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Existence and uniqueness of time-periodic solutions to the Oberbeck–Boussinesq system Oberbeck-Boussinesq系统时间周期解的存在唯一性
IF 1.8 3区 数学
Nonlinear Analysis-Real World Applications Pub Date : 2025-07-29 DOI: 10.1016/j.nonrwa.2025.104461
Tomoyuki Nakatsuka
{"title":"Existence and uniqueness of time-periodic solutions to the Oberbeck–Boussinesq system","authors":"Tomoyuki Nakatsuka","doi":"10.1016/j.nonrwa.2025.104461","DOIUrl":"10.1016/j.nonrwa.2025.104461","url":null,"abstract":"<div><div>This paper is devoted to the study of the time-periodic problem for the Oberbeck–Boussinesq system in the whole space. Our investigation is based on the reformulation of the time-periodic problem and does not depend on the analysis of the initial value problem. We construct a time-periodic solution with more information on its structure than the solutions in preceding studies. We also prove that our solution, small in an appropriate sense, is unique in the class of solutions having slightly more regularity.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"88 ","pages":"Article 104461"},"PeriodicalIF":1.8,"publicationDate":"2025-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144722113","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Steady states of the spherically symmetric Vlasov-Poisson system as fixed points of a mass-preserving algorithm 球对称Vlasov-Poisson系统作为质量保持算法不动点的稳态
IF 1.8 3区 数学
Nonlinear Analysis-Real World Applications Pub Date : 2025-07-26 DOI: 10.1016/j.nonrwa.2025.104467
Håkan Andréasson , Markus Kunze , Gerhard Rein
{"title":"Steady states of the spherically symmetric Vlasov-Poisson system as fixed points of a mass-preserving algorithm","authors":"Håkan Andréasson ,&nbsp;Markus Kunze ,&nbsp;Gerhard Rein","doi":"10.1016/j.nonrwa.2025.104467","DOIUrl":"10.1016/j.nonrwa.2025.104467","url":null,"abstract":"<div><div>We give a new proof for the existence of spherically symmetric steady states to the Vlasov-Poisson system, following a strategy that has been used successfully to approximate axially symmetric solutions numerically, both to the Vlasov–Poisson system and to the Einstein–Vlasov system. There are several reasons why a mathematical analysis of this numerical scheme is important. A generalization of the present result to the case of flat axially symmetric solutions would prove that the steady states obtained numerically in Andréasson and Rein (2015) do exist. Moreover, in the relativistic case the question whether a steady state can be obtained by this scheme seems to be related to its dynamical stability. This motivates the desire for a deeper understanding of this strategy.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"88 ","pages":"Article 104467"},"PeriodicalIF":1.8,"publicationDate":"2025-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144713222","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Stability of planar stationary solution for outflow problem on the viscous vasculogenesis model 粘性血管生成模型流出问题平面固定解的稳定性
IF 1.8 3区 数学
Nonlinear Analysis-Real World Applications Pub Date : 2025-07-25 DOI: 10.1016/j.nonrwa.2025.104459
Wenwen Fu, Qingqing Liu
{"title":"Stability of planar stationary solution for outflow problem on the viscous vasculogenesis model","authors":"Wenwen Fu,&nbsp;Qingqing Liu","doi":"10.1016/j.nonrwa.2025.104459","DOIUrl":"10.1016/j.nonrwa.2025.104459","url":null,"abstract":"<div><div>In this paper, we are concerned with a hyperbolic–parabolic–elliptic vasculogenesis model in the half-space <span><math><msubsup><mrow><mi>R</mi></mrow><mrow><mo>+</mo></mrow><mrow><mn>3</mn></mrow></msubsup></math></span> under outflow boundary conditions. It is shown that the planar stationary solution is stable with respect to small perturbations in <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> and the perturbations decay in <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>∞</mi></mrow></msup></math></span> norm as <span><math><mrow><mi>t</mi><mo>→</mo><mi>∞</mi></mrow></math></span>, provided that the magnitude of the stationary solution is sufficiently small. This result is proved by basic energy estimates. Compared with Navier–Stokes equations, we have effectively dealt with the coupling between the fluid quantities and chemoattractant in the vasculogenesis model.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"88 ","pages":"Article 104459"},"PeriodicalIF":1.8,"publicationDate":"2025-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144703763","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Extension criterion on the 3D Navier–Stokes equations via partial components in Besov space 三维Navier-Stokes方程在Besov空间的偏分量扩展准则
IF 1.8 3区 数学
Nonlinear Analysis-Real World Applications Pub Date : 2025-07-25 DOI: 10.1016/j.nonrwa.2025.104458
Koji Kanazawa , Hideo Kozono
{"title":"Extension criterion on the 3D Navier–Stokes equations via partial components in Besov space","authors":"Koji Kanazawa ,&nbsp;Hideo Kozono","doi":"10.1016/j.nonrwa.2025.104458","DOIUrl":"10.1016/j.nonrwa.2025.104458","url":null,"abstract":"<div><div>We find a new extension criterion on the 3D Navier–Stokes equations in terms of horizontal derivatives of the two velocity components in Besov spaces. We shall apply our extension theorem to regularity criterion on weak solutions. Our results generalize the results in the Morrey–Campanato space and Triebel–Lizorkin space by Chen and Gala (2011) and Wei and Li (2014), respectively.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"88 ","pages":"Article 104458"},"PeriodicalIF":1.8,"publicationDate":"2025-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144703762","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Steklov vs. Steklov: A fourth-order affair related to the Babuška paradox Steklov vs. Steklov：与Babuška悖论相关的四阶事件
IF 1.8 3区 数学
Nonlinear Analysis-Real World Applications Pub Date : 2025-07-24 DOI: 10.1016/j.nonrwa.2025.104464
Francesco Ferraresso , Pier Domenico Lamberti
{"title":"Steklov vs. Steklov: A fourth-order affair related to the Babuška paradox","authors":"Francesco Ferraresso ,&nbsp;Pier Domenico Lamberti","doi":"10.1016/j.nonrwa.2025.104464","DOIUrl":"10.1016/j.nonrwa.2025.104464","url":null,"abstract":"<div><div>We discuss two fourth-order Steklov problems and highlight a Babuška paradox appearing in their approximations on convex domains via sequences of convex polygons. To do so, we prove that the eigenvalues of one of the two problems depend with continuity upon domain perturbation in the class of convex domains, extending a result known in the literature for the first eigenvalue. This is obtained by examining in detail a nonlocal second order problem for harmonic functions introduced by Ferrero, Gazzola, and Weth. We further review how this result is connected to diverse variants of the classical Babuška paradox for the hinged plate and to a degeneration result by Maz’ya and Nazarov.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"87 ","pages":"Article 104464"},"PeriodicalIF":1.8,"publicationDate":"2025-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144695371","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 double step Rothe scheme for hyperbolic Clarke subdifferential inclusions controlled by evolution equations 演化方程控制的双曲型Clarke次微分内含体的双步Rothe格式
IF 1.8 3区 数学
Nonlinear Analysis-Real World Applications Pub Date : 2025-07-24 DOI: 10.1016/j.nonrwa.2025.104463
Jinxia Cen , Krzysztof Bartosz , Jen-Chih Yao , Shengda Zeng
{"title":"A double step Rothe scheme for hyperbolic Clarke subdifferential inclusions controlled by evolution equations","authors":"Jinxia Cen ,&nbsp;Krzysztof Bartosz ,&nbsp;Jen-Chih Yao ,&nbsp;Shengda Zeng","doi":"10.1016/j.nonrwa.2025.104463","DOIUrl":"10.1016/j.nonrwa.2025.104463","url":null,"abstract":"<div><div>In this paper we deal with a coupled system which consists of a hyperbolic Clarke subdifferential inclusion and an evolution equation in Banach spaces. Using temporally semidiscrete method based on the double step scheme, we construct a discrete approximate system. The existence of solutions and its a-priori estimates for the discrete approximate system are provided by the surjectivity of multivalued pesudomonotone operators and discrete Gronwall’s inequality. Finally, we show that the solution sequence of the discrete approximate system converges weakly to a limit element, which is a solution of the coupled original system.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"88 ","pages":"Article 104463"},"PeriodicalIF":1.8,"publicationDate":"2025-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144694866","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Maximum principle for higher order elliptic operators with inertia in general domains and any dimension 具有惯性的高阶椭圆算子在一般域和任意维上的极大值原理
IF 1.8 3区 数学
Nonlinear Analysis-Real World Applications Pub Date : 2025-07-23 DOI: 10.1016/j.nonrwa.2025.104465
Daniele Cassani , Camilla Chiara Polvara , Antonio Tarsia
{"title":"Maximum principle for higher order elliptic operators with inertia in general domains and any dimension","authors":"Daniele Cassani ,&nbsp;Camilla Chiara Polvara ,&nbsp;Antonio Tarsia","doi":"10.1016/j.nonrwa.2025.104465","DOIUrl":"10.1016/j.nonrwa.2025.104465","url":null,"abstract":"<div><div>It is well known how the Maximum Principle (MP) in general fails to hold for uniformly elliptic operators of order higher than two, even in smooth convex domains. In D. Cassani and A. Tarsia (2022) it was shown in dimension <span><math><mrow><mi>N</mi><mo>=</mo><mn>2</mn><mo>,</mo><mn>3</mn></mrow></math></span>, by establishing a new Harnack type inequality, that the validity of the positivity preserving property can be restored when lower order derivatives are taken into account as a perturbation of the higher order differential operator. The restriction to the dimension was due to regularity issues which we develop here, extending the validity of the MP to any dimension and fairly general domains. Moreover, we show that the presence of inertial terms affects the range of the perturbation parameter, providing a balance between the positivity restoring effect of lower order derivatives and the mass energy. The method provided here is flexible with respect to the form of differential operators involved and thus suitable to be further extended to other classes of operators than just elliptic.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"87 ","pages":"Article 104465"},"PeriodicalIF":1.8,"publicationDate":"2025-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144686227","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Approximate controllability for the μ-version of the b-family Camassa–Holm equations with a finite-dimensional force 具有有限维力的b族Camassa-Holm方程μ版的近似可控性
IF 1.8 3区 数学
Nonlinear Analysis-Real World Applications Pub Date : 2025-07-19 DOI: 10.1016/j.nonrwa.2025.104462
Yanpeng Jin , Xiaoping Wu
{"title":"Approximate controllability for the μ-version of the b-family Camassa–Holm equations with a finite-dimensional force","authors":"Yanpeng Jin ,&nbsp;Xiaoping Wu","doi":"10.1016/j.nonrwa.2025.104462","DOIUrl":"10.1016/j.nonrwa.2025.104462","url":null,"abstract":"<div><div>Considered herein is the approximate controllability of the <span><math><mi>μ</mi></math></span>-<span><math><mi>b</mi></math></span>-Camassa–Holm equation on the circle. We first prove the well-posedness and stability of the <span><math><mi>μ</mi></math></span>-<span><math><mi>b</mi></math></span>-family Camassa–Holm equations with a source term. Then we establish the asymptotic property of this equation. Finally, based on the Agrachev–Sarychev approach in geometric control theory, the approximate controllability for the <span><math><mi>μ</mi></math></span>-version of the <span><math><mi>b</mi></math></span>-family Camassa–Holm equations with two dimensional external force is shown.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"87 ","pages":"Article 104462"},"PeriodicalIF":1.8,"publicationDate":"2025-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144665507","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Non-convex sweeping processes in contact mechanics 接触力学中的非凸清扫过程
IF 1.8 3区 数学
Nonlinear Analysis-Real World Applications Pub Date : 2025-07-15 DOI: 10.1016/j.nonrwa.2025.104456
Erich Bauer , Victor A. Kovtunenko , Pavel Krejčí , Giselle A. Monteiro , Laetitia Paoli , Adrien Petrov
{"title":"Non-convex sweeping processes in contact mechanics","authors":"Erich Bauer ,&nbsp;Victor A. Kovtunenko ,&nbsp;Pavel Krejčí ,&nbsp;Giselle A. Monteiro ,&nbsp;Laetitia Paoli ,&nbsp;Adrien Petrov","doi":"10.1016/j.nonrwa.2025.104456","DOIUrl":"10.1016/j.nonrwa.2025.104456","url":null,"abstract":"<div><div>We propose a model for irreversible dynamics of the rail foundation under the effects of rail traffic, taking into account the granular structure of the ballast subject to changing void ratio and to mechanical degradation. The rail is modeled as an Euler–Bernoulli beam with distributed forcing terms representing the moving traffic load as well as the interaction with the foundation. This interaction is described by an implicit variational inequality with non-convex constraint depending in turn on the solution of the underlying PDE. The problem is reduced to a fixed point problem in a suitable Banach space, and its unique solvability is proved using the contraction principle.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"87 ","pages":"Article 104456"},"PeriodicalIF":1.8,"publicationDate":"2025-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144631493","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Fractional Orlicz–Sobolev embeddings into Campanato type spaces Campanato类型空间中的分数阶Orlicz-Sobolev嵌入
IF 1.8 3区 数学
Nonlinear Analysis-Real World Applications Pub Date : 2025-07-12 DOI: 10.1016/j.nonrwa.2025.104455
Angela Alberico , Andrea Cianchi , Luboš Pick , Lenka Slavíková
{"title":"Fractional Orlicz–Sobolev embeddings into Campanato type spaces","authors":"Angela Alberico ,&nbsp;Andrea Cianchi ,&nbsp;Luboš Pick ,&nbsp;Lenka Slavíková","doi":"10.1016/j.nonrwa.2025.104455","DOIUrl":"10.1016/j.nonrwa.2025.104455","url":null,"abstract":"<div><div>Optimal embeddings for fractional Orlicz–Sobolev spaces into (generalized) Campanato spaces on the Euclidean space are exhibited. Embeddings into vanishing Campanato spaces are also characterized. Sharp embeddings into <span><math><mrow><mo>BMO</mo><mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>)</mo></mrow></mrow></math></span> and <span><math><mrow><mo>VMO</mo><mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>)</mo></mrow></mrow></math></span> are derived as special instances. Dissimilarities to corresponding embeddings for classical fractional Sobolev spaces are pointed out.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"87 ","pages":"Article 104455"},"PeriodicalIF":1.8,"publicationDate":"2025-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144605282","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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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