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The anisotropic Cahn–Hilliard equation: Regularity theory and strict separation properties 各向异性Cahn-Hilliard方程:正则性理论和严格分离性质
IF 1.8 4区 数学
Discrete and Continuous Dynamical Systems-Series S Pub Date : 2023-05-29 DOI: 10.3934/dcdss.2023146
H. Garcke, P. Knopf, J. Wittmann
{"title":"The anisotropic Cahn–Hilliard equation: Regularity theory and strict separation properties","authors":"H. Garcke, P. Knopf, J. Wittmann","doi":"10.3934/dcdss.2023146","DOIUrl":"https://doi.org/10.3934/dcdss.2023146","url":null,"abstract":"The Cahn--Hilliard equation with anisotropic energy contributions frequently appears in many physical systems. Systematic analytical results for the case with the relevant logarithmic free energy have been missing so far. We close this gap and show existence, uniqueness, regularity, and separation properties of weak solutions to the anisotropic Cahn--Hilliard equation with logarithmic free energy. Since firstly, the equation becomes highly non-linear, and secondly, the relevant anisotropies are non-smooth, the analysis becomes quite involved. In particular, new regularity results for quasilinear elliptic equations of second order need to be shown.","PeriodicalId":48838,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series S","volume":"31 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89481144","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
On nonlocal Dirichlet problems with oscillating term 关于振荡项的非局部狄利克雷问题
IF 1.8 4区 数学
Discrete and Continuous Dynamical Systems-Series S Pub Date : 2023-05-16 DOI: 10.3934/dcdss.2022130
Boštjan Gabrovšek, Giovanni Molica Bisci, Dušan D. Repovš
{"title":"On nonlocal Dirichlet problems with oscillating term","authors":"Boštjan Gabrovšek, Giovanni Molica Bisci, Dušan D. Repovš","doi":"10.3934/dcdss.2022130","DOIUrl":"https://doi.org/10.3934/dcdss.2022130","url":null,"abstract":"<p style='text-indent:20px;'>In this paper, a class of nonlocal fractional Dirichlet problems is studied. By using a variational principle due to Ricceri (whose original version was given in J. Comput. Appl. Math. 113 (2000), 401–410), the existence of infinitely many weak solutions for these problems is established by requiring that the nonlinear term <inline-formula><tex-math id=\"M1\">begin{document}$ f $end{document}</tex-math></inline-formula> has a suitable oscillating behaviour either at the origin or at infinity.</p>","PeriodicalId":48838,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series S","volume":"121 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78428342","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
A phase-field system arising from multiscale modeling of thrombus biomechanics in blood vessels: Local well-posedness in dimension two 血管血栓生物力学多尺度建模产生的相场系统:二维局部适定性
IF 1.8 4区 数学
Discrete and Continuous Dynamical Systems-Series S Pub Date : 2023-04-06 DOI: 10.3934/dcdss.2023105
M. Grasselli, A. Poiatti
{"title":"A phase-field system arising from multiscale modeling of thrombus biomechanics in blood vessels: Local well-posedness in dimension two","authors":"M. Grasselli, A. Poiatti","doi":"10.3934/dcdss.2023105","DOIUrl":"https://doi.org/10.3934/dcdss.2023105","url":null,"abstract":"We consider a phase-field model which describes the interactions between the blood flow and the thrombus. The latter is supposed to be a viscoelastic material. The potential describing the cohesive energy of the mixture is assumed to be of Flory-Huggins type (i.e. logarithmic). This ensures the boundedness from below of the dissipation energy. In the two dimensional case, we prove the local (in time) existence and uniqueness of a strong solution, provided that the two viscosities of the pure fluid phases are close enough. We also show that the order parameter remains strictly separated from the pure phases if it is so at the initial time.","PeriodicalId":48838,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series S","volume":"33 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91284359","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
Degenerate diffusion with Preisach hysteresis 具有Preisach滞后的退化扩散
IF 1.8 4区 数学
Discrete and Continuous Dynamical Systems-Series S Pub Date : 2023-03-30 DOI: 10.3934/dcdss.2023154
Chiara Gavioli, Pavel Krejvc'i
{"title":"Degenerate diffusion with Preisach hysteresis","authors":"Chiara Gavioli, Pavel Krejvc'i","doi":"10.3934/dcdss.2023154","DOIUrl":"https://doi.org/10.3934/dcdss.2023154","url":null,"abstract":"Fluid diffusion in unsaturated porous media manifests strong hysteresis effects due to surface tension on the liquid-gas interface. We describe hysteresis in the pressure-saturation relation by means of the Preisach operator, which makes the resulting evolutionary PDE strongly degenerate. We prove the existence and uniqueness of a strong global solution in arbitrary space dimension using a special weak convexity concept.","PeriodicalId":48838,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series S","volume":"1 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82380023","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
The linear stability and basic reproduction numbers for autonomous FDEs 自主FDEs的线性稳定性和基本再现数
IF 1.8 4区 数学
Discrete and Continuous Dynamical Systems-Series S Pub Date : 2023-02-24 DOI: 10.3934/dcdss.2023082
Xiao-Qiang Zhao
{"title":"The linear stability and basic reproduction numbers for autonomous FDEs","authors":"Xiao-Qiang Zhao","doi":"10.3934/dcdss.2023082","DOIUrl":"https://doi.org/10.3934/dcdss.2023082","url":null,"abstract":"In this paper, we first prove the stability equivalence between a linear autonomous and cooperative functional differential equation (FDE) and its associated autonomous and cooperative system without time delay. Then we present the theory of basic reproduction number $mathcal{R}_0$ for general autonomous FDEs. As an illustrative example, we also establish the threshold dynamics for a time-delayed population model of black-legged ticks in terms of $mathcal{R}_0$.","PeriodicalId":48838,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series S","volume":"10 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80063197","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
Output feedback finite-time stabilization of a class of large-scale high-order nonlinear stochastic feedforward systems 一类大规模高阶非线性随机前馈系统的输出反馈有限时间镇定
IF 1.8 4区 数学
Discrete and Continuous Dynamical Systems-Series S Pub Date : 2023-01-01 DOI: 10.3934/dcdss.2023008
Xinghui Zhang, Enyong Liu, Jianlong Qiu, A. Zhang, Zhi Liu
{"title":"Output feedback finite-time stabilization of a class of large-scale high-order nonlinear stochastic feedforward systems","authors":"Xinghui Zhang, Enyong Liu, Jianlong Qiu, A. Zhang, Zhi Liu","doi":"10.3934/dcdss.2023008","DOIUrl":"https://doi.org/10.3934/dcdss.2023008","url":null,"abstract":"","PeriodicalId":48838,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series S","volume":"1 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90214021","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
Positive solutions for nonlinear singular problems with sign-changing nonlinearities 变符号非线性非线性奇异问题的正解
IF 1.8 4区 数学
Discrete and Continuous Dynamical Systems-Series S Pub Date : 2023-01-01 DOI: 10.3934/dcdss.2023131
Yunru Bai, Nikolaos S. Papageorgiou, Shengda Zeng
{"title":"Positive solutions for nonlinear singular problems with sign-changing nonlinearities","authors":"Yunru Bai, Nikolaos S. Papageorgiou, Shengda Zeng","doi":"10.3934/dcdss.2023131","DOIUrl":"https://doi.org/10.3934/dcdss.2023131","url":null,"abstract":"","PeriodicalId":48838,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series S","volume":"40 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90952586","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
On terminal value problem for fractional superdiffusive of Sobolev equation type Sobolev方程型分数阶超扩散的终值问题
4区 数学
Discrete and Continuous Dynamical Systems-Series S Pub Date : 2023-01-01 DOI: 10.3934/dcdss.2023172
Bui Duc Nam, Le Nhat Huynh, Le Dinh Long, Yusuf Gurefe
{"title":"On terminal value problem for fractional superdiffusive of Sobolev equation type","authors":"Bui Duc Nam, Le Nhat Huynh, Le Dinh Long, Yusuf Gurefe","doi":"10.3934/dcdss.2023172","DOIUrl":"https://doi.org/10.3934/dcdss.2023172","url":null,"abstract":"In this paper, we consider the terminal value problem for fractional super diffusive equation in case linear source function. This equation has many applications in physical phenomena. The results in this study are mainly provide the existence and regularity of the mild solution under the various assumptions of the input data.","PeriodicalId":48838,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series S","volume":"31 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":"135549391","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
An improved result on bounded/periodic solutions for some scalar delay differential equations 一类标量时滞微分方程有界/周期解的改进结果
4区 数学
Discrete and Continuous Dynamical Systems-Series S Pub Date : 2023-01-01 DOI: 10.3934/dcdss.2023205
Shangbing Ai
{"title":"An improved result on bounded/periodic solutions for some scalar delay differential equations","authors":"Shangbing Ai","doi":"10.3934/dcdss.2023205","DOIUrl":"https://doi.org/10.3934/dcdss.2023205","url":null,"abstract":"In [2] we established an existence theorem on bounded/periodic solutions for a class of scalar delay differential equations of the form$ begin{equation} frac{du}{dt} = f(t,u(t), u(t-r_1), cdots, u(t-r_n)), qquad t in mathbb R, ;;;;;(1)end{equation} $under the assumptions that the constant delays $ r_k&gt;0 $, $ k = 1, cdots, n $, are 'small' and $ f $ satisfies a one-sided Lipschitz condition on the variables $ u(t), u(t-r_1), cdots, u(t-r_n) $. In this paper, we improve this result in the case that $ f $ is strictly increasing in some variables $ u(t-r_k) $ and obtain a new result that allows larger values of $ r_k $ with which the equation (1) still has a bounded/periodic solution. We illustrate this result via some population models.","PeriodicalId":48838,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series S","volume":"29 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":"135559412","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
On the Cahn–Hilliard–Oono equation with singular potential and volume constraint 具有奇异势和体积约束的Cahn-Hilliard-Oono方程
4区 数学
Discrete and Continuous Dynamical Systems-Series S Pub Date : 2023-01-01 DOI: 10.3934/dcdss.2023198
Takeshi Fukao, Giulio Schimperna
{"title":"On the Cahn–Hilliard–Oono equation with singular potential and volume constraint","authors":"Takeshi Fukao, Giulio Schimperna","doi":"10.3934/dcdss.2023198","DOIUrl":"https://doi.org/10.3934/dcdss.2023198","url":null,"abstract":"","PeriodicalId":48838,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series S","volume":"63 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":"135561006","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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