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Communications on Analysis and Computation最新文献

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Reconstruction of extended regions in EIT with a generalized Robin transmission condition 利用广义罗宾传输条件重建 EIT 中的扩展区域
Communications on Analysis and Computation Pub Date : 2023-10-12 DOI: 10.3934/cac.2023017
G. Granados, Isaac Harris, Heejin Lee
{"title":"Reconstruction of extended regions in EIT with a generalized Robin transmission condition","authors":"G. Granados, Isaac Harris, Heejin Lee","doi":"10.3934/cac.2023017","DOIUrl":"https://doi.org/10.3934/cac.2023017","url":null,"abstract":"We consider an inverse shape problem coming from electrical impedance tomography with a generalized Robin transmission condition. We will derive an algorithm in order to detect whether two materials that should be in contact are separated or delaminated. More precisely, we assume that the undamaged material or background state is known and shares an interface or boundary with the damaged subregion. The Robin transmission condition on this boundary asymptotically models delamination. We assume that the DtN operator is given from measuring the current on the surface of the material from an imposed voltage. We show that this mapping uniquely recovers the boundary parameters. Furthermore, using this electrostatic Cauchy data as physical measurements, we can determine if all of the coefficients from the Robin transmission condition are real-valued or complex-valued. We study these two cases separately and show that the regularized factorization method can be used to detect whether delamination has occurred and recover the damaged subregion. Numerical examples will be presented for both cases in two dimensions in the unit circle.","PeriodicalId":139109,"journal":{"name":"Communications on Analysis and Computation","volume":"173 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139320258","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Stability of determining the potential from partial boundary data in a Schrödinger equation in the high frequency limit 高频极限下Schrödinger方程部分边界数据确定电位的稳定性
Communications on Analysis and Computation Pub Date : 2023-07-01 DOI: 10.3934/cac.2023012
M. Choulli
{"title":"Stability of determining the potential from partial boundary data in a Schrödinger equation in the high frequency limit","authors":"M. Choulli","doi":"10.3934/cac.2023012","DOIUrl":"https://doi.org/10.3934/cac.2023012","url":null,"abstract":"We establish stability inequalities for the problem of determining the potential, appearing in a Sch\"odinger equation, from partial boundary data in the high frequency limit. These stability inequalities hold under the assumption that the potential is known near the boundary of the domain under consideration.","PeriodicalId":139109,"journal":{"name":"Communications on Analysis and Computation","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133594282","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Stability in determination of states for the mean field game equations 平均场博弈方程状态确定的稳定性
Communications on Analysis and Computation Pub Date : 2023-04-12 DOI: 10.3934/cac.2023009
Hongyu Liu, Masahiro Yamamoto
{"title":"Stability in determination of states for the mean field game equations","authors":"Hongyu Liu, Masahiro Yamamoto","doi":"10.3934/cac.2023009","DOIUrl":"https://doi.org/10.3934/cac.2023009","url":null,"abstract":"We consider solutions satisfying the Neumann zero boundary condition and a linearized mean field game system in $Omega times (0,T)$, where $Omega$ is a bounded domain in $mathbb{R}^d$ and $(0,T)$ is the time interval. We prove two kinds of stability results in determining the solutions. The first is H\"older stability in time interval $(epsilon, T)$ with arbitrarily fixed $epsilon>0$ by data of solutions in $Omega times {T}$. The second is the Lipschitz stability in $Omega times (epsilon, T-epsilon)$ by data of solutions in arbitrarily given subdomain of $Omega$ over $(0,T)$.","PeriodicalId":139109,"journal":{"name":"Communications on Analysis and Computation","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129696997","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
Optimal estimate of field concentration between multiscale nearly-touching inclusions for 3-D Helmholtz system 三维亥姆霍兹系统多尺度近接触夹杂物场浓度的最优估计
Communications on Analysis and Computation Pub Date : 2022-11-10 DOI: 10.3934/cac.2023004
Youjun Deng, Yueguang Hu, Hongyu Liu, Wanjing Tang
{"title":"Optimal estimate of field concentration between multiscale nearly-touching inclusions for 3-D Helmholtz system","authors":"Youjun Deng, Yueguang Hu, Hongyu Liu, Wanjing Tang","doi":"10.3934/cac.2023004","DOIUrl":"https://doi.org/10.3934/cac.2023004","url":null,"abstract":"We are concerned with the field concentration between two nearly-touching inclusions with high-contrast material parameters, which is a central topic in the theory of composite materials. The degree of concentration is characterised by the blowup rate of the gradient of the underlying field. In this paper, we derive optimal gradient estimates for the wave filed of the 3-D Helmholtz system in the quasi-static regime. There are two salient features of our results that are new to the literature. First, we cover all the possible scenarios that the size of the inclusions are in different scales in terms of the asymptotic distance parameter $epsilon$, which can be used to characterise the curvature effects of the shape of the inclusions on the field concentration. Second, our estimates can not only recover the known results in the literature for the static case, but can also reveal the interesting frequency effect on the field concentration. In fact, a novel phenomena is shown that even if the static part vanishes, field blowup can still occur due to the (low) frequency effect.","PeriodicalId":139109,"journal":{"name":"Communications on Analysis and Computation","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122228113","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Inverse problems for fractional equations with a minimal number of measurements 具有最小测量数的分数阶方程的反问题
Communications on Analysis and Computation Pub Date : 2022-03-06 DOI: 10.3934/cac.2023005
Yi-Hsuan Lin, Hongyu Liu
{"title":"Inverse problems for fractional equations with a minimal number of measurements","authors":"Yi-Hsuan Lin, Hongyu Liu","doi":"10.3934/cac.2023005","DOIUrl":"https://doi.org/10.3934/cac.2023005","url":null,"abstract":"In this paper, we study several inverse problems associated with a fractional differential equation of the following form: [ (-Delta)^s u(x)+sum_{k=0}^N a^{(k)}(x) [u(x)]^k=0, 0<s<1, Ninmathbb{N}cup{0}cup{infty}, ] which is given in a bounded domain $Omegasubsetmathbb{R}^n$, $ngeq 1$. For any finite $N$, we show that $a^{(k)}(x)$, $k=0,1,ldots, N$, can be uniquely determined by $N+1$ different pairs of Cauchy data in $Omega_e:=mathbb{R}^nbackslashoverline{Omega}$. If $N=infty$, the uniqueness result is established by using infinitely many pairs of Cauchy data. The results are highly intriguing in that it generally does not hold true in the local case, namely $s=1$, even for the simplest case when $N=0$, a fortiori $Ngeq 1$. The nonlocality plays a key role in establishing the uniqueness result. We also establish several other unique determination results by making use of a minimal number of measurements. Moreover, in the process we derive a novel comparison principle for nonlinear fractional differential equations as a significant byproduct.","PeriodicalId":139109,"journal":{"name":"Communications on Analysis and Computation","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129822961","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 13
A novel recurrent neural network of gated unit based on Euler's method and application 一种基于欧拉方法的门控单元递归神经网络及其应用
Communications on Analysis and Computation Pub Date : 1900-01-01 DOI: 10.3934/cac.2023007
P. Meng, L. Wang, W. Yin, Linhua Zhou
{"title":"A novel recurrent neural network of gated unit based on Euler's method and application","authors":"P. Meng, L. Wang, W. Yin, Linhua Zhou","doi":"10.3934/cac.2023007","DOIUrl":"https://doi.org/10.3934/cac.2023007","url":null,"abstract":"","PeriodicalId":139109,"journal":{"name":"Communications on Analysis and Computation","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122513424","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Determining the random source and initial value simultaneously in stochastic fractional diffusion equations 随机分数扩散方程中随机源和初始值的同时确定
Communications on Analysis and Computation Pub Date : 1900-01-01 DOI: 10.3934/cac.2023013
Li-Li Wang, T. Wei, G. Zheng
{"title":"Determining the random source and initial value simultaneously in stochastic fractional diffusion equations","authors":"Li-Li Wang, T. Wei, G. Zheng","doi":"10.3934/cac.2023013","DOIUrl":"https://doi.org/10.3934/cac.2023013","url":null,"abstract":"","PeriodicalId":139109,"journal":{"name":"Communications on Analysis and Computation","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127724535","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
An enriched Ciarlet-Raviart scheme for the biharmonic equation 双调和方程的富Ciarlet-Raviart格式
Communications on Analysis and Computation Pub Date : 1900-01-01 DOI: 10.3934/cac.2023001
W. Qiu
{"title":"An enriched Ciarlet-Raviart scheme for the biharmonic equation","authors":"W. Qiu","doi":"10.3934/cac.2023001","DOIUrl":"https://doi.org/10.3934/cac.2023001","url":null,"abstract":"","PeriodicalId":139109,"journal":{"name":"Communications on Analysis and Computation","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116417915","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Structured condition numbers for Sylvester matrix equation with parameterized quasiseparable matrices 具有参数化拟可分矩阵的Sylvester矩阵方程的结构条件数
Communications on Analysis and Computation Pub Date : 1900-01-01 DOI: 10.3934/cac.2023011
H. Diao, Lei Li, Qingle Meng
{"title":"Structured condition numbers for Sylvester matrix equation with parameterized quasiseparable matrices","authors":"H. Diao, Lei Li, Qingle Meng","doi":"10.3934/cac.2023011","DOIUrl":"https://doi.org/10.3934/cac.2023011","url":null,"abstract":"","PeriodicalId":139109,"journal":{"name":"Communications on Analysis and Computation","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133307931","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Convergence rates of stationary and non-stationary asymptotical regularization methods for statistical inverse problems in Banach spaces Banach空间统计反问题的平稳和非平稳渐近正则化方法的收敛速率
Communications on Analysis and Computation Pub Date : 1900-01-01 DOI: 10.3934/cac.2023003
De-Han Chen, Jingzhi Li, Ye Zhang
{"title":"Convergence rates of stationary and non-stationary asymptotical regularization methods for statistical inverse problems in Banach spaces","authors":"De-Han Chen, Jingzhi Li, Ye Zhang","doi":"10.3934/cac.2023003","DOIUrl":"https://doi.org/10.3934/cac.2023003","url":null,"abstract":"","PeriodicalId":139109,"journal":{"name":"Communications on Analysis and Computation","volume":"214 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122618045","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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