Applied Mathematics Letters最新文献

{"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}

{"title":"Local-in-space blow-up of a weakly dissipative generalized Dullin–Gottwald–Holm equation","authors":"Wenguang Cheng,&nbsp;Bingqi Li","doi":"10.1016/j.aml.2024.109445","DOIUrl":"10.1016/j.aml.2024.109445","url":null,"abstract":"<div><div>This paper addresses the problems of blow-up for a weakly dissipative generalized Dullin–Gottwald–Holm equation. A new sufficient condition on the initial data is provided to ensure the finite time local-in-space blow-up of strong solutions, which improves the local-in-space blow-up result of Novruzov and Yazar <span><span>[1]</span></span>.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"163 ","pages":"Article 109445"},"PeriodicalIF":2.9,"publicationDate":"2024-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142889271","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":"Constructing solutions of the ‘bad’ Jaulent–Miodek equation based on a relationship with the Burgers equation","authors":"Jing-Jing Su,&nbsp;Yu-Long He,&nbsp;Bo Ruan","doi":"10.1016/j.aml.2024.109440","DOIUrl":"10.1016/j.aml.2024.109440","url":null,"abstract":"<div><div>The ‘bad’ Jaulent–Miodek (JM) equation describes the wave evolution of inviscid shallow water over a flat bottom in the presence of shear, which is ill-posed and unstable so that its general initial problem on the zero plane is difficult to solve through traditional mesh-based numerical methods. In this paper, using the Darboux transformation, we find a relation between the ‘bad’ JM equation and the well-known Burgers equation. Based on the Burgers equation, we construct the analytical and numerical solutions of the ‘bad’ JM equation via the Hirota bilinear method and the time-splitting Fourier spectral method. Specifically, we numerically present the interaction between two Gaussian packets of the ‘bad’ JM equation. This approach extends the applicability of traditional numerical methods for solving general initial problems of the ‘bad’ JM equation.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"163 ","pages":"Article 109440"},"PeriodicalIF":2.9,"publicationDate":"2024-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142889360","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 second-order accurate numerical method with unconditional energy stability for the Lifshitz–Petrich equation on curved surfaces","authors":"Xiaochuan Hu ,&nbsp;Qing Xia ,&nbsp;Binhu Xia ,&nbsp;Yibao Li","doi":"10.1016/j.aml.2024.109439","DOIUrl":"10.1016/j.aml.2024.109439","url":null,"abstract":"<div><div>In this paper, we introduce an efficient numerical algorithm for solving the Lifshitz–Petrich equation on closed surfaces. The algorithm involves discretizing the surface with a triangular mesh, allowing for an explicit definition of the Laplace–Beltrami operator based on the neighborhood information of the mesh elements. To achieve second-order temporal accuracy, the backward differentiation formula scheme and the scalar auxiliary variable method are employed for Lifshitz–Petrich equation. The discrete system is subsequently solved using the biconjugate gradient stabilized method, with incomplete LU decomposition of the coefficient matrix serving as a preprocessor. The proposed algorithm is characterized by its simplicity in implementation and second-order precision in both spatial and temporal domains. Numerical experiments are conducted to validate the unconditional energy stability and efficacy of the algorithm.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"163 ","pages":"Article 109439"},"PeriodicalIF":2.9,"publicationDate":"2024-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142889361","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}