/j.nonrwa.2024.104260

Duong Xuan Vinh , Mai Duc Thanh , Nguyen Huu Hiep

Undercompressive phase transitions violating Lax shock inequalities in a model of fluid flows in a nozzle with discontinuous cross-section area are studied. The Riemann problem involving phase transitions is considered. Depending on the choice of admissibility criteria suitable for a specific application, one can obtain a Riemann solver, which may involve nonclassical shock wave. The resonance phenomenon is also observed as multiple shocks waves of the same speed can apparently appear in a single solution. The Riemann problem may admit a unique solution in some region, but may have up to three distinct solutions in other regions.

研究了具有不连续横截面积的喷嘴中流体流动模型中违反拉克斯冲击不等式的欠压相变。考虑了涉及相变的黎曼问题。根据适合特定应用的可接受性标准的选择，可以得到黎曼求解器，其中可能涉及非典型冲击波。共振现象也会被观察到，因为在一个求解中会明显出现多个相同速度的冲击波。黎曼问题在某些区域可能只有一个解，但在其他区域可能有多达三个不同的解。

引用次数: 0

Bifurcation results for a class of elliptic equations with a nonlocal reaction term and interior interface boundary conditions 一类具有非局部反应项和内部界面边界条件的椭圆方程的分岔结果

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications

Pub Date : 2024-11-16 DOI: 10.1016/j.nonrwa.2024.104258

Braulio B.V. Maia , Alânnio B. Nóbrega

In this paper, we study a class of elliptic problems with a interior interface condition, which arise in population dynamics. In these problems, each population lives in a subdomain and they interact in a common border, which acts as a geographical barrier. The main novelty in our work is the presence of a nonlocal reaction terms. To obtain our results we employ mainly bifurcation methods.

在本文中，我们研究了一类具有内部界面条件的椭圆问题，这些问题出现在人口动力学中。在这些问题中，每个种群都生活在一个子域中，它们在一个共同边界中相互作用，这个边界就像一个地理屏障。我们工作的主要新颖之处在于非局部反应项的存在。为了获得结果，我们主要采用了分岔方法。

引用次数: 0

Dynamics of an intermittent HIV treatment using piecewise smooth vector fields with two switching manifolds 使用具有两个切换流形的片断平滑矢量场的间歇性艾滋病治疗动力学

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.2024.104256

Tiago Carvalho , Jackson Cunha , Rodrigo Euzébio , Marco Florentino

In this paper we study the dynamics of a piecewise smooth vector field modeling an intermittent human immunodeficiency virus treatment where the patient is recurrently submitted and removed from drug administration. In fact, the protocol says that the drugs are administered when the level of CD4

^{+}

T defense cells is smaller than a fixed number

C_{o f f}^{T}

. When the level of CD4

^{+}

T cells is greater than a fixed number

C_{o n}^{T}

(distinct from

C_{o f f}^{T}

) the drugs are not administered to provide a better recovery from side effects. Moreover, the orbits of the piecewise smooth vector fields are trapped within a compact set, which proves that the protocol controls the disease.

在本文中，我们研究了一个片断平滑矢量场的动力学模型，它模拟了一种间歇性人类免疫缺陷病毒治疗方法，在这种治疗方法中，病人会反复服药和停药。事实上，治疗方案规定，当 CD4+ T 防御细胞的水平小于一个固定的数字 CoffT 时，就会给药。当 CD4+ T 细胞的水平大于一个固定的数字 ConT（与 CoffT 不同）时，则不用药，以便更好地从副作用中恢复过来。此外，片断平滑矢量场的轨道被困在一个紧凑集合内，这证明该方案能控制疾病。

{"title":"Dynamics of an intermittent HIV treatment using piecewise smooth vector fields with two switching manifolds","authors":"Tiago Carvalho , Jackson Cunha , Rodrigo Euzébio , Marco Florentino","doi":"10.1016/j.nonrwa.2024.104256","DOIUrl":"10.1016/j.nonrwa.2024.104256","url":null,"abstract":"<div><div>In this paper we study the dynamics of a piecewise smooth vector field modeling an intermittent human immunodeficiency virus treatment where the patient is recurrently submitted and removed from drug administration. In fact, the protocol says that the drugs are administered when the level of CD4<span><math><msup><mrow></mrow><mrow><mo>+</mo></mrow></msup></math></span> T defense cells is smaller than a fixed number <span><math><msubsup><mrow><mi>C</mi></mrow><mrow><mi>o</mi><mi>f</mi><mi>f</mi></mrow><mrow><mi>T</mi></mrow></msubsup></math></span>. When the level of CD4<span><math><msup><mrow></mrow><mrow><mo>+</mo></mrow></msup></math></span> T cells is greater than a fixed number <span><math><msubsup><mrow><mi>C</mi></mrow><mrow><mi>o</mi><mi>n</mi></mrow><mrow><mi>T</mi></mrow></msubsup></math></span> (distinct from <span><math><msubsup><mrow><mi>C</mi></mrow><mrow><mi>o</mi><mi>f</mi><mi>f</mi></mrow><mrow><mi>T</mi></mrow></msubsup></math></span>) the drugs are not administered to provide a better recovery from side effects. Moreover, the orbits of the piecewise smooth vector fields are trapped within a compact set, which proves that the protocol controls the disease.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"82 ","pages":"Article 104256"},"PeriodicalIF":1.8,"publicationDate":"2024-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142659198","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

On the existence of radial solutions to a nonlinear k-Hessian system with gradient term 论带梯度项的非线性 k-Hessian 系统径向解的存在性

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.2024.104255

Guotao Wang , Zhuobin Zhang , Bashir Ahmad

This paper investigates a nonlinear

k

-Hessian system with gradient term by the monotone iterative method. We obtain the existence criteria for the entire positive radial solution. The estimation of the entire positive bounded radial solution is given in the finite case. The existence of the entire positive blow-up radial solution is also presented in the infinite case. Finally, two examples are given to demonstrate the application of the obtained results.

本文用单调迭代法研究了一个带梯度项的非线性 k-Hessian 系统。我们得到了整个正径向解的存在性准则。在有限情况下，给出了全正有界径向解的估计。在无限情况下，也给出了整个正吹胀径向解的存在性。最后，给出了两个例子来演示所获结果的应用。

引用次数: 0

Global existence and boundedness to an N-D chemotaxis-convection model during tumor angiogenesis 肿瘤血管生成过程中 N-D 趋化-对流模型的全局存在性和有界性

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.2024.104257

Fengxiang Zhao, Jiashan Zheng, Kaiqiang Li

<div><div>In this paper, we consider the following parabolic–parabolic–elliptic system <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><mi>Δ</mi><mi>u</mi><mo>−</mo><mo>∇</mo><mi>⋅</mi><mrow><mo>(</mo><mi>u</mi><mo>∇</mo><mi>v</mi><mo>)</mo></mrow><mo>+</mo><mi>ξ</mi><mo>∇</mo><mi>⋅</mi><mrow><mo>(</mo><mi>u</mi><mo>∇</mo><mi>w</mi><mo>)</mo></mrow><mo>+</mo><mi>a</mi><mi>u</mi><mo>−</mo><mi>μ</mi><msup><mrow><mi>u</mi></mrow><mrow><mi>α</mi></mrow></msup><mo>,</mo></mtd><mtd></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><mi>Δ</mi><mi>v</mi><mo>+</mo><mo>∇</mo><mi>⋅</mi><mrow><mo>(</mo><mi>v</mi><mo>∇</mo><mi>w</mi><mo>)</mo></mrow><mo>−</mo><mi>v</mi><mo>+</mo><mi>u</mi><mo>,</mo></mtd><mtd></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><mn>0</mn><mo>=</mo><mi>Δ</mi><mi>w</mi><mo>−</mo><mi>w</mi><mo>+</mo><mi>u</mi><mo>,</mo></mtd><mtd></mtd><mtd><mi>x</mi><mo>∈</mo><mi>Ω</mi><mo>,</mo><mi>t</mi><mo>></mo><mn>0</mn></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mfenced></math></span></span></span>on a bounded domain <span><math><mrow><mi>Ω</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></mrow></math></span> (<span><math><mrow><mi>N</mi><mo>≥</mo><mn>1</mn></mrow></math></span>) with smooth boundary <span><math><mrow><mi>∂</mi><mi>Ω</mi></mrow></math></span>, where <span><math><mi>μ</mi></math></span>, <span><math><mi>a</mi></math></span>, <span><math><mi>α</mi></math></span> are positive constants and <span><math><mrow><mi>ξ</mi><mo>∈</mo><mi>R</mi></mrow></math></span>. If one of the following cases holds:</div><div>(i) <span><math><mrow><mi>N</mi><mo>≥</mo><mn>4</mn></mrow></math></span> and <span><math><mrow><mi>α</mi><mo>></mo><mfrac><mrow><mn>4</mn><mi>N</mi><mo>−</mo><mn>4</mn><mo>+</mo><mi>N</mi><msqrt><mrow><mn>2</mn><msup><mrow><mi>N</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>−</mo><mn>6</mn><mi>N</mi><mo>+</mo><mn>8</mn></mrow></msqrt></mrow><mrow><mn>2</mn><mi>N</mi></mrow></mfrac></mrow></math></span>;</div><div>(ii) <span><math><mrow><mi>N</mi><mo>=</mo><mn>3</mn></mrow></math></span>, <span><math><mrow><mi>α</mi><mo>></mo><mn>2</mn></mrow></math></span>, for any <span><math><mrow><mi>μ</mi><mo>></mo><mn>0</mn></mrow></math></span> or <span><math><mrow><mi>α</mi><mo>=</mo><mn>2</mn></mrow></math></span>, the index <span><math><mi>μ</mi></math></span> should be suitably big;</div><div>(iii) <span><math><mrow><mi>N</mi><mo>=</mo><mn>2</mn></mrow></math></span>, <span><math><mrow><mi>α</mi><mo>≥</mo><mn>2</mn></mrow></math></span>, for any <span><math><mrow><mi>μ</mi><mo>></mo><mn>0</mn></mrow></math></span>.</div><div>Without any restriction on the index <span><math><mi>ξ</m

本文考虑以下抛物-抛物-椭圆系统 ut=Δu-∇⋅(u∇v)+ξ∇(u⋅∇w)+au-μuα,x∈Ω,t>；0,vt=Δv+∇⋅（v∇w）-v+u,x∈Ω,t>0,0=Δw-w+u,x∈Ω,t>0在具有光滑边界∂Ω的有界域Ω⊂RN（N≥1）上，其中μ、a、α为正常数和ξ∈R。如果以下情况之一成立：(i) N≥4 且 α>4N-4+N2N2-6N+82N；(ii) N=3, α>2，对于任意 μ>0 或 α=2, 索引 μ 应适当大；(iii) N=2, α≥2, 对于任意 μ>0。在不限制指数ξ的情况下，对于任何给定的适当规则的初始数据，相应的诺伊曼初始-边界问题都有唯一的全局有界经典解。

引用次数: 0

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。

{"title":"The matching of two Markus-Yamabe piecewise smooth systems in the plane","authors":"Denis de Carvalho Braga , Fabio Scalco Dias , Jaume Llibre , Luis Fernando Mello","doi":"10.1016/j.nonrwa.2024.104254","DOIUrl":"10.1016/j.nonrwa.2024.104254","url":null,"abstract":"<div><div>A Markus-Yamabe vector field is a smooth vector field in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> having only one equilibrium point and such that the spectrum of its Jacobian matrix at any point of <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> 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 <span><math><mi>p</mi></math></span>: all the orbits tend to <span><math><mi>p</mi></math></span> 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 <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>, <span><math><mrow><mi>n</mi><mo>⩾</mo><mn>3</mn></mrow></math></span>, 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.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"82 ","pages":"Article 104254"},"PeriodicalIF":1.8,"publicationDate":"2024-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142659793","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

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。

{"title":"A general theory for the (s,p)-superposition of nonlinear fractional operators","authors":"Serena Dipierro, Edoardo Proietti Lippi, Caterina Sportelli, Enrico Valdinoci","doi":"10.1016/j.nonrwa.2024.104251","DOIUrl":"10.1016/j.nonrwa.2024.104251","url":null,"abstract":"<div><div>We consider the continuous superposition of operators of the form <span><span><span><math><mrow><msub><mrow><mo>∬</mo></mrow><mrow><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow><mo>×</mo><mrow><mo>(</mo><mn>1</mn><mo>,</mo><mi>N</mi><mo>)</mo></mrow></mrow></msub><msubsup><mrow><mrow><mo>(</mo><mo>−</mo><mi>Δ</mi><mo>)</mo></mrow></mrow><mrow><mi>p</mi></mrow><mrow><mi>s</mi></mrow></msubsup><mspace></mspace><mi>u</mi><mspace></mspace><mi>d</mi><mi>μ</mi><mrow><mo>(</mo><mi>s</mi><mo>,</mo><mi>p</mi><mo>)</mo></mrow><mo>,</mo></mrow></math></span></span></span>where <span><math><mi>μ</mi></math></span> denotes a signed measure over the set <span><math><mrow><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow><mo>×</mo><mrow><mo>(</mo><mn>1</mn><mo>,</mo><mi>N</mi><mo>)</mo></mrow></mrow></math></span>, 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 <span><math><mi>s</mi></math></span> and <span><math><mi>p</mi></math></span>.</div><div>Here we introduce a new framework which is so broad to include, for example, the scenarios of the finite sum of different (in both <span><math><mi>s</mi></math></span> and <span><math><mi>p</mi></math></span>) Laplacians, or of a fractional <span><math><mi>p</mi></math></span>-Laplacian plus a <span><math><mi>p</mi></math></span>-Laplacian, or even combinations involving some fractional Laplacians with the “wrong” sign.</div><div>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.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"82 ","pages":"Article 104251"},"PeriodicalIF":1.8,"publicationDate":"2024-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142659197","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

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

下一页尾页

类型

全部化学•材料生命科学医学物理工程技术环境•农林材料科学地球科学法学管理学化学环境科学与生态学计算机科学教育学经济学农林科学人文科学生物学数学物理与天体物理心理学综合性期刊其他工业工程理学历史学农学文学信息工程

数据库

全部 ACS Publications Elsevier ieeexplore Springer The Royal Society of Chemistry Wiley

期刊

Nonlinear Analysis-Real World Applications

全部 Acc. Chem. Res. ACS Applied Bio Materials ACS Appl. Electron. Mater. ACS Appl. Energy Mater. ACS Appl. Mater. Interfaces ACS Appl. Nano Mater. ACS Appl. Polym. Mater. ACS BIOMATER-SCI ENG ACS Catal. ACS Cent. Sci. ACS Chem. Biol. ACS Chemical Health & Safety ACS Chem. Neurosci. ACS Comb. Sci. ACS Earth Space Chem. ACS Energy Lett. ACS Infect. Dis. ACS Macro Lett. ACS Mater. Lett. ACS Med. Chem. Lett. ACS Nano ACS Omega ACS Photonics ACS Sens. ACS Sustainable Chem. Eng. ACS Synth. Biol. Anal. Chem. BIOCHEMISTRY-US Bioconjugate Chem. BIOMACROMOLECULES Chem. Res. Toxicol. Chem. Rev. Chem. Mater. CRYST GROWTH DES ENERG FUEL Environ. Sci. Technol. Environ. Sci. Technol. Lett. Eur. J. Inorg. Chem. IND ENG CHEM RES Inorg. Chem. J. Agric. Food. Chem. J. Chem. Eng. Data J. Chem. Educ. J. Chem. Inf. Model. J. Chem. Theory Comput. J. Med. Chem. J. Nat. Prod. J PROTEOME RES J. Am. Chem. Soc. LANGMUIR MACROMOLECULES Mol. Pharmaceutics Nano Lett. Org. Lett. ORG PROCESS RES DEV ORGANOMETALLICS J. Org. Chem. J. Phys. Chem. J. Phys. Chem. A J. Phys. Chem. B J. Phys. Chem. C J. Phys. Chem. Lett. Analyst Anal. Methods Biomater. Sci. Catal. Sci. Technol. Chem. Commun. Chem. Soc. Rev. CHEM EDUC RES PRACT CRYSTENGCOMM Dalton Trans. Energy Environ. Sci. ENVIRON SCI-NANO ENVIRON SCI-PROC IMP ENVIRON SCI-WAT RES Faraday Discuss. Food Funct. Green Chem. Inorg. Chem. Front. Integr. Biol. J. Anal. At. Spectrom. J. Mater. Chem. A J. Mater. Chem. B J. Mater. Chem. C Lab Chip Mater. Chem. Front. Mater. Horiz. MEDCHEMCOMM Metallomics Mol. Biosyst. Mol. Syst. Des. Eng. Nanoscale Nanoscale Horiz. Nat. Prod. Rep. New J. Chem. Org. Biomol. Chem. Org. Chem. Front. PHOTOCH PHOTOBIO SCI PCCP Polym. Chem.

﹀