Nonlinear Analysis-Real World Applications最新文献

英文中文

Existence, uniqueness and regularity of nonequilibrium steady states in multispecies ion transport 多态离子输运非平衡态的存在性、唯一性和规律性

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications

Pub Date : 2026-01-03 DOI: 10.1016/j.nonrwa.2025.104598

Fizay-Noah Lee

We consider the steady state Nernst-Planck system for multiple species with nonequilibrium boundary conditions, describing electrodiffusion of ions or charged particles. We show the existence and regularity of solutions and also establish a sufficient condition for uniqueness.

我们考虑具有非平衡边界条件的多物种稳态能-普朗克系统，描述离子或带电粒子的电扩散。给出了解的存在性和正则性，并给出了解的唯一性的充分条件。

引用次数: 0

Modelling spatiotemporal prey-predator interactions incorporating fear effect and variable handling time 包含恐惧效应和可变处理时间的时空捕食者相互作用建模

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications

Pub Date : 2025-12-30 DOI: 10.1016/j.nonrwa.2025.104582

Shri Harine P, Ankit Kumar

Classical prey-predator models often assume that the predator’s handling time is constant. However, in real ecosystems, a predator’s handling time can vary due to several biotic and abiotic factors. Based on this, we modified the Holling Type II functional response by incorporating a nonlinear handling time function. Fear in prey can lead to notable population reductions, predominantly through decreased foraging and reproduction. Considering these essential factors, we developed a prey-predator model encompassing temporal dynamics, self-diffusion and cross-diffusion. For the temporal model, we investigated the non-negativity, boundedness, and stability conditions of the existing steady states. Furthermore, bifurcations such as Hopf, transcritical, and Bautin were observed with respect to parameters like the cost of fear and the maximal achievable handling time. Bistability behaviour was observed through the analysis involving these two parameters. Sensitivity analysis was conducted to understand the influence of parameters contributing to the coexistence of prey and predator populations. Stability conditions for both spatiotemporal models (with self and cross-diffusion) were established, highlighting the role of cross-diffusion coefficients in inducing Turing instability and pattern formation. Spatial patterns such as spots and vertically aligned chains were observed. An increase in the maximal achievable handling time was found to support prey occupation in high-density regions, promoting coexistence, whereas excessively high maximal handling time can lead to predator extinction.

经典的捕食者-猎物模型通常假设捕食者的处理时间是恒定的。然而，在真实的生态系统中，掠食者的处理时间可能会因几种生物和非生物因素而变化。在此基础上，通过引入非线性处理时间函数对Holling II型函数响应进行了修正。对猎物的恐惧会导致显著的种群减少，主要是通过减少觅食和繁殖。考虑到这些重要因素，我们建立了一个包含时间动力学、自扩散和交叉扩散的捕食者-捕食者模型。对于时间模型，我们研究了现有稳态的非负性、有界性和稳定性条件。此外，在恐惧成本和最大可实现处理时间等参数方面，观察到Hopf、跨临界和Bautin等分岔。通过对这两个参数的分析，观察到双稳性行为。通过敏感性分析了解各参数对食饵种群和捕食者种群共存的影响。建立了两种时空模型（自扩散和交叉扩散）的稳定性条件，突出了交叉扩散系数在诱导图灵不稳定性和模式形成中的作用。观察到斑点和垂直排列的链等空间模式。在高密度区域，最大可达处理时间的增加有利于猎物的占领，促进共存，而过大的最大处理时间可能导致捕食者灭绝。

{"title":"Modelling spatiotemporal prey-predator interactions incorporating fear effect and variable handling time","authors":"Shri Harine P, Ankit Kumar","doi":"10.1016/j.nonrwa.2025.104582","DOIUrl":"10.1016/j.nonrwa.2025.104582","url":null,"abstract":"<div><div>Classical prey-predator models often assume that the predator’s handling time is constant. However, in real ecosystems, a predator’s handling time can vary due to several biotic and abiotic factors. Based on this, we modified the Holling Type II functional response by incorporating a nonlinear handling time function. Fear in prey can lead to notable population reductions, predominantly through decreased foraging and reproduction. Considering these essential factors, we developed a prey-predator model encompassing temporal dynamics, self-diffusion and cross-diffusion. For the temporal model, we investigated the non-negativity, boundedness, and stability conditions of the existing steady states. Furthermore, bifurcations such as Hopf, transcritical, and Bautin were observed with respect to parameters like the cost of fear and the maximal achievable handling time. Bistability behaviour was observed through the analysis involving these two parameters. Sensitivity analysis was conducted to understand the influence of parameters contributing to the coexistence of prey and predator populations. Stability conditions for both spatiotemporal models (with self and cross-diffusion) were established, highlighting the role of cross-diffusion coefficients in inducing Turing instability and pattern formation. Spatial patterns such as spots and vertically aligned chains were observed. An increase in the maximal achievable handling time was found to support prey occupation in high-density regions, promoting coexistence, whereas excessively high maximal handling time can lead to predator extinction.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"91 ","pages":"Article 104582"},"PeriodicalIF":1.8,"publicationDate":"2025-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145885263","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

Limit cycles of 3D piecewise linear systems with concurrent tangent lines 具有并行切线的三维分段线性系统的极限环

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications

Pub Date : 2025-12-30 DOI: 10.1016/j.nonrwa.2025.104587

Samuel Carlos S. Ferreira , Bruno R. Freitas , João Carlos R. Medrado

We analyze a 3D discontinuous piecewise linear dynamical system,

Z = (X, Y)

, with a plane Σ as its switching manifold, which contains two-fold intersection straight lines. The eigenvalues associated with DX and DY are composed of one real eigenvalue and a pair of complex conjugate eigenvalues. A canonical form is obtained using changes in variables and parameters. Two half-return Poincaré maps are generated from two closing equations derived from exponential matrices, leading to a displacement map Δ. Using the Weierstrass Preparation Theorem, we prove the existence of a subclass within this family that admits at least one large amplitude limit cycle. When the real part of the complex eigenvalues is non-zero, the restriction of Δ to space W, formed by the concatenation of bi-dimensional focal planes associated with the complex eigenvalues, can have up to three positive zeros on W ∩ Σ, corresponding to three large amplitude limit cycles. We provide examples with one, two, and three limit cycles.

我们分析了一个三维不连续分段线性动力系统Z=(X，Y)，它的切换流形是一个平面Σ，它包含两条相交的直线。与DX和DY相关的特征值由一个实特征值和一对复共轭特征值组成。通过变量和参数的变化得到标准形式。由指数矩阵导出的两个闭合方程生成两个半返回poincar图，从而生成位移图Δ。利用Weierstrass准备定理，证明了该类中存在一个至少有一个大振幅极限环的子类。当复特征值实部不为零时，由与复特征值相关的二维焦平面串接形成的Δ对空间W的限制，在W∩Σ上最多可以有三个正零，对应三个大振幅极限环。我们提供了一个、两个和三个极限环的例子。

{"title":"Limit cycles of 3D piecewise linear systems with concurrent tangent lines","authors":"Samuel Carlos S. Ferreira , Bruno R. Freitas , João Carlos R. Medrado","doi":"10.1016/j.nonrwa.2025.104587","DOIUrl":"10.1016/j.nonrwa.2025.104587","url":null,"abstract":"<div><div>We analyze a 3D discontinuous piecewise linear dynamical system, <span><math><mrow><mi>Z</mi><mo>=</mo><mrow><mo>(</mo><mi>X</mi><mo>,</mo><mi>Y</mi><mo>)</mo></mrow></mrow></math></span>, with a plane Σ as its switching manifold, which contains two-fold intersection straight lines. The eigenvalues associated with <em>DX</em> and <em>DY</em> are composed of one real eigenvalue and a pair of complex conjugate eigenvalues. A canonical form is obtained using changes in variables and parameters. Two half-return Poincaré maps are generated from two closing equations derived from exponential matrices, leading to a displacement map Δ. Using the Weierstrass Preparation Theorem, we prove the existence of a subclass within this family that admits at least one large amplitude limit cycle. When the real part of the complex eigenvalues is non-zero, the restriction of Δ to space <em>W</em>, formed by the concatenation of bi-dimensional focal planes associated with the complex eigenvalues, can have up to three positive zeros on <em>W</em> ∩ Σ, corresponding to three large amplitude limit cycles. We provide examples with one, two, and three limit cycles.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"91 ","pages":"Article 104587"},"PeriodicalIF":1.8,"publicationDate":"2025-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145885261","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

Quasilinear double phase problem on the whole space 全空间上的拟线性双相问题

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications

Pub Date : 2025-12-27 DOI: 10.1016/j.nonrwa.2025.104586

Chun-Bo Lian , Bin Ge , Qing-Hai Cao , Qing-Mei Zhou

In the present paper, we study the existence of a radial sign-changing solution to a class of quasilinear double phase problems in

R^{N}

. Without assuming the usual strictly increasing condition on

\frac{f (x, t)}{{| t |}^{q - 1}}

, we provide some sufficient conditions under which the above problems have at least one sign-changing radial ground states solution. We generalize the result of Liu and Dai [J. Math. Phys. 61(2020) 091508].

本文研究了一类拟线性双相问题径向变符号解的存在性。在不假设f(x,t)|t|q−1的通常严格递增条件的情况下，我们给出了上述问题至少有一个变号径向基态解的几个充分条件。我们推广了Liu和Dai的结果[J]。数学。物理学报，61(2020):091508。

引用次数: 0

The pointwise estimates for the incompressible Navier–Stokes–Maxwell system with Ohm’s law 用欧姆定律对不可压缩Navier-Stokes-Maxwell系统的逐点估计

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications

Pub Date : 2025-12-25 DOI: 10.1016/j.nonrwa.2025.104572

Guanghui Wang , Mingying Zhong

The pointwise estimates of the Green’s function for the incompressible Navier–Stokes–Maxwell system with Ohm’s law in 3D are given in this paper. It is shown that the Green’s function consists of the heat kernels, the diffusive waves at low-frequency, the hyperbolic waves at high-frequency with time decaying exponentially, and the singular short waves. In addition, we establish the pointwise estimate of the global solution to the nonlinear incompressible Navier–Stokes–Maxwell system with Ohm’s law based on the Green’s function. To solve the new problem that the nonlinear terms contain the nonlocal operators

\nabla d i v Δ^{- 1}

and

\nabla \times \nabla \times Δ^{- 1}

which arise from the fluid-electromagnetic decomposition, we develop some new estimates of the nonlocal operators.

本文给出了三维中具有欧姆定律的不可压缩Navier-Stokes-Maxwell系统的Green函数的点态估计。结果表明，格林函数由热核、低频扩散波、高频随时间指数衰减的双曲波和奇异短波组成。此外，基于格林函数，利用欧姆定律建立了非线性不可压缩Navier-Stokes-Maxwell系统全局解的点估计。为了解决由流体电磁分解引起的非线性项包含非局部算子∇divΔ−1和∇×∇×Δ−1的新问题，我们提出了一些新的非局部算子估计。

{"title":"The pointwise estimates for the incompressible Navier–Stokes–Maxwell system with Ohm’s law","authors":"Guanghui Wang , Mingying Zhong","doi":"10.1016/j.nonrwa.2025.104572","DOIUrl":"10.1016/j.nonrwa.2025.104572","url":null,"abstract":"<div><div>The pointwise estimates of the Green’s function for the incompressible Navier–Stokes–Maxwell system with Ohm’s law in 3D are given in this paper. It is shown that the Green’s function consists of the heat kernels, the diffusive waves at low-frequency, the hyperbolic waves at high-frequency with time decaying exponentially, and the singular short waves. In addition, we establish the pointwise estimate of the global solution to the nonlinear incompressible Navier–Stokes–Maxwell system with Ohm’s law based on the Green’s function. To solve the new problem that the nonlinear terms contain the nonlocal operators <span><math><mrow><mi>∇</mi><mrow><mrow><mi>d</mi></mrow><mi>i</mi><mi>v</mi></mrow><mstyle><mi>Δ</mi></mstyle><msup><mrow></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></math></span> and <span><math><mrow><mi>∇</mi><mo>×</mo><mi>∇</mi><mo>×</mo><mstyle><mi>Δ</mi></mstyle><msup><mrow></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></math></span> which arise from the fluid-electromagnetic decomposition, we develop some new estimates of the nonlocal operators.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"91 ","pages":"Article 104572"},"PeriodicalIF":1.8,"publicationDate":"2025-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145841570","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

Long time behavior for a Lotka-Volterra competition diffusion system in periodic medium 周期介质中Lotka-Volterra竞争扩散系统的长时间行为

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications

Pub Date : 2025-12-24 DOI: 10.1016/j.nonrwa.2025.104560

Liyan Pang , Xiao Zhang

In this paper, the long time behavior for a two-species Lotka-Volterra reaction-diffusion system with strong competition in a periodic medium is concerned. We prove that under the compactly supported initial values, the solutions of Cauchy problem converge to a pair of diverging pulsating fronts. Further, we obtain a sufficient condition for solutions to converge to 1 with two different speeds to the left and right. Due to the spatial heterogeneity, the pulsating fronts depend on its direction and any pair of rightward and leftward wave speeds be asymmetrical. Therefore, our analysis mainly depends on constructing appropriate super- and subsolutions and using the comparison principle and asymptotic behavior of bistable pulsating fronts.

本文研究了周期介质中具有强竞争的两种Lotka-Volterra反应扩散系统的长时间行为。证明了在紧支持初值条件下，柯西问题的解收敛于一对发散的脉动锋。进一步，我们得到了解在左右两种不同速度下收敛于1的充分条件。由于脉动锋的空间非均质性，其方向与脉动锋有关，任意一对左右波速都是不对称的。因此，我们的分析主要依赖于构造合适的上解和子解，并利用双稳脉冲锋的比较原理和渐近特性。

引用次数: 0

Limit cycles on rigid piecewise smooth dynamical systems governed by even polynomials 偶多项式控制的刚性分段光滑动力系统的极限环

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications

Pub Date : 2025-12-24 DOI: 10.1016/j.nonrwa.2025.104581

L.F. Gonçalves, A.C.T. Sánchez, D.J. Tonon

In this work, we establish an upper bound for the number of crossing limit cycles in a class of piecewise smooth dynamical systems. The system is formed by a linear rigid center and a rigid center governed by a homogeneous polynomial of even degree n, separated by the straight line

x = 0

. Our results complement the work of [1], which addressed the odd-degree case. Specifically, we prove that if the parameters satisfy

d_{2} = M_{2}

, the system admits at most

(n - 2) / 2

limit cycles. Furthermore, for the specific case

n = 4

, assuming d₂ ≠ M₂ and

d_{2} = 0

, we show that the system has at most one limit cycle, and this upper bound is attained. This study advances the analysis of this family of systems by covering the even-degree case under certain conditions on the affine transformation.

本文建立了一类分段光滑动力系统交叉极限环数的上界。系统由一个线性刚心和一个由偶数n次齐次多项式控制的刚心组成，由直线x=0隔开。我们的结果补充了b[1]的工作，b[1]处理了奇度情况。具体地说，我们证明了当参数满足d2=M2时，系统最多允许(n−2)/2个极限环。进一步，对于n=4的特殊情况，假设d2 ≠ M2， d2=0，我们证明了系统最多有一个极限环，并且得到了这个上限。本研究通过涵盖仿射变换在一定条件下的偶次情况，推进了这类系统的分析。

{"title":"Limit cycles on rigid piecewise smooth dynamical systems governed by even polynomials","authors":"L.F. Gonçalves, A.C.T. Sánchez, D.J. Tonon","doi":"10.1016/j.nonrwa.2025.104581","DOIUrl":"10.1016/j.nonrwa.2025.104581","url":null,"abstract":"<div><div>In this work, we establish an upper bound for the number of crossing limit cycles in a class of piecewise smooth dynamical systems. The system is formed by a linear rigid center and a rigid center governed by a homogeneous polynomial of even degree <em>n</em>, separated by the straight line <span><math><mrow><mi>x</mi><mo>=</mo><mn>0</mn></mrow></math></span>. Our results complement the work of [1], which addressed the odd-degree case. Specifically, we prove that if the parameters satisfy <span><math><mrow><msub><mi>d</mi><mn>2</mn></msub><mo>=</mo><msub><mi>M</mi><mn>2</mn></msub></mrow></math></span>, the system admits at most <span><math><mrow><mo>(</mo><mi>n</mi><mo>−</mo><mn>2</mn><mo>)</mo><mo>/</mo><mn>2</mn></mrow></math></span> limit cycles. Furthermore, for the specific case <span><math><mrow><mi>n</mi><mo>=</mo><mn>4</mn></mrow></math></span>, assuming <em>d</em><sub>2</sub> ≠ <em>M</em><sub>2</sub> and <span><math><mrow><msub><mi>d</mi><mn>2</mn></msub><mo>=</mo><mn>0</mn></mrow></math></span>, we show that the system has at most one limit cycle, and this upper bound is attained. This study advances the analysis of this family of systems by covering the even-degree case under certain conditions on the affine transformation.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"91 ","pages":"Article 104581"},"PeriodicalIF":1.8,"publicationDate":"2025-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145841571","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

Seasonal dynamics and control of malaria: A non-autonomous model incorporating vaccination and drug resistance 季节性动态和疟疾控制：一个包含疫苗接种和耐药性的非自治模型

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications

Pub Date : 2025-12-24 DOI: 10.1016/j.nonrwa.2025.104584

Ifeanyi Sunday Onah

This study develops and analyzes a seasonally forced malaria transmission model that incorporates vaccination, treatment, and the emergence of drug-resistant parasite strains. Using the periodic next-generation approach, we derive the vaccination-adjusted basic reproduction number R_v and establish conditions for the stability of the disease-free periodic solution. When R_v < 1, we show that malaria cannot persist and the disease-free state is globally asymptotically stable. Conversely, for R_v > 1, the infection is uniformly persistent and the system admits at least one positive T-periodic solution. A reduced autonomous version of the model reveals biologically interpretable thresholds for the dominance of either sensitive or resistant strains as well as coexistence scenarios. The model is calibrated using monthly malaria case data from Nigeria (2018–2024). The estimated reproduction number remains consistently above unity, indicating that malaria transmission is sustained under current intervention levels. Numerical simulations confirm these analytical results and illustrate the influence of vaccination coverage and drug resistance on long-term disease dynamics. Our findings highlight the need for strengthened intervention strategies to reduce R_v below one and interrupt sustained transmission.

本研究开发并分析了一个季节性强迫疟疾传播模型，其中包括疫苗接种、治疗和耐药寄生虫菌株的出现。利用周期新一代方法，导出了接种调整后的基本繁殖数Rv，并建立了无病周期溶液稳定的条件。当Rv <； 1时，我们证明疟疾不能持续存在，无病状态是全局渐近稳定的。相反，对于Rv >； 1，感染是一致持续的，并且系统允许至少一个正t周期解。该模型的简化自主版本揭示了敏感或耐药菌株的优势以及共存情景的生物学可解释阈值。该模型使用尼日利亚每月疟疾病例数据（2018-2024年）进行校准。估计的繁殖数始终高于1，这表明在目前的干预水平下，疟疾传播仍在继续。数值模拟证实了这些分析结果，并说明了疫苗接种覆盖率和耐药性对长期疾病动态的影响。我们的研究结果强调需要加强干预策略，以将Rv降低到1以下并中断持续传播。

{"title":"Seasonal dynamics and control of malaria: A non-autonomous model incorporating vaccination and drug resistance","authors":"Ifeanyi Sunday Onah","doi":"10.1016/j.nonrwa.2025.104584","DOIUrl":"10.1016/j.nonrwa.2025.104584","url":null,"abstract":"<div><div>This study develops and analyzes a seasonally forced malaria transmission model that incorporates vaccination, treatment, and the emergence of drug-resistant parasite strains. Using the periodic next-generation approach, we derive the vaccination-adjusted basic reproduction number <em>R<sub>v</sub></em> and establish conditions for the stability of the disease-free periodic solution. When <em>R<sub>v</sub></em> < 1, we show that malaria cannot persist and the disease-free state is globally asymptotically stable. Conversely, for <em>R<sub>v</sub></em> > 1, the infection is uniformly persistent and the system admits at least one positive <em>T</em>-periodic solution. A reduced autonomous version of the model reveals biologically interpretable thresholds for the dominance of either sensitive or resistant strains as well as coexistence scenarios. The model is calibrated using monthly malaria case data from Nigeria (2018–2024). The estimated reproduction number remains consistently above unity, indicating that malaria transmission is sustained under current intervention levels. Numerical simulations confirm these analytical results and illustrate the influence of vaccination coverage and drug resistance on long-term disease dynamics. Our findings highlight the need for strengthened intervention strategies to reduce <em>R<sub>v</sub></em> below one and interrupt sustained transmission.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"91 ","pages":"Article 104584"},"PeriodicalIF":1.8,"publicationDate":"2025-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145841572","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

Describing smooth small-data solutions to a quasilinear hyperbolic-parabolic system by W1,p energy analysis 用W1，p能量分析描述拟线性双曲抛物型系统的光滑小数据解

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications

Pub Date : 2025-12-24 DOI: 10.1016/j.nonrwa.2025.104580

Leander Claes , Michael Winkler

<div><div>In bounded <em>n</em>-dimensional domains with <em>n</em> ≥ 1, this manuscript examines an initial-boundary value problem for the system<span><span><span><math><mtable><mtr><mtd><mrow><mo>{</mo><mtable><mtr><mtd><mrow><msub><mi>u</mi><mrow><mi>t</mi><mi>t</mi></mrow></msub><mo>=</mo><mi>∇</mi><mo>·</mo><mrow><mo>(</mo><mi>γ</mi><mrow><mo>(</mo><mstyle><mi>Θ</mi></mstyle><mo>)</mo></mrow><mi>∇</mi><msub><mi>u</mi><mi>t</mi></msub><mo>)</mo></mrow><mo>+</mo><mi>a</mi><mi>∇</mi><mo>·</mo><mrow><mo>(</mo><mi>γ</mi><mrow><mo>(</mo><mstyle><mi>Θ</mi></mstyle><mo>)</mo></mrow><mi>∇</mi><mi>u</mi><mo>)</mo></mrow><mo>+</mo><mi>∇</mi><mo>·</mo><mi>f</mi><mrow><mo>(</mo><mstyle><mi>Θ</mi></mstyle><mo>)</mo></mrow><mo>,</mo></mrow></mtd></mtr><mtr><mtd><mrow><msub><mstyle><mi>Θ</mi></mstyle><mi>t</mi></msub><mo>=</mo><mi>D</mi><mstyle><mi>Δ</mi></mstyle><mstyle><mi>Θ</mi></mstyle><mo>+</mo><mstyle><mi>Γ</mi></mstyle><mrow><mo>(</mo><mstyle><mi>Θ</mi></mstyle><mo>)</mo></mrow><msup><mrow><mo>|</mo><mi>∇</mi><msub><mi>u</mi><mi>t</mi></msub><mo>|</mo></mrow><mn>2</mn></msup><mo>+</mo><mi>F</mi><mrow><mo>(</mo><mstyle><mi>Θ</mi></mstyle><mo>)</mo></mrow><mo>·</mo><mi>∇</mi><msub><mi>u</mi><mi>t</mi></msub><mo>,</mo></mrow></mtd></mtr></mtable></mrow></mtd></mtr></mtable></math></span></span></span>which in the case <span><math><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow></math></span> and with <em>γ</em> ≡ Γ as well as <em>f</em> ≡ <em>F</em> reduces to the classical model for the evolution of displacement and temperatures in thermoviscoelasticity. Unlike in previous related studies, the focus here is on situations in which besides <em>f</em> and <em>F</em>, also the core ingredients <em>γ</em> and Γ may depend on the temperature variable Θ. Firstly, a statement on local existence of classical solutions is derived for arbitrary <em>a</em> > 0, <em>D</em> > 0 as well as 0 < <em>γ</em> ∈ <em>C</em><sup>2</sup>([0, ∞)) and 0 ≤ Γ ∈ <em>C</em><sup>1</sup>([0, ∞)), for functions <span><math><mrow><mi>f</mi><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><msup><mi>R</mi><mi>n</mi></msup><mo>)</mo></mrow></mrow></math></span> and <span><math><mrow><mi>F</mi><mo>∈</mo><msup><mi>C</mi><mn>1</mn></msup><mrow><mo>(</mo><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mi>∞</mi><mo>)</mo></mrow><mo>;</mo><msup><mi>R</mi><mi>n</mi></msup><mo>)</mo></mrow></mrow></math></span> with <span><math><mrow><mi>F</mi><mo>(</mo><mn>0</mn><mo>)</mo><mo>=</mo><mn>0</mn></mrow></math></span>, and for suitably regular initial data of arbitrary size. Secondly, it is seen that under an additional assumption on smallness of <em>a, f</em>′ and <em>F</em>, as well as on the deviation of the initial data from the constant state given by <span><math><mrow><mi>u</mi><mo>=</mo><mn>0</mn></mrow></math></span> and <span><math><mrow><mstyle><mi>Θ</mi></mstyle><mo>=</mo><msub><mstyle><mi>Θ</mi></mstyle><mi>★</mi>

在有界与n n维域 ≥ 1,这手稿检查系统的初边值问题{utt =∇·(γ(Θ)∇ut) +一个∇·(γ(Θ)∇u) +∇·f(Θ)Θt = DΔΘ+Γ(Θ)|∇ut | 2 + f(Θ)·∇ut,对于n = 1和γ ≡ Γ以及f ≡ f减少的经典模型的进化在thermoviscoelasticity位移和温度。与以往的相关研究不同，这里的重点是除了f和f之外，核心成分γ和Γ也可能取决于温度变量Θ的情况。首先,声明对当地古典解的存在性推导出任意一个 祝辞 0 D 祝辞 0 0 & lt; γ ∈ C2([0,∞))和0 ≤ Γ ∈ C1([0,∞)),函数f∈C2([0,∞);Rn), F∈C1([0,∞)；Rn)， F(0)=0，对于任意大小的适当规则初始数据。其次，我们可以看到，在附加假设a， f '和f的小性，以及初始数据与任意固定的Θ - ≥ 0给出的u=0和Θ=Θ★的恒定状态的偏差下，在凸域上，这些解在时间上实际上是全局的，并且具有∇ut，∇u和∇Θ在Lp中呈指数级快速衰减的性质。这是通过在Lp空间中检测涉及这些梯度范数的泛函的合适耗散性质来实现的。

引用次数: 0

Mathematical analysis of a levitation model 悬浮模型的数学分析

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications

Pub Date : 2025-12-23 DOI: 10.1016/j.nonrwa.2025.104573

Rafael Muñoz-Sola

The aim of this paper is to study a model of electromagnetic levitation for a metallic rigid body. The model is constituted by the transient linear model of eddy currents under the hypothesis of axisymmetry, written in terms of a magnetic potential vector, coupled with an ODE which governs the vertical motion of the body. The electromagnetic model is a parabolic-elliptic PDE which parabolicity region is the position occupied by the body, which changes with time. Besides, Lorentz force appears in the RHS of the ODE. Thus, the model exhibits a coupling of geometrical nature. We establish the existence and uniqueness of solution of the coupled problem and we study its maximally defined solution. In particular, we prove that a blow-up of the velocity of the body cannot happen. Our techniques involve: a reformulation of the coupled problem as a causal differential equation, an adaptation of the theory about this kind of equations and a result of locally Lipschitz dependence of the magnetic potential vector with respect to the velocity of the body.

本文的目的是研究金属刚体的电磁悬浮模型。该模型是在轴对称假设下涡流的瞬态线性模型，用磁势向量表示，加上控制物体垂直运动的ODE。电磁模型为抛物-椭圆偏微分方程，抛物区域为物体所占位置，抛物区域随时间变化。此外，洛伦兹力出现在ODE的RHS中。因此，该模型表现出几何性质的耦合。建立了该耦合问题解的存在唯一性，并研究了其最大定义解。特别地，我们证明了物体的速度不可能突然增大。我们的技术包括：耦合问题作为因果微分方程的重新表述，关于这类方程的理论的改编，以及磁势矢量相对于物体速度的局部利普希茨依赖的结果。

引用次数: 0

首页上一页

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.

﹀