Journal of Mathematical Analysis and Applications最新文献

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Asymptotic behavior of large solutions to a class of Monge-Ampère equations with nonlinear gradient terms 一类具有非线性梯度项的monge - ampantere方程大解的渐近性质

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Mathematical Analysis and Applications

Pub Date : 2026-01-07 DOI: 10.1016/j.jmaa.2026.130396

Zhijun Zhang

This paper is mainly concerned with the global and boundary asymptotic behavior of convex large classical solutions to the Monge-Ampère equation

\det D^{2} u (x) = f (u (x)) + b (x) | \nabla u (x) |^{q}

x \in Ω

, where Ω is a strictly convex and bounded smooth domain in

R^{n}

with

n \geq 2

q > 0

f (s) = s^{p}

with

p > 0

, or

f (s) = \exp s

, and

b \in C^{\infty} (Ω)

with

b_{1} d^{α} (x) \leq b (x) \leq b_{2} d^{α} (x), x \in Ω

for some

b_{1}, b_{2} > 0

and

α \geq q - n - 1

. We completely describe how

n, p, q, α

and ∂Ω affect the asymptotic behavior of solutions to such problem.

本文主要研究了monge - ampontre方程detD2u(x)=f(u(x))+b(x)|∇u(x)|q, x∈Ω，其中Ω是Rn中n≥2，q>0, f(s)=sp, p>0，或f(s)=exp (s)的严格凸有界光滑域，b∈C∞（Ω）， b1dα(x)≤b(x)≤b2dα(x),x∈Ω，对于某些b1，b2>；0和α≥q−n−1。我们完整地描述了n，p,q，α和∂Ω如何影响此类问题解的渐近行为。

引用次数: 0

Normalized solutions for the p-Laplacian equations with potentials and general nonlinearities 具有势和一般非线性的p-拉普拉斯方程的归一化解

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Mathematical Analysis and Applications

Pub Date : 2026-01-07 DOI: 10.1016/j.jmaa.2026.130393

Jianwen Zhou, Puming Yang, Yuanyang Yu

<div><div>In this paper, we study a type of p-Laplacian equation<math><mo>−</mo><msub><mrow><mi>Δ</mi></mrow><mrow><mi>p</mi></mrow></msub><mi>u</mi><mo>+</mo><mi>V</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>|</mo><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>p</mi><mo>−</mo><mn>2</mn></mrow></msup><mi>u</mi><mo>+</mo><mi>λ</mi><msup><mrow><mo>|</mo><mi>u</mi><mo>|</mo></mrow><mrow><mi>p</mi><mo>−</mo><mn>2</mn></mrow></msup><mi>u</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>u</mi><mo>)</mo><mo>,</mo><mi>x</mi><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></math> with the prescribed mass<math><msup><mrow><mo>(</mo><munder><mo>∫</mo><mrow><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></mrow></munder><msup><mrow><mo>|</mo><mi>u</mi><mo>|</mo></mrow><mrow><mi>p</mi></mrow></msup><mi>d</mi><mi>x</mi><mo>)</mo></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mi>p</mi></mrow></mfrac></mrow></msup><mo>=</mo><mi>c</mi><mo>></mo><mn>0</mn></math> where <math><mi>N</mi><mo>≥</mo><mn>3</mn></math>, <math><mn>1</mn><mo><</mo><mi>p</mi><mo><</mo><mi>N</mi></math>, <math><mi>f</mi><mo>∈</mo><mi>C</mi><mo>(</mo><mi>R</mi><mo>,</mo><mi>R</mi><mo>)</mo></math>, <math><mi>V</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mo>|</mo><mi>x</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>k</mi></mrow></msup><mspace></mspace><mo>(</mo><mi>k</mi><mo>></mo><mn>1</mn><mo>)</mo></math>, <math><msub><mrow><mi>Δ</mi></mrow><mrow><mi>p</mi></mrow></msub><mi>u</mi><mo>=</mo><mtext>div</mtext><mrow><mo>(</mo><msup><mrow><mo>|</mo><mi>∇</mi><mi>u</mi><mo>|</mo></mrow><mrow><mi>p</mi><mo>−</mo><mn>2</mn></mrow></msup><mi>∇</mi><mi>u</mi><mo>)</mo></mrow></math> is the p-Laplacian of u, <math><mi>λ</mi><mo>∈</mo><mi>R</mi></math> is Lagrange multiplier. We assume that f is odd and <math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math>-supercritical. By some constrained minimization methods, we obtain a local minimizer <math><msub><mrow><mi>u</mi></mrow><mrow><mi>c</mi></mrow></msub></math> which is a ground state for small mass <math><mi>c</mi><mo>></mo><mn>0</mn></math> and we describe a mass collapse behavior of the minimizers as <math><mi>c</mi><mo>→</mo><msup><mrow><mn>0</mn></mrow><mrow><mo>+</mo></mrow></msup></math>. Furthermore, under some assumptions of k, we study the asymptotic behavior of the corresponding Lagrange multiplier as <math><mi>c</mi><mo>→</mo><msup><mrow><mn>0</mn></mrow><mrow><mo>+</mo></mrow></msup></math>. In addition, by a minimax approach based on the σ-homotopy stable family of the working space, we obtain a mountain pass type solution <math><msub><mrow><mover><mrow><mi>u</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mro

本文研究一类p-拉普拉斯方程- Δpu+V(x)|u|p - 2u+λ|u|p - 2u=f(u)，x∈RN具有规定质量（∫RN|u|pdx）1p=c>；0其中N≥3,1 <p<；N, f∈C(R，R)， V(x)=|x|k(k>1)， Δpu=div（|∇u|p - 2∇u）是u的p-拉普拉斯算子，λ∈R是拉格朗日乘子。我们假设f是奇数且lp是超临界的。通过约束最小化方法，我们得到了一个局部最小值uc，它是小质量c>；0的基态，并将其描述为c→0+的质量坍缩行为。进一步，在k的某些假设下，研究了相应拉格朗日乘子在c→0+时的渐近性。此外，利用基于工作空间σ-同伦稳定族的极大极小方法，得到了一个山口型解u¯c。

引用次数: 0

Fractional torsional rigidity of compact metric graphs 紧度规图的分数阶扭转刚度

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Mathematical Analysis and Applications

Pub Date : 2026-01-07 DOI: 10.1016/j.jmaa.2026.130391

Sedef Özcan

This paper investigates fractional torsional rigidity on compact, connected metric graphs, a novel extension of the classical concept to nonlocal operators. The fractional torsional rigidity is defined as the

L^{1}

-norm of the fractional torsion function, which is the unique solution to the boundary value problem

{(- Δ_{G})}^{α} u_{α} = 1

on a graph

G

with zero boundary conditions at Dirichlet vertices. We establish a variational characterization for this quantity, which serves as a powerful tool to prove a series of results on its geometric dependence. By applying surgery principles, we derive explicit upper and lower bounds, indicating that the interval serves as an upper comparison case and the flower graph as a lower one among graphs of fixed total length. These findings mirror the classical case, yet the methods required are substantially different due to the nonlocal nature of the fractional Laplacian.

本文研究紧致连通度量图上的分数扭转刚度，这是经典概念在非局部算子上的一个新推广。将分数阶扭转刚度定义为分数阶扭转函数的l1范数，它是在Dirichlet顶点处具有零边界条件的图G上的边值问题（−ΔG）αuα=1的唯一解。我们建立了该量的变分表征，这是证明其几何相关性的一系列结果的有力工具。应用外科原理，推导出明确的上界和下界，表明区间作为总长度固定的图的上比较情形，花图作为下比较情形。这些发现反映了经典的情况下，但所需的方法是本质上不同的，由于分数拉普拉斯的非局部性质。

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引用次数: 0

The convergence rate of the viscosity vanishing limit for a Keller-Segel-fluid system of consumption type 消耗型keller - segel流体系统粘度消失极限的收敛速度

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Mathematical Analysis and Applications

Pub Date : 2026-01-07 DOI: 10.1016/j.jmaa.2026.130399

Min Li

In this paper, we investigate the viscosity vanishing limit of the Cauchy problem of the Keller-Segel-Navier-Stokes system with consumption type

{\begin{matrix} \partial_{t} n_{ϵ} + u_{ϵ} \cdot \nabla n_{ϵ} & = ϵ Δ n_{ϵ} - \nabla \cdot (n_{ϵ} \nabla c_{ϵ}), \\ \partial_{t} c_{ϵ} + u_{ϵ} \cdot \nabla c_{ϵ} & = Δ c_{ϵ} - n_{ϵ} c_{ϵ}, \\ \partial_{t} u_{ϵ} + u_{ϵ} \cdot \nabla u_{ϵ} + \nabla P_{ϵ} & = ϵ Δ u_{ϵ} + n_{ϵ} \nabla ϕ, \\ \nabla \cdot u_{ϵ} & = 0 \end{matrix}

in the two-dimensional and three-dimensional setting as

ϵ \to 0

. Precisely, we reveal that the solutions of the Keller-Segel-Navier-Stokes system with viscosity will converge to the corresponding solution of the partially inviscid Keller-Segel-Euler system, and establish an algebraic convergence rate of the viscosity vanishing limit for general initial data by developing a series of subtle coupled functional evolution estimates.

在本文中，我们研究了keller - sekel - navier - stokes系统的柯西问题的黏度消失极限，该系统的消费类型为{∂tnλ + uλ·∇nλ =ϵΔnϵ -∇⋅(nλ∇cλ),∂tcλ + uλ·∇cλ =Δcϵ - nϵcϵ，∂tuλ + uλ·∇uλ +∇pλ =ϵΔuϵ+ nλ∇φ，在二维和三维设置中为λ→0。准确地说，我们揭示了具有黏性的Keller-Segel-Navier-Stokes系统的解将收敛到部分无黏性的Keller-Segel-Euler系统的相应解，并通过一系列微妙的耦合泛函演化估计建立了一般初始数据的黏性消失极限的代数收敛速率。

引用次数: 0

Asymptotics of the spectral data of perturbed Stark operators on the half-line with mixed boundary conditions 混合边界条件下半线上摄动Stark算子谱数据的渐近性

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Mathematical Analysis and Applications

Pub Date : 2026-01-06 DOI: 10.1016/j.jmaa.2025.130383

Julio H. Toloza , Alfredo Uribe

We obtain sharp asymptotic formulas for the eigenvalues and norming constants of Sturm-Liouville operators associated with the differential expression

- \frac{d^{2}}{d x^{2}} + x + q (x), x \in [0, \infty),

together with the boundary condition

φ^{'} (0) - b φ (0) = 0

b \in R

, where

q \in {p \in L_{R}^{2} (R_{+}, {(1 + x)}^{r} d x) : p^{'} \in L_{R}^{2} (R_{+}, {(1 + x)}^{r} d x)}

and

r > 1

得到了与微分表达式−d2dx2+x+q(x),x∈[0,∞)相关的Sturm-Liouville算子的特征值和赋范常数的尖锐渐近公式，以及边界条件φ ' (0) - bφ(0)=0, b∈R，其中q∈{p∈LR2(R+,(1+x)rdx):p '∈LR2(R+,(1+x)rdx)}和r>；1。

引用次数: 0

Finite element analysis of a coupled Navier–Stokes flow – linear elasticity problem Navier-Stokes流动-线性弹性耦合问题的有限元分析

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Mathematical Analysis and Applications

Pub Date : 2026-01-06 DOI: 10.1016/j.jmaa.2025.130384

Nagaiah Chamakuri , Volker John , Nishant Ranwan

A semi-discrete finite element approximation of a fluid-structure interaction problem is analyzed. The fluid part is modeled by the incompressible Navier–Stokes equations. Both the fluid and the solid subdomains are considered to be stationary. In the discretization of the Navier–Stokes equations, a grad-div stabilization term is included, and a special form of the convective term is used. The existence of a finite element solution is shown, a priori estimates are proved, and a finite element error estimate is derived. The dependency of the error bounds on the coefficients of the problem is tracked. Error bounds are obtained whose constants do not depend on the Reynolds number.

分析了流固耦合问题的半离散有限元近似。流体部分采用不可压缩的Navier-Stokes方程进行建模。流体子域和固体子域都被认为是静止的。在Navier-Stokes方程的离散化过程中，引入了梯度镇定项，并采用了对流项的一种特殊形式。证明了有限元解的存在性，证明了一个先验估计，导出了一个有限元误差估计。跟踪了误差界对问题系数的依赖关系。得到了其常数不依赖于雷诺数的误差边界。

引用次数: 0

Existence of solutions to diffusive logistic models with transmission conditions on normal derivatives 正则导数上具有传输条件的扩散逻辑模型解的存在性

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Mathematical Analysis and Applications

Pub Date : 2026-01-06 DOI: 10.1016/j.jmaa.2025.130388

Zhiyuan Wen, Lijuan Zhou

In this paper, we will consider a boundary value problem of the diffusive logistic equation which is defined on the N-dimensional unit ball. The boundary conditions include not only the Neumann condition on the outer sphere but also an interior jump condition involving the normal derivatives on a sphere located within the ball. To establish the existence and uniqueness of the solution, we first analyze an approximate problem associated with the jump condition. We will show that this approximate problem admits a unique solution, which can be expressed as a power series in terms of the parameter in the jump condition. Secondly, we will show this power series converges to the unique solution of the original jump problem.

本文研究了一类定义在n维单位球上的扩散logistic方程的边值问题。边界条件不仅包括外球面上的诺伊曼条件，还包括球内球面上的法向导数的内跳条件。为了证明解的存在唯一性，我们首先分析了一个与跳跃条件相关的近似问题。我们将证明这个近似问题有一个唯一解，它可以表示为跳跃条件下参数的幂级数。其次，我们将证明这个幂级数收敛于原跳跃问题的唯一解。

引用次数: 0

On the existence of periodic solutions for ϕ-Laplacian inclusion systems 关于周期解的存在性

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Mathematical Analysis and Applications

Pub Date : 2026-01-06 DOI: 10.1016/j.jmaa.2025.130385

Stefania M. Demaria, Fernando D. Mazzone

We apply the direct method of the calculus of variations to prove existence of periodic solutions for differential inclusion systems involving an anisotropic ϕ-Laplacian operator.

我们应用变分法的直接方法证明了涉及各向异性的 -拉普拉斯算子的微分包含系统周期解的存在性。

引用次数: 0

An eco-epidemiological model with prey-taxis and “slow” diffusion: global existence, boundedness and novel dynamics 具有猎物趋向性和“慢”扩散的生态流行病学模型：全球存在性、有界性和新动态

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Mathematical Analysis and Applications

Pub Date : 2026-01-06 DOI: 10.1016/j.jmaa.2025.130387

Ranjit Kumar Upadhyay , Rana D. Parshad , Namrata Mani Tripathi , Nishith Mohan

In this manuscript, an attempt has been made to understand the effects of prey-taxis on the existence of global-in-time solutions and dynamics in an eco-epidemiological model, particularly under the influence of slow dispersal characterized by the p-Laplacian operator and enhanced mortality of the infected prey, subject to specific assumptions on the taxis sensitivity functions. We prove the global existence of classical solutions when the infected prey undergoes random motion and exhibits standard mortality. Under the assumption that the infected prey disperses slowly and exhibits enhanced mortality, we prove the global existence of weak solutions. Following a detailed mathematical investigation of the proposed model, we shift our focus to analyze the stability of the positive equilibrium in the case where all species exhibit linear diffusion, the infected prey experiences standard mortality, and the predator exhibits taxis exclusively toward the infected prey. Within this framework, we establish the occurrence of a steady-state bifurcation. Thereafter, we focus on the long-term dynamics of the system and analytically study the finite-time extinction of the infected prey under enhanced mortality, covering both the standard Laplacian and p-Laplacian cases. Numerical simulations are then carried out to illustrate the dynamical behavior, with particular emphasis on the finite-time extinction phenomenon. Our results have large-scale applications to biological invasions and biological control of pests, under the prevalence of disease in the pest population.

在这篇论文中，我们试图理解在一个生态流行病学模型中，猎物趋向性对全局实时解的存在性和动力学的影响，特别是在以p-拉普拉斯算子为特征的缓慢扩散和受感染猎物死亡率增加的影响下，受到对趋向性敏感性函数的特定假设的影响。我们证明了当被感染的猎物经历随机运动并表现出标准死亡率时，经典解的全局存在性。在被感染猎物扩散缓慢且死亡率增加的假设下，我们证明了弱解的全局存在性。在对所提出的模型进行详细的数学研究之后，我们将重点转移到分析所有物种都表现出线性扩散、被感染猎物经历标准死亡率、捕食者只向被感染猎物表现出趋向性的情况下，正平衡的稳定性。在这个框架内，我们建立了一个稳态分岔的发生。此后，我们将重点放在系统的长期动力学上，并分析研究了在提高死亡率下被感染猎物的有限时间灭绝，包括标准拉普拉斯和p-拉普拉斯情况。然后进行数值模拟来说明动力学行为，特别强调有限时间消光现象。我们的研究结果对生物入侵和害虫的生物防治具有广泛的应用价值。

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引用次数: 0

Analysis of operator splitting methods for the dispersive-Fisher equation 色散- fisher方程算子分裂方法分析

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Mathematical Analysis and Applications

Pub Date : 2026-01-05 DOI: 10.1016/j.jmaa.2025.130382

Fatma Zürnacı-Yetiş , Muaz Seydaoğlu

Operator splitting is a powerful method for the numerical investigation of complicated problems. The basic idea behind operator splitting methods is to split a problem into simpler sub-problems. This study focuses on analyzing the convergence of operator splitting methods applied to the dispersive-Fisher equation. The equation is initially split into unbounded linear and bounded nonlinear components. Operator splitting techniques of the Lie-Trotter and Strang types are then applied to the equation. Local error bounds are derived using an approach based on the differential theory of operators in Banach space and the error terms of one- and two-dimensional numerical quadratures using Lie commutator bounds. Global error estimates are derived using Lady Windermere's fan argument. Finally, a numerical example is examined to confirm the expected rate of convergence.

算子分裂是研究复杂问题的一种有效方法。算子拆分方法的基本思想是将一个问题拆分为更简单的子问题。本文着重分析了算子分裂方法在色散- fisher方程中的收敛性。该方程最初分为无界线性分量和有界非线性分量。然后将Lie-Trotter和strange类型的算子分裂技术应用于方程。采用基于巴拿赫空间算子微分理论的方法推导了局部误差界，利用李氏换易子界推导了一维和二维数值正交的误差项。全局误差估计是使用温德米尔夫人的扇形论证得出的。最后，通过数值算例验证了期望的收敛速度。

引用次数: 0

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Journal of Mathematical Analysis and Applications

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