arXiv - MATH - Analysis of PDEs最新文献_第7页

Steady Ring-Shaped Vortex Sheets 稳定的环形涡流片

arXiv - MATH - Analysis of PDEs Pub Date : 2024-09-12 DOI: arxiv-2409.08220

David Meyer, Christian Seis

引用次数: 0

Emergence of peaked singularities in the Euler-Poisson system 欧拉-泊松系统中峰值奇点的出现

arXiv - MATH - Analysis of PDEs Pub Date : 2024-09-12 DOI: arxiv-2409.08018

Junsik Bae, Sang-Hyuck Moon, Kwan Woo

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Global existence and asymptotic behavior for diffusive Hamilton-Jacobi equations with Neumann boundary conditions 具有新曼边界条件的扩散性汉密尔顿-雅可比方程的全局存在性和渐近行为

arXiv - MATH - Analysis of PDEs Pub Date : 2024-09-11 DOI: arxiv-2409.07338

Joaquin Dominguez-de-Tena, Philippe Souplet

引用次数: 0

Log-type ultra-analyticity of elliptic equations with gradient terms 带梯度项的椭圆方程的对数型超解析性

arXiv - MATH - Analysis of PDEs Pub Date : 2024-09-11 DOI: arxiv-2409.07027

Hongjie Dong, Ming Wang

引用次数: 0

Translating solutions and the entire Hessian curvature flow in Minkowski space 闵科夫斯基空间中的平移解和全黑森曲率流

arXiv - MATH - Analysis of PDEs Pub Date : 2024-09-11 DOI: arxiv-2409.07301

Qu Changzheng, Wang Zhizhang, Wo Weifeng

引用次数: 0

Weak solutions to a model for phase separation coupled with finite-strain viscoelasticity subject to external distortion 受外部变形影响的相分离与有限应变粘弹性耦合模型的弱解

arXiv - MATH - Analysis of PDEs Pub Date : 2024-09-11 DOI: arxiv-2409.07066

Thomas Eiter, Leonie Schmeller

{"title":"Weak solutions to a model for phase separation coupled with finite-strain viscoelasticity subject to external distortion","authors":"Thomas Eiter, Leonie Schmeller","doi":"arxiv-2409.07066","DOIUrl":"https://doi.org/arxiv-2409.07066","url":null,"abstract":"We study the coupling of a viscoelastic deformation governed by a\u0000Kelvin-Voigt model at equilibrium, based on the concept of second-grade\u0000nonsimple materials, with a plastic deformation due to volumetric swelling,\u0000described via a phase-field variable subject to a Cahn-Hilliard model expressed\u0000in a Lagrangian frame. Such models can be used to describe the time evolution\u0000of hydrogels in terms of phase separation within a deformable substrate. The\u0000equations are mainly coupled via a multiplicative decomposition of the\u0000deformation gradient into both contributions and via a Korteweg term in the\u0000Eulerian frame. To treat time-dependent Dirichlet conditions for the\u0000deformation, an auxiliary variable with fixed boundary values is introduced,\u0000which results in another multiplicative structure. Imposing suitable growth\u0000conditions on the elastic and viscous potentials, we construct weak solutions\u0000to this quasistatic model as the limit of time-discrete solutions to\u0000incremental minimization problems. The limit passage is possible due to\u0000additional regularity induced by the hyperelastic and viscous stresses.","PeriodicalId":501165,"journal":{"name":"arXiv - MATH - Analysis of PDEs","volume":"3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142179040","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

Existence and Regularity Results for a Nonlinear Fluid-Structure Interaction Problem with Three-Dimensional Structural Displacement 具有三维结构位移的非线性流固相互作用问题的存在性和正则性结果

arXiv - MATH - Analysis of PDEs Pub Date : 2024-09-11 DOI: arxiv-2409.06939

Sunčica Čanić, Boris Muha, Krutika Tawri

{"title":"Existence and Regularity Results for a Nonlinear Fluid-Structure Interaction Problem with Three-Dimensional Structural Displacement","authors":"Sunčica Čanić, Boris Muha, Krutika Tawri","doi":"arxiv-2409.06939","DOIUrl":"https://doi.org/arxiv-2409.06939","url":null,"abstract":"In this paper we investigate a nonlinear fluid-structure interaction (FSI)\u0000problem involving the Navier-Stokes equations, which describe the flow of an\u0000incompressible, viscous fluid in a 3D domain interacting with a thin\u0000viscoelastic lateral wall. The wall's elastodynamics is modeled by a\u0000two-dimensional plate equation with fractional damping, accounting for\u0000displacement in all three directions. The system is nonlinearly coupled through\u0000kinematic and dynamic conditions imposed at the time-varying fluid-structure\u0000interface, whose location is not known a priori. We establish three key\u0000results, particularly significant for FSI problems that account for vector\u0000displacements of thin structures. Specifically, we first establish a hidden\u0000spatial regularity for the structure displacement, which forms the basis for\u0000proving that self-contact of the structure will not occur within a finite time\u0000interval. Secondly, we demonstrate temporal regularity for both the structure\u0000and fluid velocities, which enables a new compactness result for\u0000three-dimensional structural displacements. Finally, building on these\u0000regularity results, we prove the existence of a local-in-time weak solution to\u0000the FSI problem. This is done through a constructive proof using time\u0000discretization via the Lie operator splitting method. These results are\u0000significant because they address the well-known issues associated with the\u0000analysis of nonlinearly coupled FSI problems capturing vector displacements of\u0000elastic/viscoelastic structures in 3D, such as spatial and temporal regularity\u0000of weak solutions and their well-posedness.","PeriodicalId":501165,"journal":{"name":"arXiv - MATH - Analysis of PDEs","volume":"12 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142179041","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

The Least Action Admissibility Principle 最小行动可受理性原则

arXiv - MATH - Analysis of PDEs Pub Date : 2024-09-11 DOI: arxiv-2409.07191

Heiko Gimperlein, Michael Grinfeld, Robin J. Knops, Marshall Slemrod

引用次数: 0

The radiation condition for Helmholtz equations above locally perturbed periodic surfaces 局部扰动周期表面上方亥姆霍兹方程的辐射条件

arXiv - MATH - Analysis of PDEs Pub Date : 2024-09-11 DOI: arxiv-2409.07141

Ruming Zhang

{"title":"The radiation condition for Helmholtz equations above locally perturbed periodic surfaces","authors":"Ruming Zhang","doi":"arxiv-2409.07141","DOIUrl":"https://doi.org/arxiv-2409.07141","url":null,"abstract":"The radiation condition is the key question in the mathematical modelling for\u0000scattering problems in unbounded domains. Mathematically, it plays the role as\u0000the \"boundary condition\" at the infinity, which guarantees the well-posedness\u0000of the mathematical problem; physically, it describes the behaviour of the\u0000physical waves. In this paper, we focus on the radiation conditions for\u0000scattering problems with periodic media embedded in two dimensional\u0000half-spaces. According to Hu et al. (2021), the radiating solution satisfies\u0000the Sommerfeld radiation condition: $$frac{partial u}{partial r}-i k\u0000u=o(r^{-1/2}).$$ Although there are literature which have studied this problem, there is no\u0000specific method for dealing with periodic structures. Due to this reason, the\u0000important properties for the periodic structures are always ignored. Moreover,\u0000the existing method is not extendable to bi-periodic structures in three\u0000dimensional spaces. In this paper, we study the radiation condition for the scattering problem\u0000with periodic medium, which is modelled by the Helmholtz equation. We introduce\u0000a novel method based on the Floquet-Bloch transform, which, to the best of the\u0000author's knowledge, is the first method that works particularly for periodic\u0000media. With this method, we improve the Sommerfeld radiation condition for the\u0000scattered field from periodic surface to: $$frac{partial u}{partial r}-i k\u0000u=O(r^{-3/2}).$$ Moreover, the prospect of extending this method to 3D cases is optimistic.","PeriodicalId":501165,"journal":{"name":"arXiv - MATH - Analysis of PDEs","volume":"81 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142179038","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

Non-local dissipative Aw-Rascle model and its relation with Matrix-valued communication in Euler alignment 非局部耗散 Aw-Rascle 模型及其与欧拉排列中的矩阵值通信的关系

arXiv - MATH - Analysis of PDEs Pub Date : 2024-09-11 DOI: arxiv-2409.07593

Nilasis Chaudhuri, Jan Peszek, Maja Szlenk, Ewelina Zatorska

引用次数: 0