生成时间: 2026年05月08日 05:26:08
运行状态: 部分完成
计划处理论文数量: 27
已完成论文数量: 17
未完成论文数量: 10
重点关注论文数量: 0
了解领域论文数量: 5
不相关论文数量: 12
了解领域论文（摘要翻译）
1. Hirota-Satsuma 系统的尖锐局部适定性
Sharp local well-posedness for the Hirota-Satsuma system
作者: Rafael Deiga
类别: math.AP
发布日期: 2026-05-07
arXiv ID: 2605.06503v1
链接: http://arxiv.org/abs/2605.06503v1
摘要翻译
中文标题: Hirota-Satsuma 系统的尖锐局部适定性
摘要翻译: 我们在 $H^k(\mathbb{R}) \times H^s(\mathbb{R})$ 中建立了 Hirota-Satsuma 系统的尖锐局部存在性结果，其适定性范围依赖于两个分量色散强度的比值。这些定理显著推广了此前仅限于正则性相等（即 $s=k$）对角情形的已有工作。此外，我们将已知的整体适定性理论延拓至非对角区域。该论证依赖于 Fourier 限制范数方法，并结合了分部积分型强解（integrated-by-parts strong solution）的概念——这一框架推广了经典强解的定义。
2. 散焦非线性薛定谔方程带点相互作用的驻波
Standing waves for defocusing nonlinear Schrödinger equations with point interaction
作者: Noriyoshi Fukaya, Yuki Osada, Mario Rastrelli
类别: math.AP
发布日期: 2026-05-07
arXiv ID: 2605.06038v1
链接: http://arxiv.org/abs/2605.06038v1
摘要翻译
中文标题: 散焦非线性薛定谔方程带点相互作用的驻波
摘要翻译: 我们研究散焦情形下二维 $N=2$ 和三维 $N=3$ 中非线性薛定谔方程 $i\partial_t u = -\Delta_\alpha u + |u|^{p-1}u$ 的驻波。此处 $-\Delta_\alpha$ 表示带点相互作用的拉普拉斯算子。该算子有下界，其下界为一负常数；因此，与自由情形不同，相应的能量泛函存在非平凡极小元。我们建立了驻波的存在性与唯一性，并进一步证明了若干定性性质，包括径向对称性、正性及稳定性。此外，我们为零质量情形构造了适当的功能空间，并在此情形下建立了尖锐的衰减估计。
3. $s$-调和函数在小阶数极限下的性质
$s$-harmonic functions in the small order limit
作者: Sven Jarohs, Abhrojyoti Sen, Tobias Weth
类别: math.AP
发布日期: 2026-05-07
arXiv ID: 2605.06102v1
链接: http://arxiv.org/abs/2605.06102v1
摘要翻译
中文标题: $s$-调和函数在小阶数极限下的性质
摘要翻译: 我们研究定义在光滑有界开集 $Ω\subset \mathbb{R}^N$ 上、满足方程 $(-Δ)^s u_s=0$（其中 $s \in (0,1)$）的函数族 $u_s$。本文的主要目的有二：其一，细致分析该函数族在零阶极限 $s \to 0^+$ 下的渐近行为；其二，研究 $u_s$ 关于参数 $s$ 的可微性。我们的大部分结果聚焦于相应的Poisson问题，即函数族 $u_s$ 由外部条件 $u_s = g$ 在 $\mathbb{R}^N \setminus Ω$ 上给定，其中 $g \in L^\infty(\mathbb{R}^N \setminus Ω)$ 是某个固定函数。我们的结果表明，$u_s$ 的零阶渐近行为及其关于 $s$ 的可微性均可通过 $g$ 的适当延拓的对数Laplacian $\log Δ$ 来刻画。由此可推出：对一大类函数 $g$，$u_s$ 关于阶数参数 $s$ 具有逐点单调性。
4. 水波的联合均匀化与浅水极限的一致性分析
Consistency analysis for combined homogenization and shallow water limit of water waves
作者: Antoine Gloria, David Lee
类别: math.AP
发布日期: 2026-05-07
arXiv ID: 2605.05869v1
链接: http://arxiv.org/abs/2605.05869v1
摘要翻译
中文标题: 水波的联合均匀化与浅水极限的一致性分析
摘要翻译: 我们考虑一个处于均匀化框架下的浅水模型。对于周期性地形，Craig、Lannes 和 Sulem 在某些非共振条件下建立了一致性结果。在本文中，我们显著弱化了周期性条件，并在极小假设下处理一般地形。
5. 超双曲型方程特征初值问题解的渐近性质
Asymptotic properties of solutions to the characteristic problem for the ultrahyperbolic equation
作者: Maxim N. Demchenko
类别: math.AP
发布日期: 2026-05-07
arXiv ID: 2605.05839v1
链接: http://arxiv.org/abs/2605.05839v1
摘要翻译
中文标题: 超双曲型方程特征初值问题解的渐近性质
摘要翻译: 本文研究欧氏空间中以特征超平面为初始数据的超双曲型方程问题。考察了解沿横截于初始超平面的特征直线的光滑性与渐近性。
不相关论文（基本信息）
1. 有限状态图上的带个体噪声的主方程
Master equations with an individual noise on finite state graphs
作者: Wilfrid Gangbo, Sebastian Munoz, Jeremy Wu, Zhaoyu Zhang
类别: math.AP, math.OC
发布日期: 2026-05-07
arXiv ID: 2605.06589v1
链接: http://arxiv.org/abs/2605.06589v1
摘要: We develop a classical well-posedness and regularity theory on a finite connected weighted graph for an extended mean field game system, its associated master equation, and a Hamilton-Jacobi- Bellman equation on the probability simplex, all in the presence of an individual noise operator. The geometric structure is inherited from the logarithmic-mean activation functional of discrete optimal transport, under which the entropic Fokker-Planck equation appears as a gradient flow on the graph and the individual noise operator is a bilinear form in the probability vector and the Wasserstein gradient. A central technical step is a quantitative preservation-of-positivity estimate for the discrete continuity equation, which rules out finite-time boundary degeneracy and yields a classical solution theory for the master equation on the open simplex without imposing any boundary condition. As an application, we recover a Nash equilibrium interpretation of the discrete system in terms of Markov chains on the graph. Our setup is inspired by the computational algorithms for optimal mass transport of [10, 11] and provides a rigorous well-posedness theory for several of the equations derived in [25].
2. 量子猫映射本征函数的等分布性
Equidistribution of Eigenfunctions of Quantum Cat Maps
作者: Robert Koirala
类别: math.AP, math-ph, math.DS, math.NT, math.SP
发布日期: 2026-05-07
arXiv ID: 2605.06569v1
链接: http://arxiv.org/abs/2605.06569v1
摘要: We prove that the short-period eigenfunctions of quantum cat maps constructed by Kim and the author equidistribute on $\mathbb{T}^2$ in the sense of semiclassical measures. We also show that their logarithmically large $\ell^\infty$-norm is asymptotically concentrated on a bounded number of coordinates. Thus, for this explicit family, strong coordinate localization coexists with semiclassical equidistribution. These results confirm the behavior suggested by earlier numerical evidence of Kim and the author, and contrast with the scarring phenomena for short-period eigenfunctions observed by Faure, Nonnenmacher, and De Bièvre.
3. 与一维柔性壳相互作用的简化二维Ericksen-Leslie液晶模型
The simplified 2D Ericksen-Leslie liquid crystal model interacting with a 1D flexible shell
作者: Prince Romeo Mensah
类别: math.AP
发布日期: 2026-05-07
arXiv ID: 2605.06463v1
链接: http://arxiv.org/abs/2605.06463v1
摘要: We consider the evolution and interaction of a 2-dimensional nematic liquid crystal of Ericksen-Leslie type within a 1-dimensional flexible viscoelastic structure. This is a fully macroscopic model in which the nematic liquid crystal is modelled by the simplified Ericksen-Leslie system with Ginzburg-Landau approximation. The liquid crystal is contained in a thin viscoelastic shell of arbitrary reference configuration that evolves with respect to the forces exerted by the liquid crystal. Barring any degeneracies in the shell, we construct a global weak solution for the coupled system. We then show that any family of such weak solutions that are parametrized by the Ginzburg-Landau coefficient, converges to a weak solution of the original simplified Ericksen-Leslie system without the Ginzburg-Landau term.
4. 极小曲面的内蕴面积估计与外蕴面积估计的等价性
Equivalence of intrinsic and extrinsic area bounds for minimal surfaces
作者: Enric Florit-Simon
类别: math.DG, math.AP
发布日期: 2026-05-07
arXiv ID: 2605.06468v1
链接: http://arxiv.org/abs/2605.06468v1
摘要: We show that intrinsic and extrinsic area density bounds are equivalent, with matching asymptotic values, for complete, connected, smooth minimal immersions $i:Σ^d\to\mathbb{R}^N$ of any dimension and codimension. Combining our results with a recent breakthrough by Bellettini, we extend the Schoen–Simon–Yau curvature estimates for smoothly immersed, two-sided, stable minimal hypersurfaces $i:Σ^n\to\mathbb{R}^{n+1}$ with bounded intrinsic area density to the missing case $n=6$, which had remained open since.
5. Lorentz–Minkowski 空间中具有给定平均曲率的整 spacelike 径向图
Entire spacelike radial graphs with prescribed mean curvature in the Lorentz–Minkowski space
作者: Gabriele Cora, Alessandro Iacopetti, Lorenzo Maniscalco
类别: math.AP
发布日期: 2026-05-07
arXiv ID: 2605.06409v1
链接: http://arxiv.org/abs/2605.06409v1
摘要: In this paper we address the existence and uniqueness of entire spacelike hypersurfaces in the Lorentz–Minkowski space $\mathbb{L}^{m+1}$ with prescribed mean curvature that are star-shaped with respect to a point and asymptotic to a light cone. We also establish a Willmore-type inequality and prove a non-existence result for spacelike radial graphs asymptotic to the light cone whose mean curvature belongs to $L^p$ for $1 \leq p\leq m$, in particular in the case of compactly supported mean curvature.
6. 分数阶几何问题的一致小能量正则性
Uniform small energy regularity for fractional geometric problems
作者: Marco Badran, Giacomo Cozzi
类别: math.AP
发布日期: 2026-05-07
arXiv ID: 2605.06128v1
链接: http://arxiv.org/abs/2605.06128v1
摘要: We prove small energy regularity for a parabolic boundary reaction Ginzburg-Landau problem in the full range $s\in (0,1)$, answering a question posed by Hyder, Segatti, Sire and Wang. We also obtain a similar small energy regularity result for fractional harmonic maps to spheres. Both results are uniform as $s\to 1$.
7. 从有限维解析反问题的精确唯一性导出的Hölder稳定性
Hölder Stability from Exact Uniqueness for Finite-Dimensional Analytic Inverse Problems
作者: Cătălin I. Cârstea
类别: math.AP
发布日期: 2026-05-07
arXiv ID: 2605.06354v1
链接: http://arxiv.org/abs/2605.06354v1
摘要: We prove a stability theorem for finite-dimensional analytic inverse problems. Let $U\subset\R^m$ be an open parameter set, let $F(p)$ be a boundary measurement operator, and let $R(p)$ be the finite-dimensional quantity to be recovered. If $F$ is real analytic and
then $R$ satisfies a Hölder stability estimate on every compact subset of $U$. The proof uses a Hilbert–Schmidt scalarization of the operator equation $F(p)=F(q)$ and the Łojasiewicz distance inequality. We also prove that, after fixing countable dense families of boundary inputs and tests, finitely many scalar matrix elements of the data give the same Hölder recovery on compact parameter sets. This finite-measurement conclusion is qualitative: the proof does not give an effective measurement list, exponent, or constant. The finite-measurement statement follows from finite determinacy of real analytic zero sets. We apply the result to local Neumann-to-Dirichlet data for piecewise constant anisotropic conductivities and to localized Dirichlet-to-Neumann data for piecewise homogeneous anisotropic elasticity.
8. 带局域白噪声的随机Allen–Cahn方程的指数混合
Exponential mixing for the stochastic Allen–Cahn equation with localized white noise
作者: Ziyu Liu, Shengquan Xiang, Zhifei Zhang
类别: math.PR, math.AP, math.OC
发布日期: 2026-05-07
arXiv ID: 2605.06009v1
链接: http://arxiv.org/abs/2605.06009v1
摘要: This paper studies the 1D stochastic Allen–Cahn equation on a bounded domain driven by localized white noise. We prove that the associated Markov process admits a unique invariant measure and is exponential mixing. The main challenge lies in the interaction between localized nature of the noise and non-trivial global dynamics of the system. To overcome this, our approach relies on two ingredients from PDE control theory: stabilization for the linearized system and global steady-state controllability for the nonlinear equation. The stabilization result is derived using the weak observability and Fenchel–Rockafellar duality, while the global controllability relies on quasi-static deformations combined with global dynamics.
9. 非局部薄膜的多尺度分析与均匀化
Multiscale analysis and homogenization of nonlocal thin films
作者: Nadia Ansini, Antonio Tribuzio
类别: math.AP
发布日期: 2026-05-07
arXiv ID: 2605.05988v1
链接: http://arxiv.org/abs/2605.05988v1
摘要: In this paper, we introduce a nonlocal, variational model for thin films. We consider convolution-type functionals defined on a thin domain whose thickness is of order $γ$, where the effective interactions range between points is of order $\varepsilon$. We study the $Γ$-convergence of these energies, as both parameters vanish, to a local integral functional defined on a lower-dimensional domain. In the periodic homogenization setting, the limit energy density is characterized by an asymptotic formula that depends on the interplay between $\varepsilon$ and $γ$. Under suitable assumptions, this formula exhibits a separation of scales effect, namely, the limit energy can be obtained by performing two successive $Γ$-limits, first letting one parameter tend to zero while keeping the other fixed.
10. 关于非齐次折扣Hamilton-Jacobi方程
On the inhomogeneous discounted Hamilton-Jacobi equations
作者: Liang Jin, Jun Yan, Kai Zhao
类别: math.AP, math.DS
发布日期: 2026-05-07
arXiv ID: 2605.05670v1
链接: http://arxiv.org/abs/2605.05670v1
摘要: In this paper, we study the family of inhomogeneous discounted Hamilton-Jacobi equations \begin{equation}\label{hjs1} λ(x)u+h(x,d_x u)=c \quad \tag{$\ast$} \end{equation} on a closed manifold $M$ with a non-identically vanishing discount factor $λ(x)$. There is a critical value $c_0\in[-\infty,\infty)$ such that \eqref{hjs1} admits a viscosity solution if $c>c_0$ and no solution if $c<c_0$. Inspired by the recent development [34] on the stability theory of viscosity solution, we show that the equation admits an asymptotically stable solution if and only if $c>c_0$. In this case, we determine the basin of the stable solution and investigate the long time behavior of the solution semigroup associated to \eqref{hjs1}. In particular, we relate the lowest convergence rate to the integral of $λ$ over Mather measures, which leads to an asymptotic behavior of Mather measures when $c$ goes to infinity. Assume $c\geqslant c_0$ and the equation admits a solution, we classify ergodic Mather measures and locate their distribution in the phase space.
11. 关于曲面上调和-Ricci 流的注记
Notes on harmonic-Ricci flow on surface
作者: Xiang-Zhi Cao
类别: math.DG, math.AP
发布日期: 2026-05-07
arXiv ID: 2605.05599v1
链接: http://arxiv.org/abs/2605.05599v1
摘要: In this note, we want to establish several formulas about functionals along harmonic Ricci flow on surface with boundary
12. 反演子扩散方程中时空依赖源项的数值分析
Numerical Analysis of Space-Time Dependent Source Identification in Subdiffusion Equations
作者: Siyu Cen, Bangti Jin, Yavar Kian, Zhi Zhou
类别: math.NA, math.AP
发布日期: 2026-05-07
arXiv ID: 2605.05579v1
链接: http://arxiv.org/abs/2605.05579v1
摘要: In this work, we propose an easy-to-implement fixed-point algorithm for reconstructing a space-time dependent source in a subdiffusion model from lateral boundary measurements. The numerical scheme combines a Galerkin finite element method for spatial discretization with a finite difference method for temporal discretization. We establish the linear convergence of the fixed-point iteration and derive an error bound that depends explicitly on the discretization parameters and the noise level. The error analysis relies on stability properties of the continuous inverse problem and technical estimates for the associated direct problem with limited-regularity data. Numerical experiments are presented to support and complement the theoretical analysis.