Nonlinear Analysis-Real World Applications最新文献

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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

Approximation theorem of quaternion-valued almost periodic functions of two variables 二变量四元值几乎周期函数的近似定理

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications

Pub Date : 2024-10-25 DOI: 10.1016/j.nonrwa.2024.104245

Chao Wang , Ling Guo , Ravi P. Agarwal

In this paper, the quaternion Fourier-Stieltjes transform of two variables is studied. By orthogonal-split method, some fundamental properties of the quaternion-valued almost periodic functions of two variables are obtained. Through introducing the almost periodic approximation via quaternion Fourier-Stieltjes integrals, we establish the quaternion orthogonal-split mean-value theorem. Finally, the approximation theorem of quaternion-valued almost periodic functions of two variables is established.

本文研究了两变量的四元数傅里叶-斯蒂尔杰斯变换。通过正交拆分方法，得到了双变量的四元数值近周期函数的一些基本性质。通过引入四元数 Fourier-Stieltjes 积分的近周期近似，我们建立了四元数正交分裂均值定理。最后，建立了双变量四元数值近似周期函数的近似定理。

引用次数: 0

Local in time solution to an integro-differential system for motion with large deformations and defects 大变形和缺陷运动积分微分系统的局部时间解法

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications

Pub Date : 2024-10-22 DOI: 10.1016/j.nonrwa.2024.104231

Abramo Agosti , Michel Frémond

In this paper we consider and generalize a model, recently proposed and analytically investigated in its quasi-stationary approximation by the authors and a co-author, for the motion of a medium with large deformations and conditional compatibility, with occurrence of defects when the magnitude of an internal force is above a given threshold. The model takes the form of a system of integro-differential coupled equations, expressed in terms of the stretch and the rotation tensors variables. Here, its derivation is generalized to consider mixed boundary conditions, which may represent a wider range of physical applications then the case with Dirichlet boundary conditions considered in our previous contribution. This also introduces nontrivial technical difficulties in the theoretical framework, related to the definition and the regularity of the solutions of elliptic operators with mixed boundary conditions. As a novel contribution, we develop the analysis of the fully non-stationary version of the system where we consider inertia. In this context, we prove the existence of a local in time weak solution in three space dimensions, employing techniques from PDEs and convex analysis.

在本文中，我们考虑并概括了作者和一位合著者最近提出并分析研究的准稳态近似模型，该模型适用于具有大变形和条件兼容性的介质运动，当内力的大小超过给定阈值时会出现缺陷。该模型采用积分微分耦合方程组的形式，用拉伸和旋转张量变量表示。在此，我们对其推导进行了概括，以考虑混合边界条件，这与我们之前的研究中考虑的迪里希特边界条件相比，可能代表了更广泛的物理应用。这也在理论框架中引入了与混合边界条件下椭圆算子解的定义和正则性有关的非难技术难题。作为一项新贡献，我们在考虑惯性的情况下，对系统的完全非稳态版本进行了分析。在此背景下，我们运用 PDEs 和凸分析技术，证明了在三维空间中存在局部时间弱解。

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引用次数: 0

Persistence and zero-Hopf equilibrium in the tritrophic food chain model with Holling functional response 具有霍林功能响应的三营养食物链模型中的持久性和零霍普夫平衡

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications

Pub Date : 2024-10-19 DOI: 10.1016/j.nonrwa.2024.104232

Víctor Castellanos , Jaume Llibre

In this paper, we analyze the persistence of three species in a three-level food chain model. We characterize when such a model exhibits a zero-Hopf equilibrium point and show that it is possible only if the functional responses in the model are of type Holling III or IV.

本文分析了三级食物链模型中三个物种的持久性。我们描述了这种模型何时会出现零霍普夫平衡点，并证明只有当模型中的功能反应属于霍林 III 型或 IV 型时，才有可能出现零霍普夫平衡点。

引用次数: 0

Effects of marine reserve creation in single species and prey–predator models 在单一物种和猎物-食肉动物模型中建立海洋保护区的影响

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications

Pub Date : 2024-10-10 DOI: 10.1016/j.nonrwa.2024.104230

Aleksander Ćwiszewski , Sławomir Plaskacz

Implementations of marine protected areas (MPA’s) for over-exploited single species fisheries and prey–predator models with environment capacity are studied. The situations when fishing effort reaches the extinction threshold that fits over-exploited open-access fisheries are considered. The discrepancy for single-species and prey–predator models in the context of food security is obtained. Due quantitative indicators for biodiversity and food security are introduced and analyzed.

研究了针对过度开发的单一物种渔业和具有环境容量的猎物-食肉动物模型的海洋保护区（MPA）的实施情况。考虑了捕捞强度达到灭绝阈值的情况，该阈值适合过度开发的开放式渔业。得出了单一物种模型和捕食-掠食者模型在粮食安全方面的差异。引入并分析了生物多样性和粮食安全的适当量化指标。

引用次数: 0

A simple proof of uniqueness for the nonlocal positive solutions 非局部正解唯一性的简单证明

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications

Pub Date : 2024-10-10 DOI: 10.1016/j.nonrwa.2024.104233

Ming-Ming Fan, Jian-Wen Sun

In this paper, we prove a general uniqueness result for the positive solution of nonlocal dispersal equations. Our simple and elementary proof simplifies previously known proofs based on eigenvalue theory and solution estimates.

在本文中，我们证明了非局部分散方程正解的一般唯一性结果。我们简单而基本的证明简化了之前已知的基于特征值理论和解估计的证明。

引用次数: 0

Dynamic bifurcation of nonautonomous evolution equations under Landesman–Lazer condition with cohomology methods 兰德斯曼-拉泽尔条件下非自治演化方程的动态分岔与同调方法

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications

Pub Date : 2024-10-05 DOI: 10.1016/j.nonrwa.2024.104228

Chunqiu Li, Jintao Wang

In this article we study the dynamic bifurcation of nonautonomous evolution equations by using cohomology methods. First, we construct a homotopy equivalence relation between the nonautonomous system and a product flow. Then, we slightly extend some continuation theorems on bifurcations for autonomous equations, and prove some new cohomology consequences on the reduced singular groups. Based on this homotopy equivalence relation and these conclusions, we establish some typical results on the dynamic bifurcation from infinity of the abstract nonautonomous evolution equation. Finally, we consider the parabolic equation

u_{t} - Δ u = λ u + f (x, u) + g (x, t)

associated with the Dirichlet boundary condition, where

f (x, u)

satisfies the appropriate Landesman–Lazer type condition. Some new results on the dynamical behaviors of this equation near resonance of the equation are derived.

本文利用同调方法研究了非自治演化方程的动态分岔。首先，我们构建了非自治系统与乘积流之间的同调等价关系。然后，我们略微扩展了一些关于自主方程分岔的延续定理，并证明了一些关于还原奇异群的新同调后果。基于这种同调等价关系和这些结论，我们建立了抽象非自治演化方程的无穷动态分岔的一些典型结果。最后，我们考虑了与迪里夏特边界条件相关的抛物方程 ut-Δu=λu+f(x,u)+g(x,t) ，其中 f(x,u) 满足适当的 Landesman-Lazer 类型条件。推导出了该方程在共振附近的动力学行为的一些新结果。

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引用次数: 0

Local Lipschitz continuity for energy integrals with slow growth and lower order terms 具有缓慢增长和低阶项的能量积分的局部 Lipschitz 连续性

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications

Pub Date : 2024-10-03 DOI: 10.1016/j.nonrwa.2024.104224

Michela Eleuteri , Stefania Perrotta , Giulia Treu

We consider integral functionals with slow growth and explicit dependence on

u

of the Lagrangian; this includes many relevant examples as, for instance, in elastoplastic torsion problems or in image restoration problems. Our aim is to prove that the local minimizers are locally Lipschitz continuous. The proof makes use of recent results concerning the Bounded Slope Conditions.

我们考虑的是增长缓慢且明确依赖于拉格朗日 u 的积分函数；这包括许多相关的例子，例如弹塑性扭转问题或图像复原问题。我们的目的是证明局部最小值是局部 Lipschitz 连续的。该证明利用了有关有界斜率条件的最新成果。

引用次数: 0

New generalization of non-autonomous Bernfeld–Haddock conjecture and its proof 非自治伯恩费尔德-哈道克猜想的新概括及其证明

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications

Pub Date : 2024-10-01 DOI: 10.1016/j.nonrwa.2024.104226

Chuangxia Huang , Xiaodan Ding

In this paper, the famous Bernfeld–Haddock conjecture is generalized to a broader form combining with a class of non-autonomous delay differential equations. With the help of differential inequality technique and Dini derivative theory, it is proved that each solution of the addressed equations has boundedness and tends to a constant without requiring the delay feedback function to be strictly increasing, which greatly refines and extends the corresponding results in the existing literature. In particular, an explanatory example is performed to substantiate the obtained analytical findings.

本文将著名的伯恩费尔德-哈多克猜想推广到更广泛的形式，并与一类非自治延迟微分方程相结合。借助微分不等式技术和迪尼导数理论，证明了所涉及方程的每个解都有界且趋于常数，而不要求延迟反馈函数严格递增，这极大地完善和扩展了现有文献中的相应结果。特别是，通过一个解释性实例来证实所获得的分析结果。

引用次数: 0

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