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Annals of Applied Mathematics最新文献

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Existence of Global Attractor for Weakly Damped FDS Nonlinear Wave Equations 弱阻尼 FDS 非线性波方程的全局吸引器的存在性
Annals of Applied Mathematics Pub Date : 2024-06-01 DOI: 10.4208/aam.oa-2024-0009
Boling Guo and Ying Zhang
{"title":"Existence of Global Attractor for Weakly Damped FDS Nonlinear Wave Equations","authors":"Boling Guo and Ying Zhang","doi":"10.4208/aam.oa-2024-0009","DOIUrl":"https://doi.org/10.4208/aam.oa-2024-0009","url":null,"abstract":"","PeriodicalId":517399,"journal":{"name":"Annals of Applied Mathematics","volume":"43 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141277361","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
Entire Sign-Changing Solutions to the Fractional Critical Schrodinger Equation 分数临界薛定谔方程的全符号变化解
Annals of Applied Mathematics Pub Date : 2024-06-01 DOI: 10.4208/aam.oa-2024-0006
Xingdong Tang, Guixiang Xu, Chunyan Zhang and Jihui Zhang
{"title":"Entire Sign-Changing Solutions to the Fractional Critical Schrodinger Equation","authors":"Xingdong Tang, Guixiang Xu, Chunyan Zhang and Jihui Zhang","doi":"10.4208/aam.oa-2024-0006","DOIUrl":"https://doi.org/10.4208/aam.oa-2024-0006","url":null,"abstract":"","PeriodicalId":517399,"journal":{"name":"Annals of Applied Mathematics","volume":"42 23","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141280261","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
On a Hybrid Method for Inverse Transmission Eigenvalue Problems 论逆传输特征值问题的混合方法
Annals of Applied Mathematics Pub Date : 2024-05-01 DOI: 10.4208/aam.oa-2024-0003
Weishi Yin,Zhaobin Xu,Pinchao Meng, Hongyu Liu
{"title":"On a Hybrid Method for Inverse Transmission Eigenvalue Problems","authors":"Weishi Yin,Zhaobin Xu,Pinchao Meng, Hongyu Liu","doi":"10.4208/aam.oa-2024-0003","DOIUrl":"https://doi.org/10.4208/aam.oa-2024-0003","url":null,"abstract":"In this paper, we are concerned with the inverse transmission eigenvalue problem to recover the shape as well as the constant refractive index of\u0000a penetrable medium scatterer. The linear sampling method is employed to\u0000determine the transmission eigenvalues within a certain wavenumber interval\u0000based on far-field measurements. Based on a prior information given by the\u0000linear sampling method, the neural network approach is proposed for the reconstruction of the unknown scatterer. We divide the wavenumber intervals\u0000into several subintervals, ensuring that each transmission eigenvalue is located\u0000in its corresponding subinterval. In each such subinterval, the wavenumber that\u0000yields the maximum value of the indicator functional will be included in the\u0000input set during the generation of the training data. This technique for data\u0000generation effectively ensures the consistent dimensions of model input. The\u0000refractive index and shape are taken as the output of the network. Due to the\u0000fact that transmission eigenvalues considered in our method are relatively small,\u0000certain super-resolution effects can also be generated. Numerical experiments\u0000are presented to verify the effectiveness and promising features of the proposed\u0000method in two and three dimensions.","PeriodicalId":517399,"journal":{"name":"Annals of Applied Mathematics","volume":"24 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140932874","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
Numerical Study of Semidiscrete Penalty Approach for Stabilizing Boussinesq System with Localized Feedback Control 利用局部反馈控制稳定 Boussinesq 系统的半离散惩罚法数值研究
Annals of Applied Mathematics Pub Date : 2024-05-01 DOI: 10.4208/aam.oa-2024-0013
Mejdi Azaiez, Kévin Le Balc’h
{"title":"Numerical Study of Semidiscrete Penalty Approach for Stabilizing Boussinesq System with Localized Feedback Control","authors":"Mejdi Azaiez, Kévin Le Balc’h","doi":"10.4208/aam.oa-2024-0013","DOIUrl":"https://doi.org/10.4208/aam.oa-2024-0013","url":null,"abstract":"We investigate the numerical approximation for stabilizing the\u0000semidiscrete linearized Boussinesq system around an unstable stationary state.\u0000Stabilization is attained through internal feedback controls applied to the velocity and temperature equations, localized within an arbitrary open subset. This\u0000study follows the framework presented in [14], considering the continuous linearized Boussinesq system. The primary objective is to explore the penalization-based approximation of the free divergence condition in the semidiscrete case\u0000and provide a numerical validation of these results in a two-dimensional setting.","PeriodicalId":517399,"journal":{"name":"Annals of Applied Mathematics","volume":"131 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140932887","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
On the Monotonicity of $Q^3$ Spectral Element Method for Laplacian 论拉普拉卡矩的 $Q^3$ 谱元法的单调性
Annals of Applied Mathematics Pub Date : 2024-05-01 DOI: 10.4208/aam.oa-2024-0007
Logan J. Cross, Xiangxiong Zhang
{"title":"On the Monotonicity of $Q^3$ Spectral Element Method for Laplacian","authors":"Logan J. Cross, Xiangxiong Zhang","doi":"10.4208/aam.oa-2024-0007","DOIUrl":"https://doi.org/10.4208/aam.oa-2024-0007","url":null,"abstract":"The monotonicity of discrete Laplacian, i.e., inverse positivity of\u0000stiffness matrix, implies discrete maximum principle, which is in general not true\u0000for high order accurate schemes on unstructured meshes. On the other hand,\u0000it is possible to construct high order accurate monotone schemes on structured\u0000meshes. All previously known high order accurate inverse positive schemes are\u0000or can be regarded as fourth order accurate finite difference schemes, which is\u0000either an M-matrix or a product of two M-matrices. For the $Q^3$ spectral element\u0000method for the two-dimensional Laplacian, we prove its stiffness matrix is a\u0000product of four M-matrices thus it is unconditionally monotone. Such a scheme\u0000can be regarded as a fifth order accurate finite difference scheme. Numerical tests\u0000suggest that the unconditional monotonicity of $Q^k$ spectral element methods will\u0000be lost for $k≥9$ in two dimensions, and for $k≥4$ in three dimensions. In other\u0000words, for obtaining a high order monotone scheme, only $Q^2$ and $Q^3$ spectral\u0000element methods can be unconditionally monotone in three dimensions.","PeriodicalId":517399,"journal":{"name":"Annals of Applied Mathematics","volume":"84 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140932911","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
A Convergent Numerical Algorithm for the Stochastic Growth-Fragmentation Problem 随机增长-破碎问题的收敛数值算法
Annals of Applied Mathematics Pub Date : 2024-02-01 DOI: 10.4208/aam.oa-2023-0035
Dawei Wu, Zhennan Zhou
{"title":"A Convergent Numerical Algorithm for the Stochastic Growth-Fragmentation Problem","authors":"Dawei Wu, Zhennan Zhou","doi":"10.4208/aam.oa-2023-0035","DOIUrl":"https://doi.org/10.4208/aam.oa-2023-0035","url":null,"abstract":"The stochastic growth-fragmentation model describes the temporal evolution of a structured cell population through a discrete-time and\u0000continuous-state Markov chain. The simulations of this stochastic process and\u0000its invariant measure are of interest. In this paper, we propose a numerical\u0000scheme for both the simulation of the process and the computation of the invariant measure, and show that under appropriate assumptions, the numerical\u0000chain converges to the continuous growth-fragmentation chain with an explicit\u0000error bound. With a triangle inequality argument, we are also able to quantitatively estimate the distance between the invariant measures of these two\u0000Markov chains.","PeriodicalId":517399,"journal":{"name":"Annals of Applied Mathematics","volume":"4 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140011661","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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