Mathematical Models and Methods in Applied Sciences最新文献_第4页

Global solvability of a two-species chemotaxis-fluid system with Lotka-Volterra type competitive kinetics 具有洛特卡-伏特拉竞争动力学的双物种趋化-流体系统的全局可解性

Mathematical Models and Methods in Applied Sciences Pub Date : 2024-01-19 DOI: 10.1142/s0218202524500167

Guoqiang Ren, Bin Liu

引用次数: 0

Korn–Maxwell–Sobolev inequalities for general incompatibilities 一般不相容的 Korn-Maxwell-Sobolev 不等式

Mathematical Models and Methods in Applied Sciences Pub Date : 2024-01-15 DOI: 10.1142/s0218202524500088

Franz Gmeineder, Peter Lewintan, Patrizio Neff

{"title":"Korn–Maxwell–Sobolev inequalities for general incompatibilities","authors":"Franz Gmeineder, Peter Lewintan, Patrizio Neff","doi":"10.1142/s0218202524500088","DOIUrl":"https://doi.org/10.1142/s0218202524500088","url":null,"abstract":"We establish a family of coercive Korn-type inequalities for generalized incompatible fields in the superlinear growth regime under sharp criteria. This extends and unifies several previously known inequalities that are pivotal to the existence theory for a multitude of models in continuum mechanics in an optimal way. Different from our preceding work [F. Gmeineder, P. Lewintan and P. Neff, Optimal incompatible Korn–Maxwell–Sobolev inequalities in all dimensions, Calc. Var. PDE 62 (2023) 182], where we focused on the case <math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mi>p</mi><mo>=</mo><mn>1</mn></math> and incompatibilities governed by the matrix curl, the case <math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mi>p</mi><mo>></mo><mn>1</mn></math> considered in this paper gives us access to substantially stronger results from harmonic analysis but conversely deals with more general incompatibilities. Especially, we obtain sharp generalizations of recently proved inequalities by P. Lewintan, S. Müller and P. Neff [Korn inequalities for incompatible tensor fields in three space dimensions with conformally invariant dislocation energy, Calc. Var. PDE 60 (2021) 150] in the realm of incompatible Korn-type inequalities with conformally invariant dislocation energy. However, being applicable to higher-order scenarios as well, our approach equally gives the first and sharp inequalities involving Kröner’s incompability tensor inc.","PeriodicalId":18311,"journal":{"name":"Mathematical Models and Methods in Applied Sciences","volume":"15 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140203466","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

An Analysis Of Nonconforming Virtual Element Methods On Polytopal Meshes With Small Faces 带小面的多边形网格上不符合要求的虚拟元素方法分析

Mathematical Models and Methods in Applied Sciences Pub Date : 2024-01-12 DOI: 10.1142/s021820252450009x

Hyeokjoo Park, Do Y. Kwak

引用次数: 0

Inexpensive polynomial-degree-robust equilibrated flux a posteriori estimates for isogeometric analysis 用于等时线分析的低成本多项式度稳健均衡通量后验估计值

Mathematical Models and Methods in Applied Sciences Pub Date : 2024-01-10 DOI: 10.1142/s0218202524500076

Gregor Gantner, Martin Vohralík

{"title":"Inexpensive polynomial-degree-robust equilibrated flux a posteriori estimates for isogeometric analysis","authors":"Gregor Gantner, Martin Vohralík","doi":"10.1142/s0218202524500076","DOIUrl":"https://doi.org/10.1142/s0218202524500076","url":null,"abstract":"In this paper, we consider isogeometric discretizations of the Poisson model problem, focusing on high polynomial degrees and strong hierarchical refinements. We derive a posteriori error estimates by equilibrated fluxes, i.e. vector-valued mapped piecewise polynomials lying in the <math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mstyle mathvariant=\"bold-italic\"><mi>H</mi></mstyle><mo stretchy=\"false\">(</mo><mstyle><mtext mathvariant=\"normal\">div</mtext></mstyle><mo stretchy=\"false\">)</mo></math> space which appropriately approximate the desired divergence constraint. Our estimates are constant-free in the leading term, locally efficient, and robust with respect to the polynomial degree. They are also robust with respect to the number of hanging nodes arising in adaptive mesh refinement employing hierarchical B-splines, though not with respect to the smoothness and support overlaps. Two partitions of unity are designed, one with larger supports corresponding to the mapped splines, and one with small supports corresponding to mapped piecewise multilinear finite element hat basis functions. The equilibration is only performed on the small supports, avoiding the higher computational price of equilibration on the large supports or even the solution of a global system. Thus, the derived estimates are also as inexpensive as possible. An abstract framework for such a setting is developed, whose application to a specific situation only requests a verification of a few clearly identified assumptions. Numerical experiments illustrate the theoretical developments.","PeriodicalId":18311,"journal":{"name":"Mathematical Models and Methods in Applied Sciences","volume":"4 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140203467","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

Author index Volume 33 作者索引第 33 卷

Mathematical Models and Methods in Applied Sciences Pub Date : 2023-12-23 DOI: 10.1142/s0218202523990014

引用次数: 0

Local well-posedness for the compressible Navier–Stokes–BGK model in Sobolev spaces with exponential weight 具有指数权重的索波列夫空间中可压缩纳维-斯托克斯-BGK 模型的局部好求解性

Mathematical Models and Methods in Applied Sciences Pub Date : 2023-11-23 DOI: 10.1142/s0218202524500039

Young-Pil Choi, Jinwook Jung

引用次数: 0

Surveys and essays towards research perspectives on complex systems 面向复杂系统研究视角的调查和论文

Mathematical Models and Methods in Applied Sciences Pub Date : 2023-11-18 DOI: 10.1142/s0218202524020019

N. Bellomo, F. Brezzi

引用次数: 0

Structured Population Models on Polish Spaces: A Unified Approach including Graphs, Riemannian Manifolds and Measure Spaces to Describe Dynamics of Heterogeneous Populations 波兰空间上的结构种群模型:一种包括图、黎曼流形和度量空间的描述异质种群动态的统一方法

Mathematical Models and Methods in Applied Sciences Pub Date : 2023-11-08 DOI: 10.1142/s0218202524400037

Christian Dull, Piotr Gwiazda, Anna Marciniak-Czochra, Jakub Skrzeczkowski

{"title":"Structured Population Models on Polish Spaces: A Unified Approach including Graphs, Riemannian Manifolds and Measure Spaces to Describe Dynamics of Heterogeneous Populations","authors":"Christian Dull, Piotr Gwiazda, Anna Marciniak-Czochra, Jakub Skrzeczkowski","doi":"10.1142/s0218202524400037","DOIUrl":"https://doi.org/10.1142/s0218202524400037","url":null,"abstract":"This paper presents a mathematical framework for modeling the dynamics of heterogeneous populations. Models describing local and non-local growth and transport processes appear in a variety of applications, such as crowd dynamics, tissue regeneration, cancer development and coagulation-fragmentation processes. The diverse applications pose a common challenge to mathematicians due to the multiscale nature of the structures that underlie the system’s self-organization and control. Similar abstract mathematical problems arise when formulating problems in the language of measure evolution on a multi-faceted state space. Motivated by these observations, we propose a general mathematical framework for nonlinear structured population models on abstract metric spaces, which are only assumed to be separable and complete. We exploit the structure of the space of non-negative Radon measures with the dual bounded Lipschitz distance (flat metric), which is a generalization of the Wasserstein distance, capable of addressing non-conservative problems. The formulation of models on general metric spaces allows considering infinite-dimensional state spaces or graphs and coupling discrete and continuous state transitions. This opens up exciting possibilities for modeling single-cell data, crowd dynamics or coagulation-fragmentation processes.","PeriodicalId":18311,"journal":{"name":"Mathematical Models and Methods in Applied Sciences","volume":" 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135293108","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: 1

Isogeometric analysis in computation of complex-geometry flow problems with moving boundaries and interfaces 具有移动边界和界面的复杂几何流动问题计算中的等几何分析

Mathematical Models and Methods in Applied Sciences Pub Date : 2023-11-04 DOI: 10.1142/s0218202524400013

Tayfun E. Tezduyar, Kenji Takizawa, Yuri Bazilevs

引用次数: 0

Confined run-and-tumble model with boundary aggregation: Long-time behavior and convergence to the confined Fokker–Planck model 具有边界聚集的受限滚跑模型:长期行为和收敛于受限Fokker-Planck模型

Mathematical Models and Methods in Applied Sciences Pub Date : 2023-11-01 DOI: 10.1142/s0218202523500604

Jingyi Fu, Jiuyang Liang, Benoit Perthame, Min Tang, Chuhan Zhong

{"title":"Confined run-and-tumble model with boundary aggregation: Long-time behavior and convergence to the confined Fokker–Planck model","authors":"Jingyi Fu, Jiuyang Liang, Benoit Perthame, Min Tang, Chuhan Zhong","doi":"10.1142/s0218202523500604","DOIUrl":"https://doi.org/10.1142/s0218202523500604","url":null,"abstract":"The motile micro-organisms such as Escherichia coli, sperm, or some seaweed are usually modeled by self-propelled particles that move with the run-and-tumble process. Individual-based stochastic models are usually employed to model the aggregation phenomenon at the boundary, which is an active research field that has attracted a lot of biologists and biophysicists. Self-propelled particles at the microscale have complex behaviors, while characteristics at the population level are more important for practical applications but rely on individual behaviors. Kinetic PDE models that describe the time evolution of the probability density distribution of the motile micro-organisms are widely used. However, how to impose the appropriate boundary conditions that take into account the boundary aggregation phenomena is rarely studied. In this paper, we propose the boundary conditions for a 2D confined run-and-tumble model (CRTM) for self-propelled particle populations moving between two parallel plates with a run-and-tumble process. The proposed model satisfies the relative entropy inequality and thus long-time convergence. We establish the relation between CRTM and the confined Fokker–Planck model (CFPM) studied in [J. Fu, B. Perthame and M. Tang, Fokker–Plank system for movement of micro-organism population in confined environment, J. Statist. Phys. 184 (2021) 1–25]. We prove theoretically that when the tumble is highly forward peaked and frequent enough, CRTM converges asymptotically to the CFPM. A numerical comparison of the CRTM with aggregation and CFPM is given. The time evolution of both the deterministic PDE model and individual-based stochastic simulations are displayed, which match each other well.","PeriodicalId":18311,"journal":{"name":"Mathematical Models and Methods in Applied Sciences","volume":"63 6","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135372938","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