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Discrete and Continuous Dynamical Systems-Series S最新文献

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Strict separation and numerical approximation for a non–local Cahn–Hilliard equation with single–well potential 具有单井势的非局部卡恩-希利亚德方程的严格分离与数值近似
IF 1.8 4区 数学
Discrete and Continuous Dynamical Systems-Series S Pub Date : 2023-12-18 DOI: 10.3934/dcdss.2023213
Abramo Agosti, Elisabetta Rocca, Luca Scarpa
{"title":"Strict separation and numerical approximation for a non–local Cahn–Hilliard equation with single–well potential","authors":"Abramo Agosti, Elisabetta Rocca, Luca Scarpa","doi":"10.3934/dcdss.2023213","DOIUrl":"https://doi.org/10.3934/dcdss.2023213","url":null,"abstract":"","PeriodicalId":48838,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series S","volume":"22 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140026153","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
Key ingredients for wall-modeled LES with the Lattice Boltzmann method: Systematic comparison of collision schemes, SGS models, and wall functions on simulation accuracy and efficiency for turbulent channel flow 采用晶格玻尔兹曼法的壁面模型 LES 的关键要素：系统比较碰撞方案、SGS 模型和壁面函数对湍流通道流模拟精度和效率的影响
IF 1.8 4区 数学
Discrete and Continuous Dynamical Systems-Series S Pub Date : 2023-12-14 DOI: 10.3934/dcdss.2023212
Gregorio Gerardo Spinelli, Jana Gericke, Kannan Masilamani, Harald Günther Klimach
{"title":"Key ingredients for wall-modeled LES with the Lattice Boltzmann method: Systematic comparison of collision schemes, SGS models, and wall functions on simulation accuracy and efficiency for turbulent channel flow","authors":"Gregorio Gerardo Spinelli, Jana Gericke, Kannan Masilamani, Harald Günther Klimach","doi":"10.3934/dcdss.2023212","DOIUrl":"https://doi.org/10.3934/dcdss.2023212","url":null,"abstract":"","PeriodicalId":48838,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series S","volume":"23 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140025997","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
Mathematical and numerical challenges in diffuse optical tomography inverse problems 漫反射光学断层成像逆问题的数学和数值挑战
IF 1.8 4区 数学
Discrete and Continuous Dynamical Systems-Series S Pub Date : 2023-11-23 DOI: 10.3934/dcdss.2023210
Andrea Aspri, Alessandro Benfenati, Paola Causin, Cecilia Cavaterra, Giovanni Naldi
{"title":"Mathematical and numerical challenges in diffuse optical tomography inverse problems","authors":"Andrea Aspri, Alessandro Benfenati, Paola Causin, Cecilia Cavaterra, Giovanni Naldi","doi":"10.3934/dcdss.2023210","DOIUrl":"https://doi.org/10.3934/dcdss.2023210","url":null,"abstract":"","PeriodicalId":48838,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series S","volume":"104 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140025882","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
Abstract action spaces and their topological and dynamic properties 抽象作用空间及其拓扑和动态特性
IF 1.8 4区 数学
Discrete and Continuous Dynamical Systems-Series S Pub Date : 2023-11-20 DOI: 10.3934/dcdss.2023208
Riccarda Rossi, Giuseppe Savaré
{"title":"Abstract action spaces and their topological and dynamic properties","authors":"Riccarda Rossi, Giuseppe Savaré","doi":"10.3934/dcdss.2023208","DOIUrl":"https://doi.org/10.3934/dcdss.2023208","url":null,"abstract":"","PeriodicalId":48838,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series S","volume":"42 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140025995","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 mobility-SAV approach for a Cahn-Hilliard equation with degenerate mobilities 具有退化流动性的卡恩-希利亚德方程的流动性-SAV方法
IF 1.8 4区 数学
Discrete and Continuous Dynamical Systems-Series S Pub Date : 2023-09-21 DOI: 10.3934/dcdss.2023177
Elie Bretin, Luca Calatroni, Simon Masnou
{"title":"A mobility-SAV approach for a Cahn-Hilliard equation with degenerate mobilities","authors":"Elie Bretin, Luca Calatroni, Simon Masnou","doi":"10.3934/dcdss.2023177","DOIUrl":"https://doi.org/10.3934/dcdss.2023177","url":null,"abstract":"","PeriodicalId":48838,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series S","volume":"49 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140026325","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
Well-posedness and optimal control for a viscous Cahn–Hilliard–Oono system with dynamic boundary conditions 具有动态边界条件的粘性Cahn-Hilliard-Oono系统的适定性与最优控制
IF 1.8 4区 数学
Discrete and Continuous Dynamical Systems-Series S Pub Date : 2023-09-16 DOI: 10.3934/dcdss.2023127
G. Gilardi, E. Rocca, A. Signori
{"title":"Well-posedness and optimal control for a viscous Cahn–Hilliard–Oono system with dynamic boundary conditions","authors":"G. Gilardi, E. Rocca, A. Signori","doi":"10.3934/dcdss.2023127","DOIUrl":"https://doi.org/10.3934/dcdss.2023127","url":null,"abstract":"In this paper we consider a nonlinear system of PDEs coupling the viscous Cahn-Hilliard-Oono equation with dynamic boundary conditions enjoying a similar structure on the boundary. After proving well-posedness of the corresponding initial boundary value problem, we study an associated optimal control problem related to a tracking-type cost functional, proving first-order necessary conditions of optimality. The controls enter the system in the form of a distributed and a boundary source. We can account for general potentials in the bulk and in the boundary part under the common assumption that the boundary potential is dominant with respect to the bulk one. For example, the regular quartic potential as well as the logarithmic potential can be considered in our analysis.","PeriodicalId":48838,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series S","volume":"32 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84527366","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
Nutrient control for a viscous Cahn–Hilliard–Keller–Segel model with logistic source describing tumor growth 描述肿瘤生长的logistic源粘性Cahn-Hilliard-Keller-Segel模型的营养控制
IF 1.8 4区 数学
Discrete and Continuous Dynamical Systems-Series S Pub Date : 2023-09-16 DOI: 10.3934/dcdss.2023123
G. Gilardi, A. Signori, J. Sprekels
{"title":"Nutrient control for a viscous Cahn–Hilliard–Keller–Segel model with logistic source describing tumor growth","authors":"G. Gilardi, A. Signori, J. Sprekels","doi":"10.3934/dcdss.2023123","DOIUrl":"https://doi.org/10.3934/dcdss.2023123","url":null,"abstract":"In this paper, we address a distributed control problem for a system of partial differential equations describing the evolution of a tumor that takes the biological mechanism of chemotaxis into account. The system describing the evolution is obtained as a nontrivial combination of a Cahn-Hilliard type system accounting for the segregation between tumor cells and healthy cells, with a Keller-Segel type equation accounting for the evolution of a nutrient species and modeling the chemotaxis phenomenon. First, we develop a robust mathematical background that allows us to analyze an associated optimal control problem. This analysis forced us to select a source term of logistic type in the nutrient equation and to restrict the analysis to the case of two space dimensions. Then, the existence of an optimal control and first-order necessary conditions for optimality are established.","PeriodicalId":48838,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series S","volume":"103 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79454287","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
Kobayashi-Warren-Carter system of singular type under dynamic boundary condition 动态边界条件下奇异型Kobayashi-Warren-Carter系统
IF 1.8 4区 数学
Discrete and Continuous Dynamical Systems-Series S Pub Date : 2023-08-17 DOI: 10.3934/dcdss.2023162
Ryota Nakayashiki, K. Shirakawa
{"title":"Kobayashi-Warren-Carter system of singular type under dynamic boundary condition","authors":"Ryota Nakayashiki, K. Shirakawa","doi":"10.3934/dcdss.2023162","DOIUrl":"https://doi.org/10.3934/dcdss.2023162","url":null,"abstract":"In this paper, we consider a coupled system, known as Kobayashi--Warren--Carter system, abbreviated as the KWC system. KWC system consists of an Allen--Cahn type equation and a singular diffusion equation, and it was proposed by [Kobayashi et al, Phys. D, 140, 141--150 (2000)] as a possible mathematical model of grain boundary motion. The focus of this work is on the dynamic boundary condition imposed in our KWC system, and the mathematical interest is in a conflicting situation between: the continuity of the transmission condition included in the dynamic boundary condition; and the discontinuity encouraged by the singular diffusion equation. On this basis, we will prove the Main Theorem concerned with the existence of solution to our KWC system with energy-dissipation. Additionally, as a sub-result, we will prove a key-lemma that is to give a certain mathematical interpretation for the conflicting situation.","PeriodicalId":48838,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series S","volume":"78 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74509825","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
Beyond the classical strong maximum principle: Forcing changing sign near the boundary and flat solutions 超越经典强极大值原理:在边界和平面解附近强迫改变符号
IF 1.8 4区 数学
Discrete and Continuous Dynamical Systems-Series S Pub Date : 2023-08-04 DOI: 10.3934/dcdss.2023151
Jes'us Ildefonso D'iaz, J. Hern'andez
{"title":"Beyond the classical strong maximum principle: Forcing changing sign near the boundary and flat solutions","authors":"Jes'us Ildefonso D'iaz, J. Hern'andez","doi":"10.3934/dcdss.2023151","DOIUrl":"https://doi.org/10.3934/dcdss.2023151","url":null,"abstract":"We show that the classical strong maximum principle, concerning positive supersolutions of linear elliptic equations vanishing on the boundary of the domain $Omega $ can be extended, under suitable conditions, to the case in which the forcing term $f(x)$ is changing sign. In addition, in the case of solutions, the normal derivative on the boundary may also vanish on the boundary (definition of flat solutions). This leads to examples in which the unique continuation property fails. As a first application, we show the existence of positive solutions for a sublinear semilinear elliptic problem of indefinite sign. A second application, concerning the positivity of solutions of the linear heat equation, for some large values of time, with forcing and/or initial datum changing sign is also given.","PeriodicalId":48838,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series S","volume":"104 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79185232","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 nonlocal Gray-Scott model: Well-posedness and diffusive limit 非定域Gray-Scott模型:适定性和扩散极限
IF 1.8 4区 数学
Discrete and Continuous Dynamical Systems-Series S Pub Date : 2023-07-20 DOI: 10.3934/dcdss.2023158
Philippe Laurencçot, Christoph Walker
{"title":"A nonlocal Gray-Scott model: Well-posedness and diffusive limit","authors":"Philippe Laurencçot, Christoph Walker","doi":"10.3934/dcdss.2023158","DOIUrl":"https://doi.org/10.3934/dcdss.2023158","url":null,"abstract":"Well-posedness in $L_infty$ of the nonlocal Gray-Scott model is studied for integrable kernels, along with the stability of the semi-trivial spatially homogeneous steady state. In addition, it is shown that the solutions to the nonlocal Gray-Scott system converge to those to the classical Gray-Scott system in the diffusive limit.","PeriodicalId":48838,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series S","volume":"126 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87635170","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
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