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Structure-preserving schemes for Cahn–Hilliard equations with dynamic boundary conditions 具有动态边界条件的Cahn-Hilliard方程的保结构格式
4区 数学
Discrete and Continuous Dynamical Systems-Series S Pub Date : 2023-01-01 DOI: 10.3934/dcdss.2023207
Makoto Okumura, Takeshi Fukao
{"title":"Structure-preserving schemes for Cahn–Hilliard equations with dynamic boundary conditions","authors":"Makoto Okumura, Takeshi Fukao","doi":"10.3934/dcdss.2023207","DOIUrl":"https://doi.org/10.3934/dcdss.2023207","url":null,"abstract":"Two kinds of Cahn–Hilliard equations with dynamical boundary conditions have been proposed by Goldstein–Miranville–Schimperna and Liu–Wu, respectively. These models have characteristic conservation and dissipation laws. From the perspective of numerical computation, the properties often lead us to stable computation. Hence, if the designed schemes retain the properties in a discrete sense, then the schemes are expected to be stable. In this paper, we propose structure-preserving schemes for the two-dimensional setting of both models that retain the conservation and dissipation laws in a discrete sense. Also, we discuss the solvability of the proposed scheme for the model of Goldstein–Miranville–Schimperna. Moreover, computation examples demonstrate the effectiveness of our proposed schemes. Especially through computation examples, we confirm that numerical solutions can be stably obtained by our proposed schemes.","PeriodicalId":48838,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series S","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135709285","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
Boundedness and stability for an indirect signal absorption chemotaxis system with signal-dependent motility 具有信号依赖运动的间接信号吸收趋化系统的有界性和稳定性
IF 1.8 4区 数学
Discrete and Continuous Dynamical Systems-Series S Pub Date : 2023-01-01 DOI: 10.3934/dcdss.2023120
Lu Xu, Chunlai Mu, Qiao Xin
{"title":"Boundedness and stability for an indirect signal absorption chemotaxis system with signal-dependent motility","authors":"Lu Xu, Chunlai Mu, Qiao Xin","doi":"10.3934/dcdss.2023120","DOIUrl":"https://doi.org/10.3934/dcdss.2023120","url":null,"abstract":"","PeriodicalId":48838,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series S","volume":"7 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87425964","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
Mean field backward doubly stochastic Volterra integral equations and their applications 平均场倒向双随机Volterra积分方程及其应用
IF 1.8 4区 数学
Discrete and Continuous Dynamical Systems-Series S Pub Date : 2023-01-01 DOI: 10.3934/dcdss.2023016
Hao Wu, Junhao Hu
{"title":"Mean field backward doubly stochastic Volterra integral equations and their applications","authors":"Hao Wu, Junhao Hu","doi":"10.3934/dcdss.2023016","DOIUrl":"https://doi.org/10.3934/dcdss.2023016","url":null,"abstract":"","PeriodicalId":48838,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series S","volume":"283 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76826817","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
Almost periodicity and stability for solutions to networks of beams with structural damping 结构阻尼梁网解的几乎周期性和稳定性
IF 1.8 4区 数学
Discrete and Continuous Dynamical Systems-Series S Pub Date : 2023-01-01 DOI: 10.3934/dcdss.2023004
A. Bchatnia, Amina Boukhatem, K. Mufti
{"title":"Almost periodicity and stability for solutions to networks of beams with structural damping","authors":"A. Bchatnia, Amina Boukhatem, K. Mufti","doi":"10.3934/dcdss.2023004","DOIUrl":"https://doi.org/10.3934/dcdss.2023004","url":null,"abstract":"","PeriodicalId":48838,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series S","volume":"6 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76982367","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
Existence and multiplicity of sign-changing solutions for gauged nonlinear Schrödinger systems in $ mathbb R^2 $ $ mathbb R^2 $中测量非线性Schrödinger系统变符号解的存在性和多重性
IF 1.8 4区 数学
Discrete and Continuous Dynamical Systems-Series S Pub Date : 2023-01-01 DOI: 10.3934/dcdss.2023063
C. Duan, Jianjun Zhang
{"title":"Existence and multiplicity of sign-changing solutions for gauged nonlinear Schrödinger systems in $ mathbb R^2 $","authors":"C. Duan, Jianjun Zhang","doi":"10.3934/dcdss.2023063","DOIUrl":"https://doi.org/10.3934/dcdss.2023063","url":null,"abstract":"","PeriodicalId":48838,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series S","volume":"24 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80523003","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
Galerkin stability of pullback attractors for nonautonomous nonlocal equations 非自治非局部方程回拉吸引子的伽辽金稳定性
IF 1.8 4区 数学
Discrete and Continuous Dynamical Systems-Series S Pub Date : 2023-01-01 DOI: 10.3934/dcdss.2023027
Shulin Wang, Yangrong Li
{"title":"Galerkin stability of pullback attractors for nonautonomous nonlocal equations","authors":"Shulin Wang, Yangrong Li","doi":"10.3934/dcdss.2023027","DOIUrl":"https://doi.org/10.3934/dcdss.2023027","url":null,"abstract":"","PeriodicalId":48838,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series S","volume":"75 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86297553","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
Qualitative behavior of solutions for a class of coupled nonlinear Klein-Gordon equations with strongly damping terms 一类耦合非线性强阻尼Klein-Gordon方程解的定性性质
IF 1.8 4区 数学
Discrete and Continuous Dynamical Systems-Series S Pub Date : 2023-01-01 DOI: 10.3934/dcdss.2023138
Siyan Guo, Jie Liu, Yanbing Yang
{"title":"Qualitative behavior of solutions for a class of coupled nonlinear Klein-Gordon equations with strongly damping terms","authors":"Siyan Guo, Jie Liu, Yanbing Yang","doi":"10.3934/dcdss.2023138","DOIUrl":"https://doi.org/10.3934/dcdss.2023138","url":null,"abstract":"","PeriodicalId":48838,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series S","volume":"155 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83172052","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
Existence and asymptotic behaviour of the least energy solutions for a quasilinear Dirac-Poisson system 一类拟线性Dirac-Poisson系统最小能量解的存在性和渐近性
IF 1.8 4区 数学
Discrete and Continuous Dynamical Systems-Series S Pub Date : 2023-01-01 DOI: 10.3934/dcdss.2023042
Fan Zhou, Zifei Shen, Minbo Yang
{"title":"Existence and asymptotic behaviour of the least energy solutions for a quasilinear Dirac-Poisson system","authors":"Fan Zhou, Zifei Shen, Minbo Yang","doi":"10.3934/dcdss.2023042","DOIUrl":"https://doi.org/10.3934/dcdss.2023042","url":null,"abstract":"","PeriodicalId":48838,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series S","volume":"11 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88689084","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
Uniform large deviation principles of fractional stochastic reaction-diffusion equations on unbounded domains 无界区域上分数阶随机反应扩散方程的一致大偏差原理
IF 1.8 4区 数学
Discrete and Continuous Dynamical Systems-Series S Pub Date : 2023-01-01 DOI: 10.3934/dcdss.2023020
Bixiang Wang
{"title":"Uniform large deviation principles of fractional stochastic reaction-diffusion equations on unbounded domains","authors":"Bixiang Wang","doi":"10.3934/dcdss.2023020","DOIUrl":"https://doi.org/10.3934/dcdss.2023020","url":null,"abstract":"","PeriodicalId":48838,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series S","volume":"SE-12 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84640401","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: 2
State estimation of reaction-diffusion inertial neural networks with Markovian switching channels via conjunct measurement 基于联合测量的马尔可夫切换通道反应-扩散惯性神经网络状态估计
IF 1.8 4区 数学
Discrete and Continuous Dynamical Systems-Series S Pub Date : 2023-01-01 DOI: 10.3934/dcdss.2023061
Xiaona Song, Xuemei Wang, Shuai Song
{"title":"State estimation of reaction-diffusion inertial neural networks with Markovian switching channels via conjunct measurement","authors":"Xiaona Song, Xuemei Wang, Shuai Song","doi":"10.3934/dcdss.2023061","DOIUrl":"https://doi.org/10.3934/dcdss.2023061","url":null,"abstract":"","PeriodicalId":48838,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series S","volume":"4 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78327729","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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