Applied Mathematics Letters最新文献

{"title":"On a Camassa–Holm type equation describing the dynamics of viscous fluid conduits","authors":"Rafael Granero-Belinchón","doi":"10.1016/j.aml.2024.109443","DOIUrl":"10.1016/j.aml.2024.109443","url":null,"abstract":"<div><div>In this note we derive a new nonlocal and nonlinear dispersive equations capturing the main dynamics of a circular interface separating a light, viscous fluid rising buoyantly through a heavy, more viscous, miscible fluid at small Reynolds numbers. This equation that we termed the <span><math><mrow><mi>g</mi><mo>−</mo></mrow></math></span>model shares some common structure with the Camassa–Holm equation but has additional nonlocal effects. For this new PDE we study the well-posedness together with the existence of periodic traveling waves. Furthermore, we also show some numerical simulations suggesting the finite time singularity formation.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"163 ","pages":"Article 109443"},"PeriodicalIF":2.9,"publicationDate":"2025-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142968150","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":"Exponential stability of a diffusive Nicholson’s blowflies equation accompanying multiple time-varying delays","authors":"Chuangxia Huang ,&nbsp;Bingwen Liu","doi":"10.1016/j.aml.2024.109451","DOIUrl":"10.1016/j.aml.2024.109451","url":null,"abstract":"<div><div>In this paper, we explore a modified diffusive Nicholson’s blowflies equation accompanying multiple pairs of time-varying delays which include distinct diapause and maturation effects. With the help of some differential inequality analyses, we obtain a criterion to assure the stability and exponential attraction of the addressed reaction–diffusion equation accompanying Neumann boundary conditions, which fully refines and generalizes some existing ones.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"163 ","pages":"Article 109451"},"PeriodicalIF":2.9,"publicationDate":"2025-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143096578","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":"A strong mass conservative finite element method for the Navier–Stokes/Darcy coupled system","authors":"Jessika Camaño ,&nbsp;Ricardo Oyarzúa ,&nbsp;Miguel Serón ,&nbsp;Manuel Solano","doi":"10.1016/j.aml.2024.109447","DOIUrl":"10.1016/j.aml.2024.109447","url":null,"abstract":"<div><div>We revisit the continuous formulation introduced in Discacciati and Oyarzúa (2017) for the stationary Navier–Stokes/Darcy (NSD) coupled system and propose an equivalent scheme that does not require a Lagrange multiplier to enforce the continuity of normal velocities at the interface. Building on this formulation and following a similar approach to Kanschat and Rivière (2010), we derive a mass-conservative, <span><math><mrow><mi>H</mi><mrow><mo>(</mo><mi>div</mi><mo>)</mo></mrow></mrow></math></span>–conforming finite element method for the NSD system.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"163 ","pages":"Article 109447"},"PeriodicalIF":2.9,"publicationDate":"2025-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142968153","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":"Uniqueness of solution for incompressible inhomogeneous Navier–Stokes equations in dimension two","authors":"Yelei Guo,&nbsp;Chinyin Qian","doi":"10.1016/j.aml.2024.109449","DOIUrl":"10.1016/j.aml.2024.109449","url":null,"abstract":"<div><div>The global existence of solution for 2D inhomogeneous incompressible Navier–Stokes equations is established by Abidi et al. (2024), and the uniqueness of solution is also investigated under some additional conditions on initial density. The purpose of this paper is to obtain the uniqueness of the solution without any additional assumptions on the initial density in case of <span><math><mrow><mn>2</mn><mo>≤</mo><mi>p</mi><mo>&lt;</mo><mn>4</mn></mrow></math></span>. The key strategy is to establish a new estimate of solution in Lagrangian coordinates.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"163 ","pages":"Article 109449"},"PeriodicalIF":2.9,"publicationDate":"2025-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142968151","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":"A free-parameter alternating triangular splitting iteration method for time-harmonic parabolic problems","authors":"Chengliang Li ,&nbsp;Jiashang Zhu ,&nbsp;Changfeng Ma","doi":"10.1016/j.aml.2024.109429","DOIUrl":"10.1016/j.aml.2024.109429","url":null,"abstract":"<div><div>Based on the triangular splitting technique, we introduce a free-parameter alternating triangular splitting (FPATS) method for solving block two-by-two linear systems with applications to time-harmonic parabolic models. In addition, we demonstrate that the FPATS method is unconditionally convergent and outperforms other methods. Numerical results are provided to show the practicality and efficiency of our method.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"163 ","pages":"Article 109429"},"PeriodicalIF":2.9,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142929259","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":"Time periodic solution for a system of spatially inhomogeneous wave equations with nonlinear couplings","authors":"Jiayu Deng,&nbsp;Jianhua Liu,&nbsp;Shuguan Ji","doi":"10.1016/j.aml.2024.109448","DOIUrl":"10.1016/j.aml.2024.109448","url":null,"abstract":"<div><div>This paper is concerned with the existence of periodic solution for a system of spatially inhomogeneous wave equations with nonlinear couplings. The main contribution of this research lies in the fact that the coupled terms are nonlinear. For the periods having the form <span><math><mrow><mi>T</mi><mo>=</mo><mn>2</mn><mi>π</mi><mfrac><mrow><mn>2</mn><mi>a</mi><mo>−</mo><mn>1</mn></mrow><mrow><mi>b</mi></mrow></mfrac></mrow></math></span> (<span><math><mrow><mi>a</mi><mo>,</mo><mi>b</mi></mrow></math></span> are positive integers), by applying the dual variational method, we establish the existence of the time periodic solution under some Sturm–Liouville boundary conditions. To our knowledge, there is rarely papers focus on the existence of periodic solution for a system of spatially inhomogeneous wave equations with nonlinear couplings.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"163 ","pages":"Article 109448"},"PeriodicalIF":2.9,"publicationDate":"2024-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142929216","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":"Stability of 2D inviscid MHD equations with only fractional magnetic diffusion in the horizontal direction","authors":"Yueyuan Zhong","doi":"10.1016/j.aml.2024.109446","DOIUrl":"10.1016/j.aml.2024.109446","url":null,"abstract":"<div><div>This paper focuses on a special 2D magnetohydrodynamic (MHD) system with no viscosity and only fractional magnetic diffusion in the horizontal direction on the domain <span><math><mrow><mi>Ω</mi><mo>=</mo><mi>T</mi><mo>×</mo><mi>R</mi></mrow></math></span> and <span><math><mrow><mi>T</mi><mo>=</mo><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow></mrow></math></span> be a periodic box. Due to the lack of the velocity dissipation, this stability problem is not trivial. Without the presence of a magnetic field, the fluid velocity is governed by the 2D incompressible Euler equation, and its solution grow rather rapidly. However, when coupled to the magnetic field in such an MHD system, our result in this paper then shows the stabilization effect. Moreover, we will derive the exponentially decay of solutions on horizontal direction.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"163 ","pages":"Article 109446"},"PeriodicalIF":2.9,"publicationDate":"2024-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142929322","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":"Explicit solutions of Genz test integrals","authors":"Vesa Kaarnioja","doi":"10.1016/j.aml.2024.109444","DOIUrl":"10.1016/j.aml.2024.109444","url":null,"abstract":"&lt;div&gt;&lt;div&gt;A collection of test integrals introduced by Genz (1984) has remained popular to this day for assessing the robustness of high-dimensional numerical integration algorithms. However, the explicit solutions to these integrals do not appear to be readily available in the existing literature: typically the true values of the test integrals are simply approximated using “overkill” numerical solutions. In this paper, analytic solutions are presented for the Genz test integrals 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d":55497,"journal":{"name":"Applied Mathematics Letters","volume":"163 ","pages":"Article 109444"},"PeriodicalIF":2.9,"publicationDate":"2024-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142889272","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Finite time blow-up for a heat equation in RN","authors":"Kaiqiang Zhang","doi":"10.1016/j.aml.2024.109441","DOIUrl":"10.1016/j.aml.2024.109441","url":null,"abstract":"<div><div>We consider the semilinear heat equation <span><span><span><math><mrow><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>−</mo><mi>Δ</mi><mi>u</mi><mo>=</mo><msup><mrow><mrow><mo>|</mo><mi>u</mi><mo>|</mo></mrow></mrow><mrow><mi>p</mi><mo>−</mo><mn>1</mn></mrow></msup><mi>u</mi><mo>+</mo><mi>λ</mi><mi>u</mi><mo>,</mo><mspace></mspace><mspace></mspace><mtext>on</mtext><mspace></mspace><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></mrow></math></span></span></span>where <span><math><mrow><mi>p</mi><mo>&gt;</mo><mn>1</mn></mrow></math></span>, and <span><math><mrow><mi>λ</mi><mo>∈</mo><mi>R</mi></mrow></math></span> is a parameter. When <span><math><mrow><mi>λ</mi><mo>=</mo><mn>0</mn></mrow></math></span>, the equation reduces to the classical heat equation. We reveal that the parameter <span><math><mi>λ</mi></math></span> in the linear term plays an important role in the blow-up conditions. Although the solution may blow up in finite time due to the cumulative effect of the nonlinearities, interestingly, we find that for <span><math><mrow><mi>λ</mi><mo>&gt;</mo><mfrac><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></math></span>, all non-negative solutions blow up in finite time, which shows that the Fujita exponent is equal to <span><math><mrow><mo>+</mo><mi>∞</mi></mrow></math></span>. Our result extends the Theorem 17.1 in Quittner and Souplet (2007). In addition, for <span><math><mrow><mi>λ</mi><mo>&lt;</mo><mn>0</mn></mrow></math></span>, we provide a new sufficient condition for the finite time blow-up solution.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"163 ","pages":"Article 109441"},"PeriodicalIF":2.9,"publicationDate":"2024-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142889359","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":"Dynamics of a weak-kernel distributed memory-based diffusion model with nonlocal delay effect","authors":"Quanli Ji ,&nbsp;Ranchao Wu ,&nbsp;Federico Frascoli ,&nbsp;Zhenzhen Chen","doi":"10.1016/j.aml.2024.109442","DOIUrl":"10.1016/j.aml.2024.109442","url":null,"abstract":"<div><div>In this paper, we study a temporally distributed memory-based diffusion model with a weak kernel and nonlocal delay effect. Without diffusion, we present results on the stability and Hopf bifurcation of the positive constant steady state. With the inclusion of diffusion, further results on the stability and steady state bifurcation are derived. Finally, these findings are applied to a population model.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"163 ","pages":"Article 109442"},"PeriodicalIF":2.9,"publicationDate":"2024-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142889319","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}