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Bistable pulsating fronts in slowly oscillating one-dimensional environments 缓慢振荡一维环境中的双稳态脉冲锋
IF 2.1 1区 数学
Journal de Mathematiques Pures et Appliquees Pub Date : 2025-02-01 DOI: 10.1016/j.matpur.2025.103668
Weiwei Ding , François Hamel , Xing Liang
{"title":"Bistable pulsating fronts in slowly oscillating one-dimensional environments","authors":"Weiwei Ding ,&nbsp;François Hamel ,&nbsp;Xing Liang","doi":"10.1016/j.matpur.2025.103668","DOIUrl":"10.1016/j.matpur.2025.103668","url":null,"abstract":"<div><div>We consider reaction-diffusion fronts in spatially periodic bistable media with large periods. Whereas the homogenization regime associated with small periods had been well studied for bistable or Fisher-KPP reactions and, in the latter case, a formula for the limit minimal speeds of fronts in media with large periods had also been obtained thanks to the linear formulation of these minimal speeds and their monotonicity with respect to the period, the main remaining open question is concerned with fronts in bistable environments with large periods. In bistable media the unique front speeds are not linearly determined and are not monotone with respect to the spatial period in general, making the analysis of the limit of large periods more intricate. We show in this paper the existence of and an explicit formula for the limit of bistable front speeds as the spatial period goes to infinity. We also prove that the front profiles converge to a family of front profiles associated with spatially homogeneous equations. The main results are based on uniform estimates on the spatial width of the fronts, which themselves use zero number properties and intersection arguments.</div></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"194 ","pages":"Article 103668"},"PeriodicalIF":2.1,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143146796","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
Uniform concentration property for Griffith almost-minimizers Griffith几乎极小化器的均匀浓度性质
IF 2.1 1区 数学
Journal de Mathematiques Pures et Appliquees Pub Date : 2025-02-01 DOI: 10.1016/j.matpur.2025.103667
Camille Labourie , Antoine Lemenant
{"title":"Uniform concentration property for Griffith almost-minimizers","authors":"Camille Labourie ,&nbsp;Antoine Lemenant","doi":"10.1016/j.matpur.2025.103667","DOIUrl":"10.1016/j.matpur.2025.103667","url":null,"abstract":"<div><div>We prove that a Hausdorff limit of Griffith almost-minimizers remains a Griffith almost-minimizer. For this purpose, we introduce a new approach to the uniform concentration property of Dal Maso, Morel and Solimini which does not rely on the coarea formula, non available for symmetric gradient. We then develop several applications, including a general procedure to obtain global minimizers via blow-up limits.</div></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"194 ","pages":"Article 103667"},"PeriodicalIF":2.1,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143146798","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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 integral convexity, variational solutions and nonlinear semigroups 论积分凸性、变分解与非线性半群
IF 2.1 1区 数学
Journal de Mathematiques Pures et Appliquees Pub Date : 2025-02-01 DOI: 10.1016/j.matpur.2025.103662
Seonghak Kim , Baisheng Yan
{"title":"On integral convexity, variational solutions and nonlinear semigroups","authors":"Seonghak Kim ,&nbsp;Baisheng Yan","doi":"10.1016/j.matpur.2025.103662","DOIUrl":"10.1016/j.matpur.2025.103662","url":null,"abstract":"<div><div>In this paper we provide a different approach for existence of the variational solutions of the gradient flows associated to functionals on Sobolev spaces studied in the paper by Bögelein et al. (2020) <span><span>[7]</span></span>. The crucial condition is the convexity of the functional under which we show that the variational solutions coincide with the solutions generated by the nonlinear semigroup associated to the functional. For integral functionals of the form <span><math><mi>F</mi><mo>(</mo><mi>u</mi><mo>)</mo><mo>=</mo><msub><mrow><mo>∫</mo></mrow><mrow><mi>Ω</mi></mrow></msub><mi>f</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>D</mi><mi>u</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>)</mo><mi>d</mi><mi>x</mi></math></span>, where <span><math><mi>f</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>ξ</mi><mo>)</mo></math></span> is <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> in <em>ξ</em>, we also make some remarks on the connections between convexity of <strong>F</strong> (called the integral convexity of <em>f</em>) and certain monotonicity conditions of the gradient map <span><math><msub><mrow><mi>D</mi></mrow><mrow><mi>ξ</mi></mrow></msub><mi>f</mi></math></span>. In particular, we provide an example to show that even for functions of the simple form <span><math><mi>f</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>ξ</mi><mo>)</mo></math></span>, the usual quasimonotonicity of <span><math><msub><mrow><mi>D</mi></mrow><mrow><mi>ξ</mi></mrow></msub><mi>f</mi></math></span> is not sufficient for the integral convexity of <em>f</em>.</div></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"194 ","pages":"Article 103662"},"PeriodicalIF":2.1,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143146797","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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 nonlinear stability of Muskat bubbles 麝香气泡的非线性稳定性
IF 2.1 1区 数学
Journal de Mathematiques Pures et Appliquees Pub Date : 2025-02-01 DOI: 10.1016/j.matpur.2025.103664
Francisco Gancedo , Eduardo García-Juárez , Neel Patel , Robert M. Strain
{"title":"On nonlinear stability of Muskat bubbles","authors":"Francisco Gancedo ,&nbsp;Eduardo García-Juárez ,&nbsp;Neel Patel ,&nbsp;Robert M. Strain","doi":"10.1016/j.matpur.2025.103664","DOIUrl":"10.1016/j.matpur.2025.103664","url":null,"abstract":"<div><div>In this paper we consider gravity-capillarity Muskat bubbles in 2D. We obtain a new approach to improve our result in <span><span>[1]</span></span>. Due to a new bubble-adapted formulation, the improvement is twofold. We significantly condense the proof and we now obtain the global well-posedness result for Muskat bubbles in critical regularity.</div></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"194 ","pages":"Article 103664"},"PeriodicalIF":2.1,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143146939","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
Construction of weak solutions to a model of pressureless viscous flow driven by nonlocal attraction–repulsion 非局部吸引-排斥驱动无压粘性流动模型弱解的构造
IF 2.1 1区 数学
Journal de Mathematiques Pures et Appliquees Pub Date : 2025-01-15 DOI: 10.1016/j.matpur.2025.103671
Piotr B. Mucha , Maja Szlenk , Ewelina Zatorska
{"title":"Construction of weak solutions to a model of pressureless viscous flow driven by nonlocal attraction–repulsion","authors":"Piotr B. Mucha ,&nbsp;Maja Szlenk ,&nbsp;Ewelina Zatorska","doi":"10.1016/j.matpur.2025.103671","DOIUrl":"10.1016/j.matpur.2025.103671","url":null,"abstract":"<div><div>We analyze the pressureless Navier-Stokes system with nonlocal attraction–repulsion forces. Such systems appear in the context of models of collective behaviour. We prove the existence of weak solutions on the whole space <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span> in the case of density-dependent degenerate viscosity. For the nonlocal term it is assumed that the interaction kernel has the quadratic growth at infinity and almost quadratic singularity at zero. Under these assumptions, we derive the analog of the Bresch–Desjardins and Mellet–Vasseur estimates for the nonlocal system. In particular, we are able to adapt the approach of Vasseur and Yu <span><span>[37]</span></span>, <span><span>[36]</span></span> to construct a weak solution.</div></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"195 ","pages":"Article 103671"},"PeriodicalIF":2.1,"publicationDate":"2025-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143155109","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
Infinitesimal conformal restriction and unitarizing measures for Virasoro algebra Virasoro代数的无穷小共形限制和统一措施
IF 2.1 1区 数学
Journal de Mathematiques Pures et Appliquees Pub Date : 2025-01-15 DOI: 10.1016/j.matpur.2025.103669
Maria Gordina , Wei Qian , Yilin Wang
{"title":"Infinitesimal conformal restriction and unitarizing measures for Virasoro algebra","authors":"Maria Gordina ,&nbsp;Wei Qian ,&nbsp;Yilin Wang","doi":"10.1016/j.matpur.2025.103669","DOIUrl":"10.1016/j.matpur.2025.103669","url":null,"abstract":"<div><div>We use the SLE<sub><em>κ</em></sub> loop measure to construct a natural representation of the Virasoro algebra of central charge <span><math><mi>c</mi><mo>=</mo><mi>c</mi><mo>(</mo><mi>κ</mi><mo>)</mo><mo>≤</mo><mn>1</mn></math></span>. In particular, we introduce a non-degenerate bilinear Hermitian form (and non positive-definite) using the SLE loop measure and show that the representation is indefinite unitary. Our proof relies on the infinitesimal conformal restriction property of the SLE loop measure.</div></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"195 ","pages":"Article 103669"},"PeriodicalIF":2.1,"publicationDate":"2025-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143155110","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Non-linear operator-valued elliptic flows with application to quantum field theory 非线性算子值椭圆流及其在量子场论中的应用
IF 2.1 1区 数学
Journal de Mathematiques Pures et Appliquees Pub Date : 2025-01-15 DOI: 10.1016/j.matpur.2025.103657
Jean-Bernard Bru , Nathan Metraud
{"title":"Non-linear operator-valued elliptic flows with application to quantum field theory","authors":"Jean-Bernard Bru ,&nbsp;Nathan Metraud","doi":"10.1016/j.matpur.2025.103657","DOIUrl":"10.1016/j.matpur.2025.103657","url":null,"abstract":"<div><div>Differential equations on spaces of operators are very little developed in Mathematics, being in general very challenging. Here, we study a novel system of such (non-linear) differential equations. We show it has a unique solution for all times, for instance in the Schatten norm topology. This system presents remarkable ellipticity properties that turn out to be crucial for the study of the infinite-time limit of its solution, which is proven under relatively weak, albeit probably not necessary, hypotheses on the initial data. This system of differential equations is the elliptic counterpart of an hyperbolic flow applied to quantum field theory to diagonalize Hamiltonians that are quadratic in the bosonic field. In a similar way, this elliptic flow, in particular its asymptotics, has application in quantum field theory: it can be used to diagonalize Hamiltonians that are quadratic in the fermionic field while giving new explicit expressions and properties of these pivotal Hamiltonians of quantum field theory and quantum statistical mechanics.</div></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"195 ","pages":"Article 103657"},"PeriodicalIF":2.1,"publicationDate":"2025-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143155106","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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 one-sided two phase Bernoulli free boundary problem 单侧两相伯努利自由边界问题
IF 2.1 1区 数学
Journal de Mathematiques Pures et Appliquees Pub Date : 2025-01-15 DOI: 10.1016/j.matpur.2025.103659
Lorenzo Ferreri , Bozhidar Velichkov
{"title":"A one-sided two phase Bernoulli free boundary problem","authors":"Lorenzo Ferreri ,&nbsp;Bozhidar Velichkov","doi":"10.1016/j.matpur.2025.103659","DOIUrl":"10.1016/j.matpur.2025.103659","url":null,"abstract":"<div><div>We study a two-phase free boundary problem in which the two-phases satisfy an impenetrability condition. Precisely, we have two ordered positive functions, which are harmonic in their supports, satisfy a Bernoulli condition on the one-phase part of the free boundary and a transmission condition on the collapsed part of the free boundary. For this two-membrane type problem, we prove an epsilon-regularity theorem with sharp modulus of continuity. Precisely, we show that at flat points each of the two boundaries is <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn><mo>,</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup></math></span> regular surface and that the remaining singular set has Hausdorff dimension at most <span><math><mi>N</mi><mo>−</mo><mn>5</mn></math></span>, where <em>N</em> is the dimension of the space.</div></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"195 ","pages":"Article 103659"},"PeriodicalIF":2.1,"publicationDate":"2025-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143155107","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
Perturbed block Toeplitz matrices and the non-Hermitian skin effect in dimer systems of subwavelength resonators 亚波长谐振器二聚体体系中的摄动块Toeplitz矩阵和非厄米集肤效应
IF 2.1 1区 数学
Journal de Mathematiques Pures et Appliquees Pub Date : 2025-01-14 DOI: 10.1016/j.matpur.2025.103658
Habib Ammari , Silvio Barandun , Ping Liu
{"title":"Perturbed block Toeplitz matrices and the non-Hermitian skin effect in dimer systems of subwavelength resonators","authors":"Habib Ammari ,&nbsp;Silvio Barandun ,&nbsp;Ping Liu","doi":"10.1016/j.matpur.2025.103658","DOIUrl":"10.1016/j.matpur.2025.103658","url":null,"abstract":"<div><div>The aim of this paper is fourfold: (i) to obtain explicit formulas for the eigenpairs of perturbed tridiagonal block Toeplitz matrices; (ii) to make use of such formulas in order to provide a mathematical justification of the non-Hermitian skin effect in dimer systems of subwavelength resonators by proving the condensation of the system's bulk eigenmodes at one of the edges of the system; (iii) to show the topological origin of the non-Hermitian skin effect for dimer systems and (iv) to prove localisation of the interface modes between two dimer structures with non-Hermitian gauge potentials of opposite signs based on new estimates of the decay of the entries of the eigenvectors of block matrices with mirrored blocks.</div></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"195 ","pages":"Article 103658"},"PeriodicalIF":2.1,"publicationDate":"2025-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143155108","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
The 3D Euler equations with inflow, outflow and vorticity boundary conditions 具有流入、流出和涡度边界条件的三维欧拉方程
IF 2.1 1区 数学
Journal de Mathematiques Pures et Appliquees Pub Date : 2025-01-01 DOI: 10.1016/j.matpur.2024.103628
Gung-Min Gie , James P. Kelliher , Anna L. Mazzucato
{"title":"The 3D Euler equations with inflow, outflow and vorticity boundary conditions","authors":"Gung-Min Gie ,&nbsp;James P. Kelliher ,&nbsp;Anna L. Mazzucato","doi":"10.1016/j.matpur.2024.103628","DOIUrl":"10.1016/j.matpur.2024.103628","url":null,"abstract":"<div><div>The 3D incompressible Euler equations in a bounded domain are most often supplemented with impermeable boundary conditions, which constrain the fluid to neither enter nor leave the domain. We establish well-posedness with inflow, outflow of velocity when either the full value of the velocity is specified on inflow, or only the normal component is specified along with the vorticity (and an additional constraint). We derive compatibility conditions to obtain regularity in a Hölder space with prescribed arbitrary index, and allow multiply connected domains. Our results apply as well to impermeable boundaries, establishing higher regularity of solutions in Hölder spaces.</div></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"193 ","pages":"Article 103628"},"PeriodicalIF":2.1,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143129193","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
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