Discrete and Continuous Dynamical Systems-Series S最新文献_第8页

A convergence result for a Stefan problem with phase relaxation 具有相位松弛的Stefan问题的收敛性结果

IF 1.8 4区数学

Discrete and Continuous Dynamical Systems-Series S Pub Date : 2023-01-01 DOI: 10.3934/dcdss.2023119

V. Recupero

引用次数: 0

Dafermos regularization and viscous wave fan profiles for Riemann solutions of Burger's equation Burger方程黎曼解的Dafermos正则化和粘性波扇分布

IF 1.8 4区数学

Discrete and Continuous Dynamical Systems-Series S Pub Date : 2023-01-01 DOI: 10.3934/dcdss.2023047

Weishi Liu

引用次数: 2

Well-posedness and long-time behavior of a bulk-surface coupled Cahn-Hilliard-diffusion system with singular potential for lipid raft formation 具有脂质筏形成奇异势的体积-表面耦合cahn - hilliard -扩散系统的适定性和长时间行为

4区数学

Discrete and Continuous Dynamical Systems-Series S Pub Date : 2023-01-01 DOI: 10.3934/dcdss.2023169

Hao Wu, Shengqin Xu

{"title":"Well-posedness and long-time behavior of a bulk-surface coupled Cahn-Hilliard-diffusion system with singular potential for lipid raft formation","authors":"Hao Wu, Shengqin Xu","doi":"10.3934/dcdss.2023169","DOIUrl":"https://doi.org/10.3934/dcdss.2023169","url":null,"abstract":"We study a bulk-surface coupled system that describes the processes of lipid-phase separation and lipid-cholesterol interaction on cell membranes, in which cholesterol exchange between cytosol and cell membrane is also incorporated. The PDE system consists of a surface Cahn-Hilliard equation for the relative concentration of saturated/unsaturated lipids and a surface diffusion-reaction equation for the cholesterol concentration on the membrane, together with a diffusion equation for the cytosolic cholesterol concentration in the bulk. The detailed coupling between bulk and surface evolutions is characterized by a mass exchange term $q$. For the system with a physically relevant singular potential, we first prove the existence, uniqueness and regularity of global weak solutions to the full bulk-surface coupled system under suitable assumptions on the initial data and the mass exchange term $q$. Next, we investigate the large cytosolic diffusion limit that gives a reduction of the full bulk-surface coupled system to a system of surface equations with non-local contributions. Afterwards, we study the long-time behavior of global solutions in two categories, i.e., the equilibrium and non-equilibrium models according to different choices of the mass exchange term $q$. For the full bulk-surface coupled system with a decreasing total free energy, we prove that every global weak solution converges to a single equilibrium as $tto +infty$. For the reduced surface system with a mass exchange term of reaction type, we establish the existence of a global attractor.","PeriodicalId":48838,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series S","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135400449","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

Two approaches to instability analysis of the viscous Burgers' equation 粘性Burgers方程不稳定性分析的两种方法

4区数学

Discrete and Continuous Dynamical Systems-Series S Pub Date : 2023-01-01 DOI: 10.3934/dcdss.2023202

Messoud Efendiev, Taylan Sengul, Burhan Tiryakioglu

{"title":"Two approaches to instability analysis of the viscous Burgers' equation","authors":"Messoud Efendiev, Taylan Sengul, Burhan Tiryakioglu","doi":"10.3934/dcdss.2023202","DOIUrl":"https://doi.org/10.3934/dcdss.2023202","url":null,"abstract":"The 1D Burger's equation with Dirichlet boundary conditions exhibits a first transition from the trivial steady state to a sinusoidal patterned steady state as the parameter $ lambda $ which controls the linear term exceeds 1. The main goal of this paper is to present two different approaches regarding the transition of this patterned steady state. We believe that these approaches can be extended to study the dynamics of more interesting models. As a first approach, we consider an external forcing on the equation which supports a sinusoidal solution as a stable steady state which loses its stability at a critical threshold. We use the method of continued fractions to rigorously analyze the associated linear problem. In particular, we find that the system exhibits a mixed type transition with two distinct basins for initial conditions one of which leads to a local steady state and the other leaves a small neighborhood of the origin. As a second approach, we consider the dynamics on the center-unstable manifold of the first two modes of the unforced system. In this approach, the secondary transition produces two branches of steady state solutions. On one of these branches there is another transition which indicates a symmetry breaking phenomena.","PeriodicalId":48838,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series S","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135506329","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

Dimensional reduction and emergence of defects in the Oseen-Frank model for nematic liquid crystals 向列液晶的Oseen-Frank模型的降维和缺陷的出现

4区数学

Discrete and Continuous Dynamical Systems-Series S Pub Date : 2023-01-01 DOI: 10.3934/dcdss.2023174

Giacomo Canevari, Antonio Segatti

{"title":"Dimensional reduction and emergence of defects in the Oseen-Frank model for nematic liquid crystals","authors":"Giacomo Canevari, Antonio Segatti","doi":"10.3934/dcdss.2023174","DOIUrl":"https://doi.org/10.3934/dcdss.2023174","url":null,"abstract":"In this paper we discuss the behavior of the Oseen-Frank model for nematic liquid crystals in the limit of vanishing thickness. More precisely, in a thin slab $ Omegatimes (0, h) $ with $ Omegasubset mathbb{R}^2 $ and $ h>0 $ we consider the one-constant approximation of the Oseen-Frank model for nematic liquid crystals. We impose Dirichlet boundary conditions on the lateral boundary and weak anchoring conditions on the top and bottom faces of the cylinder $ Omegatimes (0, h) $. The Dirichlet datum has the form $ (g, 0) $, where $ gcolonpartialOmegato mathbb{S}^1 $ has non-zero winding number. Under appropriate conditions on the scaling, in the limit as $ hto 0 $ we obtain a behavior that is similar to the one observed in the asymptotic analysis (see [7]) of the two-dimensional Ginzburg-Landau functional. More precisely, we rigorously prove the emergence of a finite number of defect points in $ Omega $ having topological charges that sum to the degree of the boundary datum. Moreover, the position of these points is governed by a Renormalized Energy, as in the seminal results of Bethuel, Brezis and Hélein [7].","PeriodicalId":48838,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series S","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135556893","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 a two-scale phasefield model for topology optimization 拓扑优化的二尺度相场模型

4区数学

Discrete and Continuous Dynamical Systems-Series S Pub Date : 2023-01-01 DOI: 10.3934/dcdss.2023206

Moritz Ebeling-Rump, Dietmar Hömberg, Robert Lasarzik

引用次数: 0

Limiting behavior of invariant or periodic measure of Hopfield neural models driven by locally Lipschitz Lévy noise 局部Lipschitz l<s:1>杂波驱动的Hopfield神经模型不变或周期测度的极限行为

4区数学

Discrete and Continuous Dynamical Systems-Series S Pub Date : 2023-01-01 DOI: 10.3934/dcdss.2023195

Hailang Bai, Yan Wang, Yu Wang

引用次数: 0

Fractional weighted $ p $-Kirchhoff equations with general nonlinearity 具有一般非线性的分数加权$ p $-Kirchhoff方程

IF 1.8 4区数学

Discrete and Continuous Dynamical Systems-Series S Pub Date : 2023-01-01 DOI: 10.3934/dcdss.2023128

Mingqi Xiang, Chaoqun Song

引用次数: 0

Instantaneous blow-up for evolution inequalities of Sobolev type with nonlinear convolution terms 具有非线性卷积项的Sobolev型演化不等式的瞬时爆破

IF 1.8 4区数学

Discrete and Continuous Dynamical Systems-Series S Pub Date : 2023-01-01 DOI: 10.3934/dcdss.2023026

Ibtehal Alazman, M. Jleli

引用次数: 0

Existence of entropy solutions for some quasilinear anisotropic elliptic unilateral problems with variable exponents 一类变指数拟线性各向异性椭圆单侧问题熵解的存在性

IF 1.8 4区数学

Discrete and Continuous Dynamical Systems-Series S Pub Date : 2023-01-01 DOI: 10.3934/dcdss.2023034

E. Azroul, M. Bouziani, H. Hjiaj

引用次数: 0