Communications in Mathematical Sciences最新文献_第4页

Description of random level sets by polynomial chaos expansions 用多项式混沌展开描述随机水平集

IF 1 4区数学

Communications in Mathematical Sciences Pub Date : 2023-12-07 DOI: 10.4310/cms.2024.v22.n1.a4

Markus Bambach, Stephan Gerster, Michael Herty, Aleksey Sikstel

引用次数: 1

Unipolar Euler–Poisson equations with time-dependent damping: blow-up and global existence 具有随时间变化的阻尼的单极欧拉-泊松方程：爆炸和全局存在性

IF 1 4区数学

Communications in Mathematical Sciences Pub Date : 2023-12-07 DOI: 10.4310/cms.2024.v22.n1.a8

Jianing Xu, Shaohua Chen, Ming Mei, Yuming Qin

{"title":"Unipolar Euler–Poisson equations with time-dependent damping: blow-up and global existence","authors":"Jianing Xu, Shaohua Chen, Ming Mei, Yuming Qin","doi":"10.4310/cms.2024.v22.n1.a8","DOIUrl":"https://doi.org/10.4310/cms.2024.v22.n1.a8","url":null,"abstract":"This paper is concerned with the Cauchy problem for one-dimensional unipolar Euler–Poisson equations with time-dependent damping, where the time-asymptotically degenerate damping in the form of $-dfrac{mu}{(1+t)^lambda} rho mu$ for $lambda gt 0$ with $mu gt 0$ plays a crucial role for the structure of solutions. The main issue of the paper is to investigate the critical case with $lambda=1$. We first prove that, for all cases with $lambda gt 0$ and $mu gt 0$ (including the critical case of $lambda=1$), once the initial data is steep at a point, then the solutions are locally bounded but their derivatives will blow up in finite time, by means of the method of Riemann invariants and the technical convex analysis. Secondly, for the critical case of $lambda=1$ with $mu gt 7/3$, we prove that there exists a unique global solution, once the initial perturbation around the constant steady-state is sufficiently small. In particular, we derive the algebraic convergence rates of the solution to the constant steady-state, which are piecewise, related to the parameter $mu$ for $7/3 lt mu leq 3$, $3 lt mu leq 4$ and $mu gt 4$. The adopted method of proof in this critical case is the technical time-weighted energy method and the time-weight depends on the parameter $mu$. Finally, we carry out some numerical simulations in two cases for blow-up and global existence, respectively, which numerically confirm our theoretical results.","PeriodicalId":50659,"journal":{"name":"Communications in Mathematical Sciences","volume":"29 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138555866","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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

A general framework for nonlocal Neumann problems 非局部 Neumann 问题的一般框架

IF 1 4区数学

Communications in Mathematical Sciences Pub Date : 2023-12-07 DOI: 10.4310/cms.2024.v22.n1.a2

Guy Foghem, Moritz Kassmann

引用次数: 20

Energy method for the Boltzmann equation of monatomic gaseous mixtures 单原子气体混合物波尔兹曼方程的能量法

IF 1 4区数学

Communications in Mathematical Sciences Pub Date : 2023-12-07 DOI: 10.4310/cms.2024.v22.n1.a6

Laurent Boudin, Bérénice Grec, Milana Pavić-Čolić, Srboljub Simić

引用次数: 3

A variational approach for price formation models in one dimension 一维价格形成模型的变分法

IF 1 4区数学

Communications in Mathematical Sciences Pub Date : 2023-12-07 DOI: 10.4310/cms.2024.v22.n1.a10

Yuri Ashrafyan, Tigran Bakaryan, Diogo Gomes, Julian Gutierrez

引用次数: 2

Existence and decay of global strong solutions to the nonhomogeneous incompressible liquid crystal system with vacuum and density-dependent viscosity 具有真空和密度粘度的非均质不可压缩液晶系统的全局强解的存在性和衰减性

IF 1 4区数学

Communications in Mathematical Sciences Pub Date : 2023-12-07 DOI: 10.4310/cms.2024.v22.n1.a11

Xia Ye, Mingxuan Zhu

引用次数: 0

A non-equilibrium multi-component model with miscible conditions 具有混相条件的非平衡多组分模型

IF 1 4区数学

Communications in Mathematical Sciences Pub Date : 2023-11-15 DOI: 10.4310/cms.2023.v21.n8.a6

Jean Bussac

引用次数: 0

Homogenization of a transmission problem with sign-changing coefficients and interfacial flux jump 具有变符号系数和界面通量跳跃的传输问题的均匀化

IF 1 4区数学

Communications in Mathematical Sciences Pub Date : 2023-10-09 DOI: 10.4310/cms.2023.v21.n7.a13

Renata Bunoiu, Karim Ramdani, Claudia Timofte

引用次数: 2

Combining resampling and reweighting for faithful stochastic optimization 结合重采样和重加权的忠实随机优化

IF 1 4区数学

Communications in Mathematical Sciences Pub Date : 2023-09-22 DOI: 10.4310/cms.2023.v21.n6.a6

Jing An, Lexing Ying

{"title":"Combining resampling and reweighting for faithful stochastic optimization","authors":"Jing An, Lexing Ying","doi":"10.4310/cms.2023.v21.n6.a6","DOIUrl":"https://doi.org/10.4310/cms.2023.v21.n6.a6","url":null,"abstract":"Many machine learning and data science tasks require solving non-convex optimization problems. When the loss function is a sum of multiple terms, a popular method is the stochastic gradient descent. Viewed as a process for sampling the loss function landscape, the stochastic gradient descent is known to prefer flat minima. Though this is desired for certain optimization problems such as in deep learning, it causes issues when the goal is to find the global minimum, especially if the global minimum resides in a sharp valley. Illustrated with a simple motivating example, we show that the fundamental reason is that the difference in the Lipschitz constants of multiple terms in the loss function causes stochastic gradient descent to experience different gradient variances at different minima. In order to mitigate this effect and perform faithful optimization, we propose a combined resampling-reweighting scheme to balance the variance at local minima and extend to general loss functions. We explain from the numerical stability perspective how the proposed scheme is more likely to select the true global minimum, and from the local convergence analysis perspective how it converges to a minimum faster when compared with the vanilla stochastic gradient descent. Experiments from robust statistics and computational chemistry are provided to demonstrate the theoretical findings.","PeriodicalId":50659,"journal":{"name":"Communications in Mathematical Sciences","volume":"1219 ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138515178","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 1

The global generalized solution of the chemotaxis-Navier–Stokes system with logistic source 具有logistic源的chemotaxis-Navier-Stokes系统的全局广义解

4区数学

Communications in Mathematical Sciences Pub Date : 2023-01-01 DOI: 10.4310/cms.2023.v21.n6.a5

Dandan Ding, Zhong Tan, Zhonger Wu

引用次数: 0