数学最新文献

{"title":"mGFD: A meshless generalized finite difference method","authors":"Gerardo Tinoco-Guerrero,&nbsp;Francisco Javier Domínguez-Mota,&nbsp;José Alberto Guzmán-Torres,&nbsp;Gabriela Pedraza-Jiménez,&nbsp;José Gerardo Tinoco-Ruiz","doi":"10.1016/j.camwa.2025.07.034","DOIUrl":"10.1016/j.camwa.2025.07.034","url":null,"abstract":"<div><div>This work introduces a novel meshless method, the meshless Generalized Finite Difference (mGFD) scheme, which is derived from an optimization formulation that enforces the consistency condition. This approach eliminates the need for additional weight functions required by other methods, enabling efficient and accurate simulations of complex geometries. The method leverages a flexible, node-based discretization scheme that avoids a predefined mesh, providing enhanced versatility and adaptability in modeling various engineering applications. The proposed method's flexibility and adaptability are demonstrated through numerical solutions of elliptic, parabolic, and hyperbolic partial differential equations in highly irregular domains, providing satisfactory results compared to known exact solutions.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"195 ","pages":"Pages 396-418"},"PeriodicalIF":2.5,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144748781","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":"On the k-linkage problem for generalizations of semicomplete digraphs","authors":"Jia Zhou ,&nbsp;Jørgen Bang-Jensen ,&nbsp;Jin Yan","doi":"10.1016/j.disc.2025.114700","DOIUrl":"10.1016/j.disc.2025.114700","url":null,"abstract":"&lt;div&gt;&lt;div&gt;A directed graph (digraph) &lt;em&gt;D&lt;/em&gt; is &lt;em&gt;k&lt;/em&gt;&lt;strong&gt;-linked&lt;/strong&gt; if &lt;span&gt;&lt;math&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;, and for any 2&lt;em&gt;k&lt;/em&gt; distinct vertices &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mo&gt;…&lt;/mo&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mo&gt;…&lt;/mo&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; of &lt;em&gt;D&lt;/em&gt;, there exist vertex-disjoint paths &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mo&gt;…&lt;/mo&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; such that &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; is a path from &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; to &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; for each &lt;span&gt;&lt;math&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mo&gt;[&lt;/mo&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mo&gt;]&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;. In 1980, Thomassen conjectured that there exists a function &lt;span&gt;&lt;math&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; such that every &lt;span&gt;&lt;math&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;-strong digraph is &lt;em&gt;k&lt;/em&gt;-linked. He later disproved this conjecture by showing that &lt;span&gt;&lt;math&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; does not exist for general digraphs and proved that the function &lt;span&gt;&lt;math&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; exists for the class of tournaments. In this paper we consider a large class &lt;span&gt;&lt;math&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; of digraphs which includes all &lt;strong&gt;semicomplete digraphs&lt;/strong&gt; (digraphs with no pair of non-adjacent vertices) and all &lt;strong&gt;quasi-transitive digraphs&lt;/strong&gt; (a digraph &lt;em&gt;D&lt;/em&gt; is quasi-transitive if for any three vertices &lt;span&gt;&lt;math&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; of &lt;em&gt;D&lt;/em&gt;, whenever &lt;em&gt;xy&lt;/em&gt; and &lt;em&gt;yz&lt;/em&gt; are arcs, then &lt;em&gt;x&lt;/em&gt; and &lt;em&gt;z&lt;/em&gt; are adjacent). We prove that every 3&lt;em&gt;k&lt;/em&gt;-strong digraph &lt;span&gt;&lt;math&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; with minimum out-degree at least 23&lt;em&gt;k&lt;/em&gt; is &lt;em&gt;k&lt;/em&gt;-linked. A digraph &lt;em&gt;D&lt;/em&gt; is &lt;em&gt;l&lt;/em&gt;&lt;strong&gt;-quasi-transitive&lt;/strong&gt; if whenever there is a path of length &lt;em&gt;l&lt;/em&gt; between vertices &lt;em&gt;u&lt;/em&gt; and &lt;em&gt;v&lt;/em&gt; in &lt;em&gt;D&lt;/em&gt; the vertices &lt;em&gt;u&lt;/em&gt; and &lt;em&gt;v&lt;/em&gt; are adjacent. Hence 2-quasi-transitive digraphs are exactly the quasi-transitive digraphs. We prove that there is a function &lt;span&gt;&lt;math&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;l&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; so that every &lt;span&gt;&lt;math&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;l&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;-strong &lt;em&gt;l&lt;/em&gt;-quasi-transitive digraph is &lt;em&gt;k&lt;/em&gt;-linked. The main new tool in our proofs significantly strengt","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"349 2","pages":"Article 114700"},"PeriodicalIF":0.7,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144749166","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":"Robustness analysis of k-core percolation on asymmetric interdependent networks","authors":"Lili Zhou,&nbsp;Yukun Li,&nbsp;Fei Tan","doi":"10.1016/j.chaos.2025.116910","DOIUrl":"10.1016/j.chaos.2025.116910","url":null,"abstract":"<div><div>Asymmetric interdependency phenomenon is widely present in real networks, but the vast majority of the existing researches are on symmetric interdependent networks, in which when one party is failed and the other one will be failed as well. While in the asymmetric interdependent networks (AINs), the dependency relationships are unidirectional, the failure for one part may not necessarily result in that for the other part. Consequently, the exploration on the robustness of AINs is very important and meaningful. While <span><math><mi>k</mi></math></span>-core percolation theory provides an effective tool on the analysis of network performance, for this paper, we aims to the analysis on robustness of AINs with use of it. A scale gap threshold <span><math><mi>θ</mi></math></span> is defined to analyze the tolerance between dependent nodes. Then the <span><math><mi>k</mi></math></span>-core percolation equation for AINs is derived to analyze the types of phase transition. The simulations on different networks imply that the robustness of networks is improved after the introduction of asymmetric relation. It can be obtained that the reduction of <span><math><mi>θ</mi></math></span> can make the network robustness further improved, and the network exists continuous phase transition only when <span><math><mrow><mi>k</mi><mo>=</mo><mn>1</mn><mo>,</mo><mspace></mspace><mn>2</mn></mrow></math></span>, while it has a discontinuous phase transition with square root behavior at the critical point when <span><math><mrow><mi>k</mi><mo>≥</mo><mn>3</mn></mrow></math></span>. Finally, based on the characteristics of <span><math><mi>k</mi></math></span>-core structure and asymmetric dependency, and with consideration of the effect upon node failure, an improved edge attack strategy is put forward. Compared with several other attack strategies, the significance for the proposed strategy is proved by experimental simulation. This study will be beneficial for understanding the hierarchical structure of AINs and optimizing the network design, and it also provides a basis for further identifying the key nodes and vulnerable links of AINs.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"199 ","pages":"Article 116910"},"PeriodicalIF":5.6,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144750735","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}

{"title":"A multi-market model with heterogeneous agents and switching mechanism.","authors":"Serena Brianzoni, Giovanni Campisi","doi":"10.1063/5.0274253","DOIUrl":"https://doi.org/10.1063/5.0274253","url":null,"abstract":"<p><p>This paper presents a multi-market model consisting of two distinct financial markets with one risky asset. The model assumes that each market is populated by two types of interacting traders: fundamentalists and cross-sectional momentum traders. A market maker sets the price based on a nonlinear adjustment mechanism. We prove that, depending on the relative influence of traders' beliefs, the asset dynamics can exhibit large-amplitude fluctuations. Through bifurcation analysis, we derive analytical conditions that show how the intensity of investors' preferences for trading rules and the switching mechanism can destabilize the markets. Furthermore, we show that when investors hold polarized beliefs, it can introduce significant uncertainty in both markets, leading to complex price dynamics.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 8","pages":""},"PeriodicalIF":3.2,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144764638","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":"Tale of one emergent game: Opinion formation in dynamical undirected hypergraphs.","authors":"Yakun Wang, Yuan Liu, Bin Wu","doi":"10.1063/5.0283611","DOIUrl":"https://doi.org/10.1063/5.0283611","url":null,"abstract":"<p><p>Opinion dynamics in dynamical hypergraphs, mirroring the dynamical nature of high-order social interactions, are attracting increasing attention. Opinion dynamics on high-order interactions lead to non-trivial dynamical patterns compared with that on pairwise networks. How should we systematically understand the intrinsic differences between opinion dynamics in hypergraphs and that in networks? We establish a voter model in a dynamical hypergraph. We find that both opinion formation and transient topology are captured by a single multi-player game, provided that the hypergraphs evolve sufficiently fast. The Nash equilibrium analysis facilitates us to reveal the intrinsic differences between high-order interactions and pairwise interactions in the empirical system. Furthermore, we perform simulations to show how robust our theoretical results are beyond fast rewiring. Our work provides a game route for opinion dynamics and sheds a hidden connection between opinion formation on dynamical high-order interactions and multi-player games.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 8","pages":""},"PeriodicalIF":3.2,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144764645","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":"The Calderón problem for the logarithmic Schrödinger equation","authors":"Bastian Harrach ,&nbsp;Yi-Hsuan Lin ,&nbsp;Tobias Weth","doi":"10.1016/j.jde.2025.113665","DOIUrl":"10.1016/j.jde.2025.113665","url":null,"abstract":"<div><div>We investigate the Calderón problem for a logarithmic Schrödinger-type operator of the form <figure><img></figure>, where <figure><img></figure> denotes the logarithmic Laplacian—formally defined as the derivative <span><math><mfrac><mrow><mi>d</mi></mrow><mrow><mi>d</mi><mi>s</mi></mrow></mfrac><msub><mrow><mo>|</mo></mrow><mrow><mi>s</mi><mo>=</mo><mn>0</mn></mrow></msub><msup><mrow><mo>(</mo><mo>−</mo><mi>Δ</mi><mo>)</mo></mrow><mrow><mi>s</mi></mrow></msup></math></span> of the fractional Laplacian family. This operator exhibits striking nonlocal properties, including unique continuation and a Runge approximation property. Leveraging these tools, we establish uniqueness in the recovery of bounded potentials from the Dirichlet-to-Neumann map. Furthermore, we derive a constructive uniqueness result using the monotonicity method. Our results are valid in arbitrary spatial dimensions.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"444 ","pages":"Article 113665"},"PeriodicalIF":2.3,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144748963","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":"On the emergence and properties of weird quasiperiodic attractors","authors":"Laura Gardini ,&nbsp;Davide Radi ,&nbsp;Noemi Schmitt ,&nbsp;Iryna Sushko ,&nbsp;Frank Westerhoff","doi":"10.1016/j.chaos.2025.116916","DOIUrl":"10.1016/j.chaos.2025.116916","url":null,"abstract":"<div><div>We recently described a specific type of attractors of two-dimensional discontinuous piecewise linear maps, characterized by two discontinuity lines dividing the phase plane into three partitions, related to economic applications. To our knowledge, this type of attractor, which we call a weird quasiperiodic attractor, has not yet been studied in detail. It has a rather complex geometric structure and other interesting properties that are worth exploring in more depth. To this end, we consider a simpler map that can also possess weird quasiperiodic attractors, namely, a 2D discontinuous piecewise linear map <span><math><mi>F</mi></math></span> with a single discontinuity line dividing the phase plane into two partitions, where two different homogeneous linear maps are defined. Map <span><math><mi>F</mi></math></span> depends on four parameters — the traces and determinants of the two Jacobian matrices. In the parameter space of map <span><math><mi>F</mi></math></span>, we obtain specific regions associated with the existence of weird quasiperiodic attractors; describe some characteristic properties of these attractors; and explain one of the possible mechanisms of their appearance.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"199 ","pages":"Article 116916"},"PeriodicalIF":5.6,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144750736","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}

{"title":"A Localized Orthogonal Decomposition Method for Heterogeneous Stokes Problems","authors":"Moritz Hauck, Alexei Lozinski","doi":"10.1137/24m1704166","DOIUrl":"https://doi.org/10.1137/24m1704166","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 63, Issue 4, Page 1617-1641, August 2025. <br/> Abstract. In this paper, we propose a multiscale method for heterogeneous Stokes problems. The method is based on the localized orthogonal decomposition (LOD) methodology and has approximation properties independent of the regularity of the coefficients. We apply the LOD to an appropriate reformulation of the Stokes problem, which allows us to construct exponentially decaying basis functions for the velocity approximation while using a piecewise constant pressure approximation. The exponential decay motivates a localization of the basis computation, which is essential for the practical realization of the method. We perform a rigorous a priori error analysis and prove optimal convergence rates for the velocity approximation and a postprocessed pressure approximation, provided that the supports of the basis functions are logarithmically increased with the desired accuracy. Numerical experiments support the theoretical results of this paper.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"69 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144766090","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":"Effects of anisotropic diffusion in heterogeneous time-periodic environments.","authors":"Hongqiang Yu, Linlin Bu, Jianhua Wu","doi":"10.1007/s00285-025-02237-6","DOIUrl":"https://doi.org/10.1007/s00285-025-02237-6","url":null,"abstract":"<p><p>We study a reaction-diffusion system involving two species competing in temporally periodic and spatially heterogeneous environments. In this system, the species move horizontally and vertically with different probabilities, which can be regarded as dispersal strategies. The selection mechanisms in this case are more intricate than those observed in random diffusion scenarios. We investigate the stability of the semi-trivial periodic solutions in terms of the sign of the principal eigenvalue associated with a linear periodic eigenvalue problem. Furthermore, we provide sufficient conditions for the coexistence of two species. Additionally, numerical simulations are performed to facilitate further research and exploration.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"91 2","pages":"23"},"PeriodicalIF":2.3,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144762145","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":"Isogeometric discretizations of the Stokes problem on trimmed geometries","authors":"Riccardo Puppi","doi":"10.1016/j.camwa.2025.06.032","DOIUrl":"10.1016/j.camwa.2025.06.032","url":null,"abstract":"<div><div>We investigate the isogeometric approximation of the Stokes problem in a trimmed domain, where the underlying mesh is not fitted to the physical domain boundary, posing a challenge for enforcing essential boundary conditions. We introduce three families of isogeometric elements (Raviart-Thomas, Nédélec, and Taylor-Hood) and use them to discretize the problem. The widely used Nitsche method <span><span>[1]</span></span> is commonly employed to address this issue. However, we identify that the Nitsche method lacks stability in certain degenerate trimmed domain configurations, potentially polluting the computed solutions. Our remedy is twofold. On the one hand, we locally change the evaluation of the normal derivatives of the velocities in the weak formulation (generalizing the procedure introduced for the Poisson problem in <span><span>[2]</span></span>); on the other, we modify the space of the discrete pressures, eliminating the degrees of freedom associated with badly trimmed elements. We demonstrate that this approach restores the coercivity of the bilinear form for the velocities. Although numerical results show that our method restores the inf-sup stability of the discrete problem, a rigorous mathematical proof is still missing. We prove optimal a priori error estimates and provide numerical experiments to validate the theory, emphasizing the validation of the inf-sup stability of our method.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"195 ","pages":"Pages 376-395"},"PeriodicalIF":2.5,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144748780","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}