数学最新文献

{"title":"A Data-Driven Mathematical Model for Clonorchiasis with Seasonality.","authors":"Wei Wang, Xiaohui Huang, Tonghua Zhang, Zhaosheng Feng","doi":"10.1007/s11538-025-01527-w","DOIUrl":"https://doi.org/10.1007/s11538-025-01527-w","url":null,"abstract":"<p><p>Clonorchiasis is a foodborne disease caused by parasites and transmitted to humans through intermediate hosts. Clonorchis sinensis parasitizes in the bile ducts of human liver and causes organ lesions. The cercariae and metacercaria of Clonorchis sinensis have seasonal variations and may be affected by high water temperature in summer. We formulate a partial differential equations (PDE) model which incorporates seasonality, spatial heterogeneity and the extrinsic incubation period (EIP) of the parasite. We present the basic reproduction number <math><msub><mi>R</mi> <mn>0</mn></msub> </math> and discuss the global dynamics of the model. Particularly, we choose parameters to fit the Clonorchiasis epidemic data in Guangxi, China. Our study indicates that the basic reproduction number of cases of clonorchiasis in Guangxi is <math><msub><mi>R</mi> <mn>0</mn></msub> </math> =1.025 and the number of existing infection cases is still very large, if the prevention and control measures of Clonorchiasis are not strengthened.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 10","pages":"144"},"PeriodicalIF":2.2,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144991658","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The stability on the Caffarelli-Kohn-Nirenberg and Hardy-type inequalities and beyond","authors":"Yuxuan Zhou,&nbsp;Wenming Zou","doi":"10.1016/j.jde.2025.113738","DOIUrl":"10.1016/j.jde.2025.113738","url":null,"abstract":"&lt;div&gt;&lt;div&gt;In this paper, we establish several improved Caffarelli-Kohn-Nirenberg and Hardy-type inequalities. Our main results are divided into two parts.&lt;/div&gt;&lt;div&gt;In the first part, we consider the following Caffarelli-Kohn-Nirenberg inequality:&lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;munder&gt;&lt;mo&gt;∫&lt;/mo&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/munder&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;munder&gt;&lt;mo&gt;∫&lt;/mo&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/munder&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;q&lt;/mi&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;q&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;q&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mo&gt;∀&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt; where &lt;span&gt;&lt;math&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; is the sharp constant and &lt;span&gt;&lt;math&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;q&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; satisfy the relations:&lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mi&gt;q&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt; We establish gradient stability of this inequality in both functional and critical settings, and we derive some functional properties of the stability constant. Building on the gradient stability, we also obtain several refined Sobolev-type embeddings involving weak Lebesgue norms for functions supported in general domains.&lt;/div&gt;&lt;div&gt;In the second part, we focus on various classical Hardy-type inequalities, including the standard Hardy inequality, the &lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt;-logarithmic Sobolev inequality with weights, the logarithmic Hardy inequality, the Hardy-Morrey inequality, the Hardy-Sobolev interpolati","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"450 ","pages":"Article 113738"},"PeriodicalIF":2.3,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144933087","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}

{"title":"Hamilton inequality for the p-Laplacian on weighted graphs with the CDp⋅(m,K) curvature","authors":"Yongtao Liu","doi":"10.1016/j.jmaa.2025.130036","DOIUrl":"10.1016/j.jmaa.2025.130036","url":null,"abstract":"<div><div>In this paper, we study Hamilton type gradient estimates for the <em>p</em>-Laplacian on weighted graphs. For <span><math><mi>p</mi><mo>&gt;</mo><mn>5</mn></math></span> and some additional assumptions, we derive a more general gradient estimate of Hamilton type for positive solutions to the <em>p</em>-Laplacian heat equation on finite graphs satisfying the <span><math><mi>C</mi><msubsup><mrow><mi>D</mi></mrow><mrow><mi>p</mi></mrow><mrow><msqrt><mrow><mo>⋅</mo></mrow></msqrt></mrow></msubsup><mo>(</mo><mi>m</mi><mo>,</mo><mi>K</mi><mo>)</mo></math></span> curvature. The analogous result is also proved for locally finite graphs with bounded weighted vertex degree. As an application of our main results, we show that the corresponding Harnack inequality.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"555 1","pages":"Article 130036"},"PeriodicalIF":1.2,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144997594","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}

{"title":"Ideal magnetohydrodynamics around couette flow: Long time stability and vorticity–current instability","authors":"Niklas Knobel","doi":"10.1016/j.na.2025.113937","DOIUrl":"10.1016/j.na.2025.113937","url":null,"abstract":"<div><div>This article considers the ideal 2D magnetohydrodynamic equations in a infinite periodic channel close to a combination of an affine shear flow, called Couette flow, and a constant magnetic field. This incorporates important physical effects, including mixing and coupling of velocity and magnetic field. We establish the existence and stability of the velocity and magnetic field for Gevrey-class perturbations of size <span><math><mi>ɛ</mi></math></span>, valid up to times <span><math><mrow><mi>t</mi><mo>∼</mo><msup><mrow><mi>ɛ</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></math></span>. Additionally, the vorticity and current grow as <span><math><mrow><mi>O</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></math></span> and there is no inviscid damping of the velocity and magnetic field. This is similar to the above threshold case for the <span><math><mrow><mn>3</mn><mi>D</mi></mrow></math></span> Navier–Stokes (Jacob Bedrossian et al., 2022) where growth in ‘streaks’ leads to time scales of <span><math><mrow><mi>t</mi><mo>∼</mo><msup><mrow><mi>ɛ</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></math></span>. In particular, for the ideal MHD equations, our article suggests that for a wide range of initial data, the scenario “induction by shear <span><math><mo>⇒</mo></math></span> vorticity and current growth <span><math><mo>⇒</mo></math></span> vorticity and current breakdown” leads to instability and possible turbulences.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"262 ","pages":"Article 113937"},"PeriodicalIF":1.3,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144932827","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}

{"title":"Steady Compressible Navier-Stokes-Fourier System with Slip Boundary Conditions Arising from Kinetic Theory","authors":"Renjun Duan,&nbsp;Junhao Zhang","doi":"10.1007/s00021-025-00972-w","DOIUrl":"10.1007/s00021-025-00972-w","url":null,"abstract":"<div><p>This paper studies the boundary value problem on the steady compressible Navier-Stokes-Fourier system in a channel domain <span>((0,1)times mathbb {T}^2)</span> with a class of generalized slip boundary conditions that were systematically derived from the Boltzmann equation by Coron [9] and later by Aoki et al [1]. We establish the existence and uniqueness of strong solutions in <span>((L_{0}^{2}cap H^{2}(Omega ))times V^{3}(Omega )times H^{3}(Omega ))</span> provided that the wall temperature is near a positive constant. The proof relies on the construction of a new variational formulation for the corresponding linearized problem and employs a fixed point argument. The main difficulty arises from the interplay of velocity and temperature derivatives together with the effect of density dependence on the boundary.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"27 4","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144929355","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}

{"title":"Bounding the Orlov spectrum for a completion of discrete cluster categories","authors":"Dave Murphy","doi":"10.1016/j.jpaa.2025.108078","DOIUrl":"10.1016/j.jpaa.2025.108078","url":null,"abstract":"<div><div>We classify thick subcategories in a Paquette-Yıldırım completion <span><math><mover><mrow><mi>C</mi></mrow><mo>‾</mo></mover></math></span> of a discrete cluster category of Dynkin type <span><math><msub><mrow><mi>A</mi></mrow><mrow><mo>∞</mo></mrow></msub></math></span>. To do this we introduce the notion of homologically connected objects, and the hc (=homologically connected) decomposition of an object into homologically connected objects in a Hom-finite, Krull-Schmidt triangulated category. We show that any object in a <span><math><mover><mrow><mi>C</mi></mrow><mo>‾</mo></mover></math></span> has a hc decomposition, and that the hc decomposition determines the thick closure of an object. Moreover, we use this result to classify the classical generators of <span><math><mover><mrow><mi>C</mi></mrow><mo>‾</mo></mover></math></span> as homologically connected objects satisfying a maximality condition.</div><div>Every homologically connected object has an invariant, known as the homological length, and we show that in <span><math><mover><mrow><mi>C</mi></mrow><mo>‾</mo></mover></math></span> this homological length is an upper bound for the generation time of a classical generator. This allows us to provide an upper bound for the Orlov spectrum of <span><math><mover><mrow><mi>C</mi></mrow><mo>‾</mo></mover></math></span>, as well as giving the Rouquier dimension.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 10","pages":"Article 108078"},"PeriodicalIF":0.8,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144988166","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}

{"title":"Integrability and periodic orbits of a 3D jerk system with two quadratic nonlinearities","authors":"Martha Alvarez-Ramírez ,&nbsp;Johanna D. García-Saldaña ,&nbsp;Jaume Llibre","doi":"10.1016/j.nonrwa.2025.104491","DOIUrl":"10.1016/j.nonrwa.2025.104491","url":null,"abstract":"<div><div>In mechanics jerk is the rate of change of an object’s acceleration over time. Thus a jerk equation is a differential equation of the form <span><math><mrow><mover><mrow><mi>x</mi></mrow><mrow><mo>⃛</mo></mrow></mover><mo>=</mo><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mover><mrow><mi>x</mi></mrow><mrow><mo>̇</mo></mrow></mover><mo>,</mo><mover><mrow><mi>x</mi></mrow><mrow><mo>̈</mo></mrow></mover><mo>)</mo></mrow></mrow></math></span>, where <span><math><mi>x</mi></math></span>, <span><math><mover><mrow><mi>x</mi></mrow><mrow><mo>̇</mo></mrow></mover></math></span>, <span><math><mover><mrow><mi>x</mi></mrow><mrow><mo>̈</mo></mrow></mover></math></span> and <span><math><mover><mrow><mi>x</mi></mrow><mrow><mo>⃛</mo></mrow></mover></math></span> represent the position, velocity, acceleration, and jerk, respectively. The jerk differential equation can be written as the jerk differential system <span><math><mrow><mover><mrow><mi>x</mi></mrow><mrow><mo>̇</mo></mrow></mover><mo>=</mo><mi>y</mi><mo>,</mo><mspace></mspace><mover><mrow><mi>y</mi></mrow><mrow><mo>̇</mo></mrow></mover><mo>=</mo><mi>z</mi><mo>,</mo><mspace></mspace><mover><mrow><mi>z</mi></mrow><mrow><mo>̇</mo></mrow></mover><mo>=</mo><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>z</mi><mo>)</mo></mrow><mo>,</mo></mrow></math></span> in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>. In this paper we study the jerk differential system with <span><math><mrow><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>z</mi><mo>)</mo></mrow><mo>=</mo><mo>−</mo><mi>a</mi><mi>x</mi><mrow><mo>(</mo><mn>1</mn><mo>−</mo><mi>x</mi><mo>)</mo></mrow><mo>−</mo><mi>y</mi><mo>+</mo><mi>b</mi><msup><mrow><mi>y</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math></span>, previously studied by other authors showing that this system can exhibit chaos for some values of its parameters. When the parameters <span><math><mrow><mi>a</mi><mo>=</mo><mi>b</mi><mo>=</mo><mn>0</mn></mrow></math></span> the <span><math><mi>x</mi></math></span>-axis is filled with zero-Hopf equilibria, and all the other orbits are periodic. Here we prove analytically the existence of two families of periodic orbits for sufficiently small values of the parameters <span><math><mi>a</mi></math></span> and <span><math><mi>b</mi></math></span>. One family bifurcates from the non-isolated zero-Hopf equilibrium <span><math><mrow><mo>(</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo></mrow></math></span> of the jerk system with <span><math><mrow><mi>a</mi><mo>=</mo><mi>b</mi><mo>=</mo><mn>0</mn></mrow></math></span>, while the other family bifurcates from a periodic orbit of the jerk system with <span><math><mrow><mi>a</mi><mo>=</mo><mi>b</mi><mo>=</mo><mn>0</mn></mrow></math></span>.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"88 ","pages":"Article 104491"},"PeriodicalIF":1.8,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144932266","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}

{"title":"Singular velocity of the Stokes and Navier–Stokes equations near boundary in the half-space","authors":"Tongkeun Chang,&nbsp;Kyungkeun Kang","doi":"10.1016/j.na.2025.113939","DOIUrl":"10.1016/j.na.2025.113939","url":null,"abstract":"<div><div>Local behavior near the boundary is analyzed for solutions of the Stokes and Navier–Stokes equations in the half space with localized non-smooth boundary data. We construct solutions to the Stokes equations whose velocity fields are unbounded near the boundary away from the support of boundary data, although the velocity and its gradient of solutions are locally square integrable. This is an improvement compared to known results in the sense that the velocity field itself is unbounded, since previously constructed solutions were bounded near the boundary, although their normal derivatives are singular. We also establish singular solutions and their derivatives that do not belong to <span><math><msubsup><mrow><mi>L</mi></mrow><mrow><mi>loc</mi></mrow><mrow><mi>q</mi></mrow></msubsup></math></span> near the boundary for <span><math><mrow><mi>q</mi><mo>&gt;</mo><mn>1</mn></mrow></math></span>. For such examples, the corresponding pressures turn out not to be locally integrable. A similar construction, via a perturbation argument, is available to the Navier–Stokes equations near the boundary as well.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"262 ","pages":"Article 113939"},"PeriodicalIF":1.3,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144932826","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}

{"title":"Equilibrium problems with trifunctions and applications to hemivariational inequalities","authors":"Sultana Ben Aadi,&nbsp;Khalid Akhlil,&nbsp;Daniela Inoan","doi":"10.1007/s13324-025-01123-0","DOIUrl":"10.1007/s13324-025-01123-0","url":null,"abstract":"<div><p>In this paper, we define generalized monotonicity concepts related to equilibrium problems generated by trifunctions. We then study the existence of solutions to mixed equilibrium problems described as the sum of a maximal monotone trifunction and a pseudomonotone trifunction in Brézis sense. The main tools for this study are a Thikonov regularization procedure with respect to the generalized duality mapping and recession analysis adapted to trifunctions. An application consists in an existence result for a noncoercive hemivariational inequality.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 5","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144934500","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}

{"title":"General two-component long-wave short-wave resonance interaction system: Non-degenerate vector solitons and their collision dynamics","authors":"S. Stalin,&nbsp;M. Lakshmanan","doi":"10.1016/j.chaos.2025.117132","DOIUrl":"10.1016/j.chaos.2025.117132","url":null,"abstract":"<div><div>In this paper, we demonstrate the emergence of non-degenerate bright solitons and summarize their several interesting features in a completely integrable two-component long-wave–short-wave resonance interaction (LSRI) model with a general form of nonlinearity coefficients. This model describes the nonlinear resonant interaction between a low-frequency long wave and two high-frequency short waves in a one-dimensional physical setting. Through the classical Hirota’s bilinear method, we obtain a fully non-degenerate <span><math><mi>N</mi></math></span>-soliton solution in Gram determinant form for this two-component LSRI model to analyze the nature of non-degenerate vector solitons in detail. Depending on the choice of velocity conditions, the obtained non-degenerate fundamental soliton is classified into two types, namely (<span><math><mrow><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>1</mn></mrow></math></span>)- and (<span><math><mrow><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></math></span>)-non-degenerate one solitons. We then show that the basic (<span><math><mrow><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>1</mn></mrow></math></span>)-non-degenerate soliton exhibits five distinct profile structures, including a novel double-hump, a special flat-top, and a conventional single-hump profile, and (<span><math><mrow><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></math></span>)-non-degenerate soliton admits two-soliton like oblique collision, a behavior akin to KP line soliton interaction with a short stem structure. A detailed asymptotic analysis is carried out to study the long time behavior of (<span><math><mrow><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>1</mn></mrow></math></span>)-non-degenerate solitons and it reveals that they undergo both shape-preserving and shape-changing collisions. However, our analysis confirms that the shape changing collision between these solitons become elastic in nature after appropriate shift of time coordinates. Further, we identified that the (<span><math><mrow><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></math></span>)-non-degenerate solitons also undergo elastic collision. In addition, we have also investigated the formation or suppression of breathing phenomena during collision between a degenerate soliton and a (<span><math><mrow><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>1</mn></mrow></math></span>)-non-degenerate soliton by considering partially non-degenerate multi-soliton solution. For completeness, we also point out the collision scenario between the completely degenerate solitons. The results presented in this paper are broadly applicable to Bose–Einstein condensates, nonlinear optics, plasma physics, and other closely related fields where the LSRI phenomenon plays a significant role in governing the evolution of vector solitons.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"200 ","pages":"Article 117132"},"PeriodicalIF":5.6,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144932369","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}