Pub Date : 2024-01-19DOI: 10.1142/s0218202524500167
Guoqiang Ren, Bin Liu
{"title":"Global solvability of a two-species chemotaxis-fluid system with Lotka-Volterra type competitive kinetics","authors":"Guoqiang Ren, Bin Liu","doi":"10.1142/s0218202524500167","DOIUrl":"https://doi.org/10.1142/s0218202524500167","url":null,"abstract":"","PeriodicalId":18311,"journal":{"name":"Mathematical Models and Methods in Applied Sciences","volume":"9 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139525782","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}
Pub Date : 2024-01-15DOI: 10.1142/s0218202524500088
Franz Gmeineder, Peter Lewintan, Patrizio Neff
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. PDE62 (2023) 182], where we focused on the case and incompatibilities governed by the matrix curl, the case 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. PDE60 (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.
我们为超线性增长机制下的广义不相容场建立了一系列尖锐标准下的胁迫科恩式不等式。这扩展并统一了之前已知的几个不等式，这些不等式对连续介质力学中多种模型的存在性理论至关重要。不同于我们之前的工作 [F. Gmeineder, P. LewGmeineder, P. Lewintan and P. Neff, Optimal incompatible Korn-Maxwell-Sobolev inequalities in all dimensions, Calc.Calc.PDE 62 (2023) 182]，其中我们关注的是 p=1 的情况和由矩阵卷曲支配的不相容性，而本文考虑的 p>1 的情况让我们从谐波分析中获得了更强的结果，但反过来也处理了更普遍的不相容性。特别是，我们得到了 P. Lewintan、S. Müller 和 P. Neff [Korn inequalities for incompatible tensor fields in three space dimensions with conformally invariant dislocation energy, Calc.Var.PDE 60 (2021) 150]中的不相容科恩式不等式与保角不变位错能。然而，由于我们的方法也适用于高阶情形，因此同样给出了涉及克罗纳不相容张量 inc.
{"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":"<p>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, <i>Calc. Var. PDE</i> <b>62</b> (2023) 182], where we focused on the case <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mi>p</mi><mo>=</mo><mn>1</mn></math></span><span></span> and incompatibilities governed by the matrix curl, the case <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mi>p</mi><mo>></mo><mn>1</mn></math></span><span></span> 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, <i>Calc. Var. PDE</i> <b>60</b> (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 <b>inc</b>.</p>","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}
Pub Date : 2024-01-12DOI: 10.1142/s021820252450009x
Hyeokjoo Park, Do Y. Kwak
{"title":"An Analysis Of Nonconforming Virtual Element Methods On Polytopal Meshes With Small Faces","authors":"Hyeokjoo Park, Do Y. Kwak","doi":"10.1142/s021820252450009x","DOIUrl":"https://doi.org/10.1142/s021820252450009x","url":null,"abstract":"","PeriodicalId":18311,"journal":{"name":"Mathematical Models and Methods in Applied Sciences","volume":" 29","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139624927","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}
Pub Date : 2024-01-10DOI: 10.1142/s0218202524500076
Gregor Gantner, Martin Vohralík
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 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.
{"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":"<p>In this paper, we consider isogeometric discretizations of the Poisson model problem, focusing on high polynomial degrees and strong hierarchical refinements. We derive <i>a posteriori</i> error estimates by equilibrated fluxes, i.e. vector-valued mapped piecewise polynomials lying in the <span><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></span><span></span> 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.</p>","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}
Pub Date : 2023-12-23DOI: 10.1142/s0218202523990014
{"title":"Author index Volume 33","authors":"","doi":"10.1142/s0218202523990014","DOIUrl":"https://doi.org/10.1142/s0218202523990014","url":null,"abstract":"","PeriodicalId":18311,"journal":{"name":"Mathematical Models and Methods in Applied Sciences","volume":"150 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139161003","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}
Pub Date : 2023-11-23DOI: 10.1142/s0218202524500039
Young-Pil Choi, Jinwook Jung
{"title":"Local well-posedness for the compressible Navier–Stokes–BGK model in Sobolev spaces with exponential weight","authors":"Young-Pil Choi, Jinwook Jung","doi":"10.1142/s0218202524500039","DOIUrl":"https://doi.org/10.1142/s0218202524500039","url":null,"abstract":"","PeriodicalId":18311,"journal":{"name":"Mathematical Models and Methods in Applied Sciences","volume":"9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139243181","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}
Pub Date : 2023-11-18DOI: 10.1142/s0218202524020019
N. Bellomo, F. Brezzi
This editorial is dedicated to presenting the papers published in a special issue focused on modeling, qualitative analysis and simulation of the collective dynamics of systems in engineering and life sciences. All papers have a minor or major reference to living, i.e. complex systems, and a critical analysis of the overall content of the issue is proposed, leading to a forward look at research perspectives. This paper first defines the goals of the issue. Then, a brief description of the scientific contribution of the papers published in this issue is given. Finally, a look into the future is proposed.
{"title":"Surveys and essays towards research perspectives on complex systems","authors":"N. Bellomo, F. Brezzi","doi":"10.1142/s0218202524020019","DOIUrl":"https://doi.org/10.1142/s0218202524020019","url":null,"abstract":"This editorial is dedicated to presenting the papers published in a special issue focused on modeling, qualitative analysis and simulation of the collective dynamics of systems in engineering and life sciences. All papers have a minor or major reference to living, i.e. complex systems, and a critical analysis of the overall content of the issue is proposed, leading to a forward look at research perspectives. This paper first defines the goals of the issue. Then, a brief description of the scientific contribution of the papers published in this issue is given. Finally, a look into the future is proposed.","PeriodicalId":18311,"journal":{"name":"Mathematical Models and Methods in Applied Sciences","volume":"60 9","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139261807","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}
Pub Date : 2023-11-08DOI: 10.1142/s0218202524400037
Christian Dull, Piotr Gwiazda, Anna Marciniak-Czochra, Jakub Skrzeczkowski
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.
{"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}
Pub Date : 2023-11-04DOI: 10.1142/s0218202524400013
Tayfun E. Tezduyar, Kenji Takizawa, Yuri Bazilevs
{"title":"Isogeometric analysis in computation of complex-geometry flow problems with moving boundaries and interfaces","authors":"Tayfun E. Tezduyar, Kenji Takizawa, Yuri Bazilevs","doi":"10.1142/s0218202524400013","DOIUrl":"https://doi.org/10.1142/s0218202524400013","url":null,"abstract":"","PeriodicalId":18311,"journal":{"name":"Mathematical Models and Methods in Applied Sciences","volume":"284 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135775869","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}
Pub Date : 2023-11-01DOI: 10.1142/s0218202523500604
Jingyi Fu, Jiuyang Liang, Benoit Perthame, Min Tang, Chuhan Zhong
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.
{"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}
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