发布求助
文献互助 智能选刊 最新文献

Journal of Nonlinear Science最新文献

筛选
英文 中文
General Relativistic Lagrangian Continuum Theories Part I: Reduced Variational Principles and Junction Conditions for Hydrodynamics and Elasticity 广义相对论拉格朗日连续理论第一部分：流体力学和弹性的简化变量原理和交界条件
IF 3 2区 数学
Journal of Nonlinear Science Pub Date : 2024-03-19 DOI: 10.1007/s00332-024-10019-5
François Gay-Balmaz
{"title":"General Relativistic Lagrangian Continuum Theories Part I: Reduced Variational Principles and Junction Conditions for Hydrodynamics and Elasticity","authors":"François Gay-Balmaz","doi":"10.1007/s00332-024-10019-5","DOIUrl":"https://doi.org/10.1007/s00332-024-10019-5","url":null,"abstract":"<p>We establish a Lagrangian variational framework for general relativistic continuum theories that permits the development of the process of Lagrangian reduction by symmetry in the relativistic context. Starting with a continuum version of the Hamilton principle for the relativistic particle, we deduce two classes of reduced variational principles that are associated to either spacetime covariance, which is an axiom of the continuum theory, or material covariance, which is related to particular properties of the system such as isotropy. The covariance hypotheses and the Lagrangian reduction process are efficiently formulated by making explicit the dependence of the theory on given material and spacetime tensor fields that are transported by the world-tube of the continuum via the push-forward and pull-back operations. It is shown that the variational formulation, when augmented with the Gibbons–Hawking–York (GHY) boundary terms, also yields the Israel–Darmois junction conditions between the solution at the interior of the relativistic continua and the solution describing the gravity field produced outside from it. The expression of the first variation of the GHY term with respect to the hypersurface involves some extensions of previous results that we also derive in the paper. We consider in detail the application of the variational framework to relativistic fluids and relativistic elasticity. For the latter case, our setting also allows to clarify the relation between formulations of relativistic elasticity based on the relativistic right Cauchy-Green tensor or on the relativistic Cauchy deformation tensor. The setting developed here will be further exploited for modeling purpose in subsequent parts of the paper.</p>","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2024-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140167717","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
A Regularized Model for Wetting/Dewetting Problems: Positivity and Asymptotic Analysis 润湿/脱湿问题的正规化模型：正相关性和渐近分析
IF 3 2区 数学
Journal of Nonlinear Science Pub Date : 2024-03-18 DOI: 10.1007/s00332-024-10020-y
Zeyu Zhou, Wei Jiang, Zhen Zhang
{"title":"A Regularized Model for Wetting/Dewetting Problems: Positivity and Asymptotic Analysis","authors":"Zeyu Zhou, Wei Jiang, Zhen Zhang","doi":"10.1007/s00332-024-10020-y","DOIUrl":"https://doi.org/10.1007/s00332-024-10020-y","url":null,"abstract":"<p>We consider a general regularized variational model for simulating wetting/dewetting phenomena arising from solids or fluids. The regularized model leads to the appearance of a precursor layer which covers the bare substrate, with the precursor height depending on the regularization parameter <span>(varepsilon )</span>. This model enjoys lots of advantages in analysis and simulations. With the help of the precursor layer, the spatial domain is naturally extended to a larger fixed one in the regularized model, which leads to both analytical and computational eases. There is no need to explicitly track the contact line motion, and difficulties arising from free boundary problems can be avoided. In addition, topological change events can be automatically captured. Under some mild and physically meaningful conditions, we show the positivity-preserving property of the minimizers of the regularized model. By using formal asymptotic analysis and <span>(Gamma )</span>-limit analysis, we investigate the convergence relations between the regularized model and the classical sharp-interface model. Finally, numerical results are provided to validate our theoretical analysis, as well as the accuracy and efficiency of the regularized model.</p>","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2024-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140167574","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Convergence to Sharp Traveling Waves of Solutions for Burgers-Fisher-KPP Equations with Degenerate Diffusion 具有退化扩散的伯格斯-费舍尔-KPP方程的解趋近于尖锐游波
IF 3 2区 数学
Journal of Nonlinear Science Pub Date : 2024-03-16 DOI: 10.1007/s00332-024-10021-x
Tianyuan Xu, Shanming Ji, Ming Mei, Jingxue Yin
{"title":"Convergence to Sharp Traveling Waves of Solutions for Burgers-Fisher-KPP Equations with Degenerate Diffusion","authors":"Tianyuan Xu, Shanming Ji, Ming Mei, Jingxue Yin","doi":"10.1007/s00332-024-10021-x","DOIUrl":"https://doi.org/10.1007/s00332-024-10021-x","url":null,"abstract":"<p>This paper is concerned with the convergence to sharp traveling waves of solutions with semi-compactly supported initial data for Burgers-Fisher-KPP equations with degenerate diffusion. We characterize the motion of the free boundary in the long-time asymptotic of the solution to Cauchy problem and the convergence to sharp traveling wave with almost exponential decay rates. Here a key difficulty lies in the intrinsic presence of nonlinear advection effect. After providing the analysis of the nonlinear advection effect on the asymptotic propagation speed of the free boundary, we construct sub- and super-solutions with semi-compact supports to estimate the motion of the free boundary. The new method overcomes the difficulties of the non-integrability of the generalized derivatives of sharp traveling waves at the free boundary.</p>","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2024-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140156676","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 Doubly Non-local Hele-Shaw–Cahn–Hilliard System: Derivation and 2D Well-Posedness 关于双非局域 Hele-Shaw-Cahn-Hilliard 系统：推导与二维拟合
IF 3 2区 数学
Journal of Nonlinear Science Pub Date : 2024-03-15 DOI: 10.1007/s00332-024-10018-6
{"title":"On the Doubly Non-local Hele-Shaw–Cahn–Hilliard System: Derivation and 2D Well-Posedness","authors":"","doi":"10.1007/s00332-024-10018-6","DOIUrl":"https://doi.org/10.1007/s00332-024-10018-6","url":null,"abstract":"<h3>Abstract</h3> <p>Starting from a classic non-local (in space) Cahn–Hilliard–Stokes model for two-phase flow in a thin heterogeneous fluid domain, we rigorously derive by mathematical homogenization a new effective mixture model consisting of a coupling of a non-local (in time) Hele-Shaw equation with a non-local (in space) Cahn–Hilliard equation. We then analyse the resulting model and prove its well-posedness. A key to the analysis is the new concept of sigma-convergence in thin heterogeneous domains allowing to pass to the homogenization limit with respect to the heterogeneities and the domain thickness simultaneously.</p>","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140152367","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 Trajectory of a Light Small Rigid Body in an Incompressible Viscous Fluid 论不可压缩粘性流体中轻质小刚体的轨迹
IF 3 2区 数学
Journal of Nonlinear Science Pub Date : 2024-03-15 DOI: 10.1007/s00332-024-10022-w
Marco Bravin, Šárka Nečasová
{"title":"On the Trajectory of a Light Small Rigid Body in an Incompressible Viscous Fluid","authors":"Marco Bravin, Šárka Nečasová","doi":"10.1007/s00332-024-10022-w","DOIUrl":"https://doi.org/10.1007/s00332-024-10022-w","url":null,"abstract":"<p>In this paper, we study the dynamics of a small rigid body in a viscous incompressible fluid in dimension two and three. More precisely we investigate the trajectory of the rigid body in the limit when its mass and its size tend to zero. We show that the velocity of the center of mass of the rigid body coincides with the background fluid velocity in the limit. We are able to consider the limit when the volume of the rigid bodies converges to zero while their densities are a fixed constant.\u0000</p>","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140152366","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Threshold Dynamics of a Degenerate Diffusive HBV Infection Model with DNA-Containing Capsids in Heterogeneous Environment 在异质环境中含 DNA 头壳的退化扩散型 HBV 感染模型的阈值动态变化
IF 3 2区 数学
Journal of Nonlinear Science Pub Date : 2024-03-14 DOI: 10.1007/s00332-024-10017-7
Yu Yang, Cheng-Hsiung Hsu, Lan Zou, Jinling Zhou
{"title":"Threshold Dynamics of a Degenerate Diffusive HBV Infection Model with DNA-Containing Capsids in Heterogeneous Environment","authors":"Yu Yang, Cheng-Hsiung Hsu, Lan Zou, Jinling Zhou","doi":"10.1007/s00332-024-10017-7","DOIUrl":"https://doi.org/10.1007/s00332-024-10017-7","url":null,"abstract":"<p>This paper is concerned with threshold dynamics of a degenerate diffusive HBV infection model with DNA-containing capsids in heterogeneous environment. We firstly address the existence of global solutions, uniform and ultimate boundedness of solutions, asymptotic smoothness of semiflows and existence of a connected global attractor for the diffusive model. Then, we identify the basic reproduction number <span>({mathcal {R}}_0)</span> and establish a threshold-type result for the disease eradication or uniform persistence when <span>({mathcal {R}}_0le 1)</span> or <span>({mathcal {R}}_0&gt;1)</span>, respectively. Especially, when <span>({mathcal {R}}_0&gt;1)</span> and the diffusion rate of capsids or the diffusion rate of virions is zero, we further show that the model admits a unique infection steady state which is globally attractive. Our results indicate that the pathogen can be eliminated by limiting the mobility of the capsids or virions.</p>","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2024-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140152445","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Curvature Driven Complexity in the Defocusing Parametric Nonlinear Schrödinger System 离焦参数非线性薛定谔系统中曲率驱动的复杂性
IF 3 2区 数学
Journal of Nonlinear Science Pub Date : 2024-02-28 DOI: 10.1007/s00332-024-10016-8
Keith Promislow, Abba Ramadan
{"title":"Curvature Driven Complexity in the Defocusing Parametric Nonlinear Schrödinger System","authors":"Keith Promislow, Abba Ramadan","doi":"10.1007/s00332-024-10016-8","DOIUrl":"https://doi.org/10.1007/s00332-024-10016-8","url":null,"abstract":"<p>The parametric nonlinear Schrödinger equation models a variety of parametrically forced and damped dispersive waves. For the defocusing regime, we derive a normal velocity for the evolution of curved dark-soliton fronts that represent a <span>(pi )</span>-phase shift across a thin interface. We establish a simple mechanism through which the parametric term transitions the normal velocity evolution from a curvature-driven flow to motion against curvature regularized by surface diffusion of curvature. In the former case interfacial length shrinks, while in the latter case interface length generically grows until self-intersection followed by a transition to complex motion.\u0000</p>","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2024-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140003268","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Effective Estimation of Trapping/Stability Regions and Bilateral Solutions’ Bounds for Some Multidimensional Nonlinear Systems with Time-Varying Coefficients 某些时变系数多维非线性系统的陷阱/稳定区域和双边解边界的有效估计
IF 3 2区 数学
Journal of Nonlinear Science Pub Date : 2024-02-28 DOI: 10.1007/s00332-024-10013-x
{"title":"Effective Estimation of Trapping/Stability Regions and Bilateral Solutions’ Bounds for Some Multidimensional Nonlinear Systems with Time-Varying Coefficients","authors":"","doi":"10.1007/s00332-024-10013-x","DOIUrl":"https://doi.org/10.1007/s00332-024-10013-x","url":null,"abstract":"<h3>Abstract</h3> <p>Assessment of the stability/boundedness of solutions to nonlinear systems with variable coefficients brings long-standing and challenging problems which emerge in various application domains. These problems naturally evolved into more arduous and largely open problems concerned with the estimation of the corresponding stability/boundedness regions. This paper develops a novel approach furnishing computationally tractable boundedness/stability criteria which underscores a methodology providing recursive estimation of the boundaries of the trapping/stability regions for a broad class of multidimensional and nonlinear systems with variable nonperiodic coefficients. Furthermore, our approach naturally conveys the bilateral bounds for the norms of solutions to the corresponding systems via the application of successive approximations which are introduced in this paper. The developed techniques are validated in inclusive simulations which endorse their applications to systems with large and complex nonlinear components and bounded in-norm time-varying disturbances.</p>","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2024-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140003162","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Super-Exponential Convergence Rate of a Nonlinear Continuous Data Assimilation Algorithm: The 2D Navier–Stokes Equation Paradigm 非线性连续数据同化算法的超指数收敛率：二维纳维-斯托克斯方程范例
IF 3 2区 数学
Journal of Nonlinear Science Pub Date : 2024-02-24 DOI: 10.1007/s00332-024-10014-w
Elizabeth Carlson, Adam Larios, Edriss S. Titi
{"title":"Super-Exponential Convergence Rate of a Nonlinear Continuous Data Assimilation Algorithm: The 2D Navier–Stokes Equation Paradigm","authors":"Elizabeth Carlson, Adam Larios, Edriss S. Titi","doi":"10.1007/s00332-024-10014-w","DOIUrl":"https://doi.org/10.1007/s00332-024-10014-w","url":null,"abstract":"<p>We study a nonlinear-nudging modification of the Azouani–Olson–Titi continuous data assimilation (downscaling) algorithm for the 2D incompressible Navier–Stokes equations. We give a rigorous proof that the nonlinear-nudging system is globally well posed and, moreover, that its solutions converge to the true solution exponentially fast in time. Furthermore, we also prove that once the error has decreased below a certain order one threshold, the convergence becomes double exponentially fast in time, up until a precision determined by the sparsity of the observed data. In addition, we demonstrate the applicability of the analytical and sharpness of the results computationally.\u0000</p>","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2024-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139950441","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
A Two-Component Sasa–Satsuma Equation: Large-Time Asymptotics on the Line 双分量萨萨摩方程：线性大时间渐近线
IF 3 2区 数学
Journal of Nonlinear Science Pub Date : 2024-02-24 DOI: 10.1007/s00332-024-10015-9
{"title":"A Two-Component Sasa–Satsuma Equation: Large-Time Asymptotics on the Line","authors":"","doi":"10.1007/s00332-024-10015-9","DOIUrl":"https://doi.org/10.1007/s00332-024-10015-9","url":null,"abstract":"<h3>Abstract</h3> <p>We consider the initial value problem for a two-component Sasa–Satsuma equation associated with a <span> <span>(4times 4)</span> </span> Lax pair with decaying initial data on the line. By utilizing the spectral analysis, the solution of the two-component Sasa–Satsuma system is transformed into the solution of a <span> <span>(4times 4)</span> </span> matrix Riemann–Hilbert problem. Then, the long-time asymptotics of the solution is obtained by means of the nonlinear steepest descent method of Deift and Zhou for oscillatory Riemann–Hilbert problems. We show that there are three main regions in the half-plane <span> <span>(-infty&lt;x&lt;infty )</span> </span>, <span> <span>(t&gt;0)</span> </span>, where the asymptotics has qualitatively different forms: a left fast decaying sector, a central Painlevé sector where the asymptotics is described in terms of the solution to a system of coupled Painlevé II equations, which is related to a <span> <span>(4times 4)</span> </span> matrix Riemann–Hilbert problem, and a right slowly decaying oscillatory sector. </p>","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2024-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139950440","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
首页 上一页 下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：481959085
Book学术官方微信