生成时间: 2025年12月29日 04:04:07

重点关注论文数量: 0

了解领域论文数量: 8

不相关论文数量: 7

了解领域论文（摘要翻译）

1. 无限图上带吸收项的 p-Laplacian 柯西问题解的物质衰减

Decay of Mass of the Solution to the Cauchy Problem of the p-Laplacian with Absorption on Infinite Graphs

作者: Alan A. Tedeev

类别: math.AP

发布日期: 2025-12-26

arXiv ID: 2512.22095v1

链接: http://arxiv.org/abs/2512.22095v1

摘要翻译

中文标题: 无限图上带吸收项的 p-Laplacian 柯西问题解的物质衰减

摘要翻译: 我们考虑支持 Sobolev 不等式的无限图上，带有非均匀密度 $\rho(x)$ 的非稳态离散 p-Laplacian 的柯西问题。针对 $p > 2$ 的非负解，在 $\rho(x)$ 为非幂函数的条件下，我们证明了解随时间的精确稳定化速率。当 $p > 2$ 且 $\rho(x)$ 衰减足够快时，我们证明了普适界。我们的证明技术依赖于适当的能量不等式和一个新的嵌入结果。

2. 二维流体弹性波的低正则性适定性

Low regularity well-posedness for two-dimensional hydroelastic waves

作者: Lizhe Wan, Jiaqi Yang

类别: math.AP

发布日期: 2025-12-26

arXiv ID: 2512.22040v1

链接: http://arxiv.org/abs/2512.22040v1

摘要翻译

中文标题: 二维流体弹性波的低正则性适定性

摘要翻译: 我们研究了二维无旋深水流体弹性波的低正则性局部适定性。基于Ifrim-Tataru [29] 以及 Ai-Ifrim-Tataru [5] 的方法，特别是通过构造包含精心选取的拟微分权重的三次修正能量，我们证明了流体弹性波在 $\mathcal{H}^s$ ($s>\frac{3}{4}$) 空间中是局部适定的。

3. 高维空间中复时间薛定谔均值的逐点锐利收敛性

Sharp pointwise convergence of Schrödinger mean with complex time in higher dimensions

作者: Meng Wang, Zhichao Wang

类别: math.AP

发布日期: 2025-12-26

arXiv ID: 2512.22037v1

链接: http://arxiv.org/abs/2512.22037v1

摘要翻译

好的，请看以下翻译：

中文标题: 高维空间中复时间薛定谔均值的逐点锐利收敛性

摘要翻译: 本文在初始数据 $f$ 属于索博列夫空间 $ H^{s}(\mathbb{R}^d)$ 的假设下，建立了高维空间中复时间薛定谔算子解 $ P_γf(x,t) $ 的几乎处处收敛性。

4. 具有变截面的细长杆中拉普拉斯算子谱的渐近行为

Asymptotics for the spectrum of the Laplacian in thin bars with varying cross sections

作者: Pablo Benavent-Ocejo, Delfina Gómez, Maria-Eugenia Pérez-Martínez

类别: math.AP

发布日期: 2025-12-26

arXiv ID: 2512.22005v1

链接: http://arxiv.org/abs/2512.22005v1

摘要翻译

好的，作为专业的学术翻译专家，我将为您翻译这篇数学领域的论文摘要。译文将严格遵循原文的学术风格和术语，确保准确性和专业性。

中文标题: 具有变截面的细长杆中拉普拉斯算子谱的渐近行为

摘要翻译: 我们研究三维杆状结构中拉普拉斯算子的谱问题，该结构具有直径为 $O(\varepsilon)$ 的小截面，其中 $\varepsilon$ 为一正参数。此结构的边界条件为：在其两端基面上施加狄利克雷（或相应地，诺依曼）边界条件，在其侧边界上施加诺依曼边界条件。我们证明，当 $\varepsilon\to 0$ 时，原算子的谱收敛于一个一维谱模型的谱，且重数保持不变。该一维模型具有狄利克雷（或相应地，诺依曼）边界条件，它可出现在具有不同物理特性的非均匀介质的扩散或振动模型中，并且其形式考虑了三维区域的几何特征。我们主要处理低频问题，并概述了在合适的索博列夫空间中对本征函数的逼近方法。

5. 从反幂势到硬球玻尔兹曼方程极限的最优收敛估计

Optimal Convergence Estimate of the Limit from Inverse Power Potential to Hard Sphere Boltzmann Equation

作者: Zheng-Nan Hu, Jin Woo Jang, Zheng-An Yao, Yu-Long Zhou

类别: math.AP

发布日期: 2025-12-26

arXiv ID: 2512.21938v1

链接: http://arxiv.org/abs/2512.21938v1

摘要翻译

中文标题: 从反幂势到硬球玻尔兹曼方程极限的最优收敛估计

摘要翻译: 反幂势 $U(r)=r^{-1/s}, 0<s<1$ 生成的玻尔兹曼核 $B^{s}=|v-v_*|^{1-4s} b_s(θ)$ 在 $θ\to 0$ 时具有角度奇异性。Jang-Kepka-Nota-Velázquez (2023) 证明了当 $s\to 0$ 时，极限 $B^{s}\to \frac14|v-v_*|$ 成立，并基于该核的收敛性证明了解的弱收敛性。在本文中，我们建立了如下尖锐的定量估计：

$$ |b_s(θ)-\tfrac14| \le C\, s\,θ^{-2-2s}. $$

特别地，该尖锐估计为具有大初值的齐次玻尔兹曼方程的解在适当的索伯列夫空间中给出了最优的 $O(s)$ 收敛速率；即对于任意 $t\in[0,T]$，我们有

$$ f^s(t)=f^0(t)+O(s), $$

该估计由 $k\ge 2$ 的 $L^1_k$ 范数量化。

6. 含非零随机漂移的一维反应扩散方程的波传播

Wave propagation for 1-dimensional reaction-diffusion equation with nonzero random drift

作者: Dihang Guan, Hui He, Wenqing Hu, Jiaojiao Yang

类别: math.AP, math-ph, math.PR

发布日期: 2025-12-26

arXiv ID: 2512.21906v1

链接: http://arxiv.org/abs/2512.21906v1

摘要翻译

中文标题: 含非零随机漂移的一维反应扩散方程的波传播

摘要翻译: 我们研究了实轴上具有随机漂移项和 Fisher-Kolmogorov-Petrovskii-Piscounov (FKPP) 型非线性反应项的反应扩散方程的波传播。我们证明了当平均漂移为正时，向正方向和负方向传播的渐近波前均被推向负方向，导致两个波前都有可能向负无穷大方向传播。我们的证明基于随机环境中扩散过程的大偏差原理，以及对费曼-卡茨公式 (Feynman-Kac formula) 的分析。这种概率论论证还揭示了波前形成的内在物理机制：漂移类似于一个外部场，它改变了（淬火态下的）自由能参考能级，但不改变系统的内在涨落结构。

7. Schrödinger-Boussinesq 方程组孤波的轨道稳定性

Orbital stability of solitary waves for the Schr odinger-Boussinesq system

作者: Yilong Ma, Yamin Xiao

类别: math.AP

发布日期: 2025-12-26

arXiv ID: 2512.21824v1

链接: http://arxiv.org/abs/2512.21824v1

摘要翻译

中文标题: Schrödinger-Boussinesq 方程组孤波的轨道稳定性

摘要翻译: 本文研究如下 Schrödinger-Boussinesq 方程组孤波的轨道稳定性： \begin{equation*} \begin{cases} { \begin{array}{ll} i\varepsilon_t+\varepsilon_{xx}=n\varepsilon+γ|\varepsilon|^2\varepsilon, \ n_{tt}-n_{xx}+ αn_{xxxx}-β(n^2){xx}=|\varepsilon|^2{xx}, \end{array} } (t,x)\in \mathbb{R}^2. \end{cases} \end{equation*} 通过运用抽象结果与细致的谱分析，我们得到了该方程组孤波的轨道稳定性。该结果可视作 \cite{ F-P,H,W} 中结果的推广。

8. 弹性流的障碍问题及相关论题

Obstacle problems for the elastic flow and related topics

作者: Kensuke Yoshizawa

类别: math.AP

发布日期: 2025-12-25

arXiv ID: 2512.21802v1

链接: http://arxiv.org/abs/2512.21802v1

摘要翻译

中文标题: 弹性流的障碍问题及相关论题

摘要翻译: 本文研究了弹性流的一个障碍问题。我们证明了弱解在局部时间内的存在性，并讨论了当解获得额外正则性时其与经典解的关系。同时，我们还收集了与弯曲能量障碍问题相关的结果。

不相关论文（基本信息）

1. BKM 族的 Lax 对

Lax pairs for BKM hierarchy

作者: Andrey Yu. Konyaev, Vladimir S. Matveev

类别: nlin.SI, math-ph, math.AP, math.DG

发布日期: 2025-12-26

arXiv ID: 2512.22064v1

链接: http://arxiv.org/abs/2512.22064v1

摘要: We construct Lax pairs for the recently (2023) introduced integrable PDE systems known as the BKM equations. As many known and previously studied integrable systems are special cases of the BKM systems, our construction provides Lax pairs for many integrable hierarchies, including previously studied ones such as Camassa-Holm, Dullin-Gottwald-Holm, cKdV, Ito, and Marvan-Pavlov, as well as new ones. The corresponding pair is related to a Sturm-Liouville operator on the real line whose potential depends rationally on the spectral parameter.

2. 涉及对数 $p$-拉普拉斯算子的非局部 Dirichlet 问题

Nonlocal Dirichlet problems involving the Logarithmic $p$-Laplacian

作者: Rakesh Arora, Hichem Hajaiej, Kanishka Perera

类别: math.AP

发布日期: 2025-12-26

arXiv ID: 2512.21959v1

链接: http://arxiv.org/abs/2512.21959v1

摘要: In this work, we show the existence of an unbounded sequence of minimax eigenvalues for the logarithmic $p$-Laplacian via the $\mathbb{Z}_2$-cohomological index of Fadell and Rabinowitz. As an application of these minimax eigenvalues and $p$-logarithmic Sobolev inequality proved in [4], we prove new existence results for nonlocal Dirichlet problems involving logarithmic $p$-Laplacian and nonlinearities with $p$-superlinear and subcritical growth at infinity.

3. $\mathbb{R}^n$ 中混合局部与非局部临界问题正解的定性性质

Qualitative properties of positive solutions to mixed local and nonlocal critical problems in $\mathbb{R}^n$

作者: Xifeng Su, Shasha Xu

类别: math.AP

发布日期: 2025-12-26

arXiv ID: 2512.21873v1

链接: http://arxiv.org/abs/2512.21873v1

摘要: We consider the following mixed local and non-local critical elliptic equation: \begin{equation*}\label{0.1} \left{ \begin{array}{lll} -Δu+(-Δ)^su=λh u^{p}+u^{2^-1}, &\text{in},, \mathbb{R}^n, u>0, &\text {in} ,, \mathbb{R}^n, \lim\limits_{|x|\to\infty} u(x) = 0, \end{array} \right. \end{equation} where $n\geqslant4, \,\, p\in (0,2^*-1),\,\, 2^*:=\frac{2n}{n-2}$ and $h$ is a positive function. We first show the existence and regularity results of viscosity solutions to the above critical elliptic equation. More precisely, from \cite{Su-Xu} weak solutions are obtained and we prove they are indeed viscosity solutions and their regularity is: $ u \in C^α(\mathbb{R}^n) $ for $p\in(0,1);$ $ u \in C^{2,β}(\mathbb{R}^n) $ for $p\in [1, 2^*-1).$ Moreover, for $p\in [1, 2^*-1)$, these viscosity solutions are indeed classical ones and we then prove the existence of positive solutions with the qualitative properties such as the decay estimates and the radial symmetry.

4. 非零背景下的非聚焦Manakov系统的长时间渐近性

Large-time asymptotics for the defocusing Manakov system on nonzero background

作者: Xianguo Geng, Haibing Zhang, Jiao Wei

类别: nlin.SI, math.AP

发布日期: 2025-12-26

arXiv ID: 2512.21841v1

链接: http://arxiv.org/abs/2512.21841v1

摘要: The Manakov system is a two-component nonlinear Schrödinger equation. The long-time asymptotics for the defocusing or focusing Manakov system under nonzero background still remains open. In this paper, we derive the long-time asymptotic formula for the solution of the defocusing Manakov system on nonzero boundary conditions and provide a detailed proof. The solution of the defocusing Manakov system on such nonzero background is first transformed into the solution of a $3 \times 3$ matrix Riemann-Hilbert problem. Then we demonstrate how to conduct the Deift-Zhou steepest descent analysis for this Riemann-Hilbert problem, thereby obtaining the long-time asymptotic behavior of the solution in the space-time soliton region. In this region, the leading order of the solution takes the form of a modulated multisoliton. Apart from the error term, we also discover that the defocusing Manakov system has a dispersive correction term of order $t^{-1/2}$, but this term does not exist in the scalar case, and we provide the explicit expression for this dispersion term.

5. 椭圆与抛物型方程反点源问题的最优传输稳定性

Optimal-Transport Stability of Inverse Point-Source Problems for Elliptic and Parabolic Equations

作者: Lingyun Qiu, Shenwen Yu

类别: math.NA, math.AP

发布日期: 2025-12-26

arXiv ID: 2512.21821v1

链接: http://arxiv.org/abs/2512.21821v1

摘要: We establish quantitative global stability estimates, formulated in terms of optimal transport (OT) cost, for inverse point-source problems governed by elliptic and parabolic equations with spatially varying coefficients. The key idea is that the Kantorovich dual potential can be represented as a boundary functional of suitable adjoint solutions, thereby linking OT geometry with boundary observations. In the elliptic case, we construct complex geometric optics solutions that enforce prescribed pointwise constraints, whereas in the parabolic case we employ controllable adjoint solutions that transfer interior information to the boundary. Under mild regularity and separation assumptions, we obtain estimates of the form

$$ \mathcal{T}_c(μ,ν) \le C\,\|u_1 - u_2\|_{L^2(\partialΩ)} \quad \text{and} \quad \mathcal{T}_c(μ,ν) \le C\,\|u_1 - u_2\|_{L^2(\partialΩ\times[0,T])}, $$

where $μ$ and $ν$ are admissible point-source measures. These results provide a unified analytical framework connecting inverse source problems and optimal transport, and establish OT-based stability theory for inverse source problems governed by partial differential equations with spatially varying coefficients.

6. 逆随机势散射问题的稳定性

Stability for the inverse random potential scattering problem

作者: Tianjiao Wang, Xiang Xu, Yue Zhao

类别: math.AP

发布日期: 2025-12-26

arXiv ID: 2512.21814v1

链接: http://arxiv.org/abs/2512.21814v1

摘要: This paper is concerned with an inverse random potential problem for the Schrödinger equation. The random potential is assumed to be a generalized Gaussian random function, whose covariance operator is a classical pseudo-differential operator. For the direct problem, the meromorphic continuation of the resolvent of the Schrödinger operator with rough potentials is investigated, which yields the well-posedness of the direct scattering problem and a Born series expansion. For the inverse problem, we derive a probabilistic stability estimate for determining the principle symbol of the covariance operator of the random potential. The stability result provides an estimate of the probability for an event when the principle symbol can be quantitatively determined by a single realization of the multi-frequency backscattered far-field pattern. The analysis employs the ergodicity theory and quantitative analytic continuation principle.

7. 外部区域上带Robin边界条件的加权$p$-Laplacian的主特征值与渐近行为

Principal eigenvalues and asymptotic behavior for the weighted $p$-Laplacian with Robin boundary conditions on exterior domains

作者: Subha Pal, Sarath Sasi

类别: math.AP

发布日期: 2025-12-25

arXiv ID: 2512.21752v1

链接: http://arxiv.org/abs/2512.21752v1

摘要: The spectral theory of the p-Laplacian is well developed for classical Dirichlet and Neumann boundary conditions, but the transitional Robin regime on exterior domains remains largely unexplored. This paper studies a weighted p-Laplacian eigenvalue problem with Robin boundary conditions on the exterior of the unit ball in Euclidean space of dimension N, with N greater than p. The weight function belongs to a critical Lorentz class and decays at infinity. Under natural assumptions on the weight, we prove the existence, uniqueness, simplicity, and isolation of a positive principal eigenvalue and establish local first-order regularity of the associated eigenfunction. We analyze the dependence of the principal eigenvalue on the Robin parameter and recover the Neumann and Dirichlet limits as the parameter approaches zero and infinity, respectively. The far-field behavior of the eigenfunction exhibits a universal algebraic decay rate that is independent of the Robin parameter, while the near-boundary structure displays an explicit scaling with respect to the parameter. We further investigate the gradient behavior of the eigenfunction, showing the existence of a unique critical radius and providing quantitative bounds on both the critical radius and the boundary value in terms of the Robin parameter. The main contribution of this work is the derivation of unified gradient estimates that connect the near-boundary and far-field regions through a characteristic length scale determined by the Robin parameter, yielding a global description of how boundary effects penetrate into the exterior domain.