Journal de Mathematiques Pures et Appliquees最新文献

Positive temperature in nonlinear thermoviscoelasticity and the derivation of linearized models 非线性热粘弹性中的正温度及线性化模型的推导

IF 2.1 1区数学

Journal de Mathematiques Pures et Appliquees Pub Date : 2025-06-16 DOI: 10.1016/j.matpur.2025.103751

Rufat Badal , Manuel Friedrich , Martin Kružík , Lennart Machill

引用次数: 0

Convergence of free boundaries in the incompressible limit of tumor growth models 肿瘤生长模型不可压缩极限下自由边界的收敛性

IF 2.1 1区数学

Journal de Mathematiques Pures et Appliquees Pub Date : 2025-06-16 DOI: 10.1016/j.matpur.2025.103752

Jiajun Tong , Yuming Paul Zhang

引用次数: 0

Hidden asymptotics for the weak solutions of the strongly stratified Boussinesq system without rotation 无旋转强分层Boussinesq系统弱解的隐渐近性

IF 2.1 1区数学

Journal de Mathematiques Pures et Appliquees Pub Date : 2025-06-16 DOI: 10.1016/j.matpur.2025.103750

Frédéric Charve

{"title":"Hidden asymptotics for the weak solutions of the strongly stratified Boussinesq system without rotation","authors":"Frédéric Charve","doi":"10.1016/j.matpur.2025.103750","DOIUrl":"10.1016/j.matpur.2025.103750","url":null,"abstract":"<div><div>The asymptotics of the strongly stratified Boussinesq system when the Froude number goes to zero have been previously investigated, but the resulting limit system surprisingly did not depend on the thermal diffusivity <span><math><msup><mrow><mi>ν</mi></mrow><mrow><mo>′</mo></mrow></msup></math></span>. In this article we obtain richer asymptotics (depending on <span><math><msup><mrow><mi>ν</mi></mrow><mrow><mo>′</mo></mrow></msup></math></span>) for more general ill-prepared initial data.</div><div>As for the rotating fluids system, the only way to reach this limit consists in finding suitable non-conventional initial data: here, to a function classically depending on the full space variable, we add a second one only depending on the vertical coordinate.</div><div>Thanks to a refined study of the structure of the limit system and to new adapted Strichartz estimates, we obtain convergence in the context of weak Leray-type solutions providing explicit convergence rates when possible. In the usually simpler case <span><math><mi>ν</mi><mo>=</mo><msup><mrow><mi>ν</mi></mrow><mrow><mo>′</mo></mrow></msup></math></span> we are able to improve the Strichartz estimates and the convergence rates. The last part of the appendix is devoted to the proof of a new and crucial dispersion estimate, as classical methods fail.</div><div>Finally, our theorems can also be rewritten as a global existence result and asymptotic expansion for the classical Boussinesq system near an explicit stationary solution and for large non-conventional vertically stratified initial data.</div></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"202 ","pages":"Article 103750"},"PeriodicalIF":2.1,"publicationDate":"2025-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144313661","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

Formation and construction of a shock wave for 1-D n × n strictly hyperbolic conservation laws with small smooth initial data 具有小光滑初始数据的1-D n × 严格双曲守恒律激波的形成和构造

IF 2.1 1区数学

Journal de Mathematiques Pures et Appliquees Pub Date : 2025-06-16 DOI: 10.1016/j.matpur.2025.103754

Min Ding , Huicheng Yin

{"title":"Formation and construction of a shock wave for 1-D n × n strictly hyperbolic conservation laws with small smooth initial data","authors":"Min Ding , Huicheng Yin","doi":"10.1016/j.matpur.2025.103754","DOIUrl":"10.1016/j.matpur.2025.103754","url":null,"abstract":"<div><div>Under the genuinely nonlinear assumption for 1-D <span><math><mi>n</mi><mo>×</mo><mi>n</mi></math></span> strictly hyperbolic conservation laws, we investigate the geometric blowup of smooth solutions and the development of singularities when the small initial data fulfill the generic nondegenerate condition. At first, near the unique blowup point we give a precise description on the space-time blowup rate of the smooth solution and meanwhile derive the cusp singularity structure of characteristic envelope. These results are established through extending the smooth solution of the completely nonlinear blowup system across the blowup time. Subsequently, by utilizing a new form on the resulting 1-D strictly hyperbolic system with <span><math><mo>(</mo><mi>n</mi><mo>−</mo><mn>1</mn><mo>)</mo></math></span> good components and one bad component, together with the choice of an efficient iterative scheme and some involved analyses, a weak entropy shock wave starting from the blowup point is constructed. As a byproduct, our result can be applied to the shock formation and construction for the 2-D supersonic steady compressible full Euler equations (<span><math><mn>4</mn><mo>×</mo><mn>4</mn></math></span> system), 1-D MHD equations (<span><math><mn>5</mn><mo>×</mo><mn>5</mn></math></span> system), 1-D elastic wave equations (<span><math><mn>6</mn><mo>×</mo><mn>6</mn></math></span> system) and 1-D full ideal compressible MHD equations (<span><math><mn>7</mn><mo>×</mo><mn>7</mn></math></span> system).</div></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"204 ","pages":"Article 103754"},"PeriodicalIF":2.1,"publicationDate":"2025-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144321251","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 the small-time bilinear control of a nonlinear heat equation: Global approximate controllability and exact controllability to trajectories 非线性热方程的小时间双线性控制：轨迹的全局近似可控性和精确可控性

IF 2.1 1区数学

Journal de Mathematiques Pures et Appliquees Pub Date : 2025-06-16 DOI: 10.1016/j.matpur.2025.103758

Alessandro Duca , Eugenio Pozzoli , Cristina Urbani

{"title":"On the small-time bilinear control of a nonlinear heat equation: Global approximate controllability and exact controllability to trajectories","authors":"Alessandro Duca , Eugenio Pozzoli , Cristina Urbani","doi":"10.1016/j.matpur.2025.103758","DOIUrl":"10.1016/j.matpur.2025.103758","url":null,"abstract":"<div><div>In this work we analyse the small-time reachability properties of a nonlinear parabolic equation, by means of a bilinear control, posed on a torus of arbitrary dimension <em>d</em>. Under a saturation hypothesis on the control operators, we show the small-time approximate controllability between states sharing the same sign. Moreover, in the one-dimensional case <span><math><mi>d</mi><mo>=</mo><mn>1</mn></math></span>, we combine this property with a local exact controllability result, and prove the small-time exact controllability of any positive states towards the ground state of the evolution operator.</div><div>Dans ce travail, nous analysons les propriétés d'accessibilité en temps court d'une équation parabolique non linéaire, à l'aide d'un contrôle bilinéaire, posée sur un tore de dimension arbitraire <em>d</em>. Sous une hypothèse de saturation sur les opérateurs de contrôle, nous montrons la contrôlabilité approchée en temps court entre les états qui ont le même signe. De plus, dans le cas unidimensionnel <span><math><mi>d</mi><mo>=</mo><mn>1</mn></math></span>, nous combinons cette propriété avec un résultat de contrôlabilité locale exacte, et prouvons la contrôlabilité exacte en temps court de tout état positif vers l'état fondamental de l'opérateur d'évolution.</div></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"203 ","pages":"Article 103758"},"PeriodicalIF":2.1,"publicationDate":"2025-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144320781","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 quantitative study of radial symmetry for solutions to semilinear equations in Rn Rn中半线性方程解径向对称性的定量研究

IF 2.1 1区数学

Journal de Mathematiques Pures et Appliquees Pub Date : 2025-06-16 DOI: 10.1016/j.matpur.2025.103755

Giulio Ciraolo, Matteo Cozzi, Michele Gatti

引用次数: 0

Weighted gradient estimates to nonlinear elliptic equations of p(x)-growth with measure data 带测量数据的p(x)-增长非线性椭圆方程的加权梯度估计

IF 2.1 1区数学

Journal de Mathematiques Pures et Appliquees Pub Date : 2025-06-16 DOI: 10.1016/j.matpur.2025.103756

Zhaosheng Feng , Junjie Zhang , Shenzhou Zheng

引用次数: 0

Large-time asymptotics for hyperbolic systems with non-symmetric relaxation: An algorithmic approach 非对称松弛双曲型系统的大时渐近性：一种算法方法

IF 2.1 1区数学

Journal de Mathematiques Pures et Appliquees Pub Date : 2025-06-16 DOI: 10.1016/j.matpur.2025.103757

Timothée Crin-Barat , Lorenzo Liverani , Ling-Yun Shou , Enrique Zuazua

{"title":"Large-time asymptotics for hyperbolic systems with non-symmetric relaxation: An algorithmic approach","authors":"Timothée Crin-Barat , Lorenzo Liverani , Ling-Yun Shou , Enrique Zuazua","doi":"10.1016/j.matpur.2025.103757","DOIUrl":"10.1016/j.matpur.2025.103757","url":null,"abstract":"<div><div>We study the stability of one-dimensional linear hyperbolic systems with non-symmetric relaxation. Introducing a new frequency-dependent Kalman stability condition, we prove an abstract decay result underpinning a form of <em>inhomogeneous hypocoercivity</em>. In contrast with the homogeneous setting, the decay rates depend on how the Kalman condition is fulfilled and, in most cases, a loss of derivative occurs: one must require an additional regularity assumption on the initial data to ensure the decay.</div><div>Under structural assumptions, we refine our abstract result by providing an algorithm, of wide applicability, for the construction of Lyapunov functionals. This allows us to systematically establish decay estimates for a given system and uncover algebraic cancellations (beyond the reach of the Kalman-based approach) reducing the loss of derivatives in high frequencies. To demonstrate the applicability of our method, we derive new stability results for the Sugimoto model, which describes the propagation of nonlinear acoustic waves, and for a beam model of Timoshenko type with memory.</div></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"202 ","pages":"Article 103757"},"PeriodicalIF":2.1,"publicationDate":"2025-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144290769","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 isomorphism of the space of continuous functions with finite p-th variation along a partition sequence 分配序列上有限p次变分的连续函数空间的同构性

IF 2.1 1区数学

Journal de Mathematiques Pures et Appliquees Pub Date : 2025-06-16 DOI: 10.1016/j.matpur.2025.103753

Purba Das , Donghan Kim

引用次数: 0

‘t Hooft bundles on the complete flag threefold and moduli spaces of instantons t Hooft束上的完全标志三倍和模空间的实例

IF 2.1 1区数学

Journal de Mathematiques Pures et Appliquees Pub Date : 2025-06-13 DOI: 10.1016/j.matpur.2025.103763

Vincenzo Antonelli , Francesco Malaspina , Simone Marchesi , Joan Pons-Llopis

引用次数: 0