{"title":"Regularity criteria for weak solutions to 3D non-Newtonian fluid equations of MHD type","authors":"Jae-Myoung Kim","doi":"10.21136/AM.2026.0164-25","DOIUrl":"10.21136/AM.2026.0164-25","url":null,"abstract":"<div><p>We investigate regularity criteria for weak solutions to the three-dimensional non-Newtonian MHD-type system for <span>({11over{5}}leqslant q<{5over{2}})</span> under a sufficient condition involving only the magnetic field. In addition, weak-strong uniqueness in ℝ<sup>3</sup> is established for <span>(qgeqslant{5over{2}})</span>.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"71 3","pages":"393 - 407"},"PeriodicalIF":0.6,"publicationDate":"2026-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148389062","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":"Boundary layer separation and local behavior of the steady Prandtl equation with magnetic damping","authors":"Yanjun Chen, Xinhan Zhang, Hong Luo","doi":"10.21136/AM.2026.0298-25","DOIUrl":"10.21136/AM.2026.0298-25","url":null,"abstract":"<div><p>We prove the boundary layer separation of the two-dimensional steady Prandtl equation with magnetic damping under an appropriate adverse pressure gradient. We also obtain the separation rate of the solution and the local behavior of the solution near the separation point. Our results show that magnetic damping exerts a suppressive effect on boundary layer separation.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"71 3","pages":"327 - 351"},"PeriodicalIF":0.6,"publicationDate":"2026-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148389057","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":"Stability analysis for a Timoshenko system with generalized thermoelasticity","authors":"Hamed Abderrahmane Bouraoui","doi":"10.21136/AM.2026.0112-25","DOIUrl":"10.21136/AM.2026.0112-25","url":null,"abstract":"<div><p>We study the long-time behavior of solutions to a thermoelastic Timoshenko beam system with dual-phase-lag heat conduction. We prove the existence of solutions and their uniqueness using semigroup methods. Exponential energy decay is shown under the condition 2<i>τ</i><sub>2</sub> > <i>τ</i><sub>1</sub>. The analysis preserves full thermal-mechanical coupling for accurate modeling. Numerical simulations using mixed finite elements in space and a multistep time scheme (FEniCSx) confirm the theoretical energy decay and show how the lag parameters and coupling strength influence the decay rate.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"71 2","pages":"243 - 267"},"PeriodicalIF":0.7,"publicationDate":"2026-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147863191","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}
Joel Fotso Tachago, Franck Tchinda Takougoum, Joseph Dongho
{"title":"Stochastic-periodic homogenization of a class of minimization problems in Orlicz-Sobolev spaces","authors":"Joel Fotso Tachago, Franck Tchinda Takougoum, Joseph Dongho","doi":"10.21136/AM.2026.0239-25","DOIUrl":"10.21136/AM.2026.0239-25","url":null,"abstract":"<div><p>We develop the stochastic two-scale convergence method in the framework of Orlicz-Sobolev spaces, in order to deal with the homogenization of coupled stochastic-periodic problems in such spaces. One fundamental in this topic is the extension of compactness results for this method to the Orlicz setting. For the application, we show that the sequence of minimizers of a class of highly oscillatory minimizations problems involving integral functionals with convex and nonstandard growth integrands, converges to the minimizer of a homogenized problem.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"71 2","pages":"269 - 298"},"PeriodicalIF":0.7,"publicationDate":"2026-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.21136/AM.2026.0239-25.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147863186","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Dynamic contact problem with wear, damage, and thermal effect","authors":"Mohamed Selmani","doi":"10.21136/AM.2026.0169-25","DOIUrl":"10.21136/AM.2026.0169-25","url":null,"abstract":"<div><p>We consider a dynamic problem describing frictional contact between a thermo-elasto-viscoplastic body and a foundation. The contact is frictional and bilateral with a moving rigid foundation that results in the wear of the contacting surface. The constitutive law includes a temperature effect described by the first-order evolution equation and a damage effect described by the parabolic inclusion with the homogeneous Neumann boundary condition. We present a variational formulation of the problem and establish the existence and uniqueness of the weak solution. The proof is based on parabolic variational inequalities, first order evolutionary variational equations, and fixed point arguments.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"71 2","pages":"219 - 242"},"PeriodicalIF":0.7,"publicationDate":"2026-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147863194","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":"A new robust biconvex clustering method with self-paced learning","authors":"Jinyao Ma, Jiaojiao Jiang, Haibin Zhang","doi":"10.21136/AM.2026.0085-25","DOIUrl":"10.21136/AM.2026.0085-25","url":null,"abstract":"<div><p>Convex clustering formulates the clustering problem as a convex optimization task that encourages similar data points to merge into clusters by minimizing a combination of fitting error and a penalty on differences between cluster centroids. This method has attracted considerable attention due to its capacity to address the challenges associated with local optimal solutions and numerical instability prevalent in traditional nonconvex clustering methods. However, it typically relies on the standard Euclidean metric for measuring distance, which can lead to decreased performance, especially in the presence of outlier features. Additionally, it is not particularly robust against outlier samples. To address these issues, we separate the data into cluster and outlier components, effectively eliminating the outlier features. By incorporating self-paced learning, we develop a model that adaptively selects relevant examples while minimizing interference from outlier instances. This approach enhances robustness by removing outlier features and samples, forming a biconvex clustering framework with strong statistical properties. We propose an efficient, convergent algorithm and establish a finite sample bound for prediction error. Experiments on artificial and benchmarking datasets show improved clustering effectiveness compared to classical convex clustering methods.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"71 2","pages":"163 - 190"},"PeriodicalIF":0.7,"publicationDate":"2026-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147863192","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":"On the orbits of similarity classes of tetrahedra generated by the longest-edge bisection algorithm","authors":"Jérôme Michaud, Sergey Korotov","doi":"10.21136/AM.2026.0277-25","DOIUrl":"10.21136/AM.2026.0277-25","url":null,"abstract":"<div><p>We study the dynamics of similarity classes of tetrahedra generated by the longest-edge bisection (LEB) algorithm. Building on the normalization strategy introduced by F. Perdomo, Á. Plaza (2014) we construct a canonical representation of tetrahedra in a normalized space embedded in the product of the hyperbolic half-plane and the hyperbolic half-space model. This representation allows us to define the left and right refinement maps, Φ<sub><i>L</i></sub> and Φ<sub><i>R</i></sub>, acting on the space of normalized tetrahedral shapes, and to study their iterative orbits as discrete dynamical systems. Using these maps, we show that the orbit of the space-filling Sommerville tetrahedron contains only 4 similarity classes, 3 of which form an attractive cycle corresponding to the orbit of the path tetrahedron. We also show that small perturbations of elements in those orbits still lead to finite orbits. In addition, we study small perturbations of the regular tetrahedron and show that their orbits are also finite. Extensive numerical exploration of orbits for the other types of tetrahedra suggests that the LEB algorithm does not produce degenerating tetrahedra. Our framework provides a geometric and dynamical foundation for analyzing the shape evolution of tetrahedral meshes and offers a possible route towards an analytic proof of the nondegeneracy property for the tetrahedral partitions generated by the LEB refinements. This property is highly desired in e.g., the finite element methods (FEMs).</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"71 2","pages":"137 - 162"},"PeriodicalIF":0.7,"publicationDate":"2026-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.21136/AM.2026.0277-25.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147863193","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A magneto-electro-elastic problem with non-monotone contact conditions","authors":"Abderrezak Kasri","doi":"10.21136/AM.2026.0061-25","DOIUrl":"10.21136/AM.2026.0061-25","url":null,"abstract":"<div><p>We consider a static frictional contact problem between a magneto-electro-elastic body and a foundation. We assume that the friction law is non-monotone, slip dependent, and associated with a non-monotone normal compliance, which is restricted by a unilateral constraint. We derive a variational formulation for the model, which is a system that couples a variational-hemivariational inequality with a variational equation. Then, we apply abstract results to prove its weak solvability. Finally, under additional assumptions on the contact functions, we prove the uniqueness of the solution.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"71 2","pages":"191 - 218"},"PeriodicalIF":0.7,"publicationDate":"2026-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147863187","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":"Perfectly matched layers in time domain. A simplified two-dimensional error analysis","authors":"Kurt M. Bryan, Michael S. Vogelius","doi":"10.21136/AM.2026.0055-25","DOIUrl":"10.21136/AM.2026.0055-25","url":null,"abstract":"<div><p>Perfectly Matched Layers (PML) has become a very common method for the numerical approximation of wave and wave-like equations on unbounded domains. This technique allows one to obtain accurate solutions while working on a finite computational domain, and the technique is relatively simple to implement. Results concerning the accuracy of the PML method have been obtained, but mostly with regard to problems at a fixed frequency. In this paper we provide very explicit time-domain bounds on the accuracy of PML for the inhomogeneous two-dimensional wave equation with a particular type of forcing term, and illustrate our conclusions with some numerical examples.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"71 1","pages":"31 - 57"},"PeriodicalIF":0.7,"publicationDate":"2026-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147342624","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":"100 years since the birth of Professor Miloš Zlámal","authors":"Jan Franců, Michal Křížek","doi":"10.21136/AM.2026.0273-25","DOIUrl":"10.21136/AM.2026.0273-25","url":null,"abstract":"<div><p>After a brief biography of Professor Miloš Zlámal we recall his most important mathematical achievements. First, he dealt with various properties of analytical solutions of ordinary and partial differential equations. He then laid the theoretical foundation for the finite element method as the minimum angle condition, curved finite elements, the numerical solution of heat conduction problem and semiconductor equations, and superconvergence. He developed the so-called mortar finite elements used to cover a strip between two different types of finite elements. Complete chronological list of Zlámal’s publications closes the contribution.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"71 1","pages":"127 - 135"},"PeriodicalIF":0.7,"publicationDate":"2026-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147340534","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}