应用数学年刊:英文版最新文献_第4页

On Fractional Smoothness of Modulus of Functions 关于函数模的分数阶光滑性

应用数学年刊:英文版

Pub Date : 2021-06-01 DOI: 10.4208/aam.oa-2021-0006

Dong Li

We consider the Nemytskii operators $uto |u|$ and $uto u^{pm}$ in a bounded domain $Omega$ with $C^2$ boundary. We give elementary proofs of the boundedness in $H^s(Omega)$ with $0le s<3/2$.

我们考虑具有$C^2$边界的有界域$Omega$中的Nemytskii算子$uto|u|$和$uto u^｛pm｝$。我们给出了$H^s（Omega）$中$0le s<3/2$有界性的初等证明。

引用次数: 0

High-Order Fully Discrete Energy Diminishing Evolving Surface Finite Element Methods for a Class of Geometric Curvature Flows 一类几何曲率流的高阶全离散能量递减演化曲面有限元方法

应用数学年刊:英文版

Pub Date : 2021-06-01 DOI: 10.4208/aam.oa-2021-0007

global sci

引用次数: 2

Transverse Instability of the CH-KP-I Equation CH-KP-I方程的横向不稳定性

应用数学年刊:英文版

Pub Date : 2021-04-22 DOI: 10.4208/aam.oa-2021-0004

R. Chen, Jie Jin

The Camassa–Holm–Kadomtsev–Petviashvili-I equation (CH-KP-I) is a two dimensional generalization of the Camassa–Holm equation (CH). In this paper, we prove transverse instability of the line solitary waves under periodic transverse perturbations. The proof is based on the framework of [18]. Due to the high nonlinearity, our proof requires necessary modification. Specifically, we first establish the linear instability of the line solitary waves. Then through an approximation procedure, we prove that the linear effect actually dominates the nonlinear behavior.

Camassa–Holm–Kadomtsev–Petviashvili-I方程（CH-KP-I）是Camassa-Holm方程（CH）的二维推广。在本文中，我们证明了在周期性横向扰动下线性孤立波的横向不稳定性。该证明基于[18]的框架。由于高非线性，我们的证明需要必要的修改。具体来说，我们首先建立了线性孤立波的线性不稳定性。然后通过近似过程，我们证明了线性效应实际上支配着非线性行为。

引用次数: 0

Boundary Homogenization of a Class of Obstacle Problems 一类障碍问题的边界均匀化

应用数学年刊:英文版

Pub Date : 2021-04-14 DOI: 10.4208/aam.oa-2022-0001

Jingzhi Li, Hongyu Liu, Lan Tang, Jiangwen Wang

We study homogenization of a boundary obstacle problem on C domain D for some elliptic equations with uniformly elliptic coefficient matrices γ. For any ǫ ∈ R+, ∂D = Γ ∪ Σ, Γ ∩ Σ = ∅ and Sǫ ⊂ Σ with suitable assumptions, we prove that as ǫ tends to zero, the energy minimizer u of ∫ D |γ∇u|dx, subject to u ≥ φ on Sε, up to a subsequence, converges weakly in H(D) to ũ which minimizes the energy functional ∫ D |γ∇u| + ∫ Σ (u− φ)−μ(x)dSx, where μ(x) depends on the structure of Sǫ and φ is any given function in C∞(D).

研究了一类具有一致椭圆系数矩阵γ的椭圆型方程在C域D上边界障碍问题的齐次化问题。对于任何ǫ∈R +,∂D =Γ∪Σ,Γ∩Σ=∅和Sǫ⊂Σ与合适的假设,我们证明当ǫ趋于零,能量最小值你∫D |γ|∇u dx,受制于u≥φ年代ε,子序列,收敛弱在H (D)ũ最小化能量函数∫D |γ|∇u +∫Σ(u−φ)−μ(x) dSx,在μ(x)的结构取决于Sǫ和φ是任何给定函数C∞(D)。

引用次数: 0

KAM and Geodesic Dynamics of Blackholes 黑洞的测地线动力学

应用数学年刊:英文版

Pub Date : 2020-12-05 DOI: 10.4208/aam.oa-2021-0002

Jinxin Xue

In this paper we apply KAM theory and the Aubry-Mather theory for twist maps to the study of bound geodesic dynamics of a perturbed blackhole background. The general theories apply mainly to two observable phenomena: the photon shell (unstable bound spherical orbits) and the quasi-periodic oscillations. We discover there is a gap structure in the photon shell that can be used to reveal information of the perturbation.

本文将KAM理论和扭曲映射的Aubry-Mather理论应用于扰动黑洞背景的边界测地动力学研究。一般理论主要适用于两种可观测现象：光子壳层（不稳定束缚球轨道）和准周期振荡。我们发现在光子壳层中有一个间隙结构，可以用来揭示微扰的信息。

引用次数: 1

Negligible Obstructions and Turán Exponents 可忽略障碍与Turán指数

应用数学年刊:英文版

Pub Date : 2020-07-06 DOI: 10.4208/aam.OA-2022-0008

T. Jiang, Zilin Jiang, Jie Ma

We show that for every rational number $r in (1,2)$ of the form $2 - a/b$, where $a, b in mathbb{N}^+$ satisfy $lfloor a/b rfloor^3 le a le b / (lfloor b/a rfloor +1) + 1$, there exists a graph $F_r$ such that the Turan number $operatorname{ex}(n, F_r) = Theta(n^r)$. Our result in particular generates infinitely many new Turan exponents. As a byproduct, we formulate a framework that is taking shape in recent work on the Bukh--Conlon conjecture.

我们证明，对于形式为$2 - a/b$的每个有理数$r in (1,2)$，其中$a, b in mathbb{N}^+$满足$lfloor a/b rfloor^3 le a le b / (lfloor b/a rfloor +1) + 1$，存在一个图$F_r$，使得图兰数$operatorname{ex}(n, F_r) = Theta(n^r)$。我们的结果产生了无穷多个新的图兰指数。作为副产品，我们在最近的Bukh- Conlon猜想工作中形成了一个框架。

引用次数: 9