SIAM Journal on Mathematical Analysis最新文献_第6页

Partial Data Inverse Problems for the Nonlinear Time-Dependent Schrödinger Equation 非线性时变薛定谔方程的部分数据逆问题

IF 2 2区数学

SIAM Journal on Mathematical Analysis Pub Date : 2024-07-02 DOI: 10.1137/23m1587993

Ru-Yu Lai, Xuezhu Lu, Ting Zhou

引用次数: 0

Sobolev Regularity for Optimal Transport Maps of Nonconvex Planar Domains 非凸平面域最优传输映射的索波列夫正则性

IF 2 2区数学

SIAM Journal on Mathematical Analysis Pub Date : 2024-07-02 DOI: 10.1137/23m1582436

Connor Mooney, Arghya Rakshit

引用次数: 0

Distributional Extension and Invertibility of the [math]-Plane Transform and Its Dual 数学]平面变换及其对偶的分布扩展和可逆性

IF 2 2区数学

SIAM Journal on Mathematical Analysis Pub Date : 2024-07-02 DOI: 10.1137/23m1556721

Rahul Parhi, Michael Unser

引用次数: 0

Renormalization and Existence of Finite-Time Blow-Up Solutions for a One-Dimensional Analogue of the Navier–Stokes Equations 纳维-斯托克斯方程一维类比的重正化和有限时间炸裂解的存在性

IF 2 2区数学

SIAM Journal on Mathematical Analysis Pub Date : 2024-07-01 DOI: 10.1137/23m1551481

Denis Gaidashev, Alejandro Luque

引用次数: 0

Explicit Solution of the 1D Schrödinger Equation 一维薛定谔方程的显式求解

IF 2 2区数学

SIAM Journal on Mathematical Analysis Pub Date : 2024-07-01 DOI: 10.1137/22m1514441

Peter C. Gibson

引用次数: 0

Wave Breaking for the Generalized Fornberg–Whitham Equation 广义福恩贝格-惠瑟姆方程的破波作用

IF 2 2区数学

SIAM Journal on Mathematical Analysis Pub Date : 2024-07-01 DOI: 10.1137/23m1603431

Jean-Claude Saut, Shihan Sun, Yuexun Wang, Yi Zhang

引用次数: 0

Global Existence of Weak Solutions for a Model of Nematic Liquid Crystal-Colloidal Interactions 向列液晶-胶体相互作用模型弱解的全局存在性

IF 2 2区数学

SIAM Journal on Mathematical Analysis Pub Date : 2024-07-01 DOI: 10.1137/23m161149x

Zhiyuan Geng, Arnab Roy, Arghir Zarnescu

引用次数: 0

On Existence and Stability Results for Normalized Ground States of Mass-Subcritical Biharmonic Nonlinear Schrödinger Equation on [math] 论质量次临界双谐波非线性薛定谔方程在[数学]上的归一化基态的存在性和稳定性结果

IF 2 2区数学

SIAM Journal on Mathematical Analysis Pub Date : 2024-07-01 DOI: 10.1137/22m1543707

Hichem Hajaiej, Yongming Luo, Lingjie Song

{"title":"On Existence and Stability Results for Normalized Ground States of Mass-Subcritical Biharmonic Nonlinear Schrödinger Equation on [math]","authors":"Hichem Hajaiej, Yongming Luo, Lingjie Song","doi":"10.1137/22m1543707","DOIUrl":"https://doi.org/10.1137/22m1543707","url":null,"abstract":"SIAM Journal on Mathematical Analysis, Volume 56, Issue 4, Page 4415-4439, August 2024. <br/> Abstract. We study the focusing mass-subcritical biharmonic nonlinear Schrödinger equation (BNLS) on the product space [math]. Following the crucial scaling arguments introduced in [Terracini, Tzvetkov, and Visciglia, Anal. PDE, 7 (2014), pp. 73–96] we establish existence and stability results for the normalized ground states of BNLS. Moreover, in the case where lower order dispersion is absent, we prove the existence of a critical mass number [math] that sharply determines the [math]-dependence of the deduced ground states. In the mixed dispersion case, we encounter a major challenge as the BNLS is no longer scale-invariant and the arguments from [Terracini, Tzvetkov, and Visciglia, Anal. PDE, 7 (2014), pp. 73–96] for determining the sharp [math]-dependence of the ground states fail. The main novelty of the present paper is to address this difficult and interesting issue: Using a different scaling argument, we show that [math]-independence of ground states with small mass still holds in the case [math] and [math]. Additionally, we also prove that ground states with sufficiently large mass must possess nontrivial [math]-dependence by appealing to some novel construction of test functions. The latter particularly holds for all parameters lying in the full mass-subcritical regime.","PeriodicalId":51150,"journal":{"name":"SIAM Journal on Mathematical Analysis","volume":"23 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141523434","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Consistency of Fractional Graph-Laplacian Regularization in Semisupervised Learning with Finite Labels 有限标签半监督学习中分数图-拉普拉斯正则化的一致性

IF 2 2区数学

SIAM Journal on Mathematical Analysis Pub Date : 2024-07-01 DOI: 10.1137/23m1559087

Adrien Weihs, Matthew Thorpe

{"title":"Consistency of Fractional Graph-Laplacian Regularization in Semisupervised Learning with Finite Labels","authors":"Adrien Weihs, Matthew Thorpe","doi":"10.1137/23m1559087","DOIUrl":"https://doi.org/10.1137/23m1559087","url":null,"abstract":"SIAM Journal on Mathematical Analysis, Volume 56, Issue 4, Page 4253-4295, August 2024. <br/> Abstract. Laplace learning is a popular machine learning algorithm for finding missing labels from a small number of labeled feature vectors using the geometry of a graph. More precisely, Laplace learning is based on minimizing a graph-Dirichlet energy, equivalently a discrete Sobolev [math] seminorm, constrained to taking the values of known labels on a given subset. The variational problem is asymptotically ill-posed as the number of unlabeled feature vectors goes to infinity for finite given labels due to a lack of regularity in minimizers of the continuum Dirichlet energy in any dimension higher than one. In particular, continuum minimizers are not continuous. One solution is to consider higher-order regularization, which is the analogue of minimizing Sobolev [math] seminorms. In this paper we consider the asymptotics of minimizing a graph variant of the Sobolev [math] seminorm with pointwise constraints. We show that, as expected, one needs [math], where [math] is the dimension of the data manifold. We also show that there must be an upper bound on the connectivity of the graph; that is, highly connected graphs lead to degenerate behavior of the minimizer even when [math].","PeriodicalId":51150,"journal":{"name":"SIAM Journal on Mathematical Analysis","volume":"72 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141523590","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Partial Data Inverse Problems for Magnetic Schrödinger Operators with Potentials of Low Regularity 具有低正则性势的磁薛定谔算子的部分数据反问题

IF 2 2区数学

SIAM Journal on Mathematical Analysis Pub Date : 2024-07-01 DOI: 10.1137/22m1530707

Salem Selim

引用次数: 0