Applied Mathematics Letters最新文献

{"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":"https://doi.org/10.1016/j.aml.2024.109446","url":null,"abstract":"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 <mml:math altimg=\"si1.svg\" display=\"inline\"><mml:mrow><mml:mi>Ω</mml:mi><mml:mo linebreak=\"goodbreak\" linebreakstyle=\"after\">=</mml:mo><mml:mi mathvariant=\"double-struck\">T</mml:mi><mml:mo linebreak=\"goodbreak\" linebreakstyle=\"after\">×</mml:mo><mml:mi mathvariant=\"double-struck\">R</mml:mi></mml:mrow></mml:math> and <mml:math altimg=\"si2.svg\" display=\"inline\"><mml:mrow><mml:mi mathvariant=\"double-struck\">T</mml:mi><mml:mo linebreak=\"goodbreak\" linebreakstyle=\"after\">=</mml:mo><mml:mrow><mml:mo>[</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mn>1</mml:mn><mml:mo>]</mml:mo></mml:mrow></mml:mrow></mml:math> 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.","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"37 1","pages":""},"PeriodicalIF":3.7,"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":"https://doi.org/10.1016/j.aml.2024.109444","url":null,"abstract":"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 &lt;ce:display&gt;&lt;ce:formula&gt;&lt;mml:math altimg=\"si1.svg\" display=\"block\"&gt;&lt;mml:mrow&gt;&lt;mml:munderover&gt;&lt;mml:mrow&gt;&lt;mml:mo linebreak=\"badbreak\"&gt;∫&lt;/mml:mo&gt;&lt;/mml:mrow&gt;&lt;mml:mrow&gt;&lt;mml:mn&gt;0&lt;/mml:mn&gt;&lt;/mml:mrow&gt;&lt;mml:mrow&gt;&lt;mml:mn&gt;1&lt;/mml:mn&gt;&lt;/mml:mrow&gt;&lt;/mml:munderover&gt;&lt;mml:mo linebreak=\"goodbreak\"&gt;⋯&lt;/mml:mo&gt;&lt;mml:munderover&gt;&lt;mml:mrow&gt;&lt;mml:mo linebreak=\"badbreak\"&gt;∫&lt;/mml:mo&gt;&lt;/mml:mrow&gt;&lt;mml:mrow&gt;&lt;mml:mn&gt;0&lt;/mml:mn&gt;&lt;/mml:mrow&gt;&lt;mml:mrow&gt;&lt;mml:mn&gt;1&lt;/mml:mn&gt;&lt;/mml:mrow&gt;&lt;/mml:munderover&gt;&lt;mml:mo&gt;cos&lt;/mml:mo&gt;&lt;mml:mrow&gt;&lt;mml:mo fence=\"true\"&gt;(&lt;/mml:mo&gt;&lt;mml:mrow&gt;&lt;mml:mn&gt;2&lt;/mml:mn&gt;&lt;mml:mi&gt;π&lt;/mml:mi&gt;&lt;mml:msub&gt;&lt;mml:mrow&gt;&lt;mml:mi&gt;w&lt;/mml:mi&gt;&lt;/mml:mrow&gt;&lt;mml:mrow&gt;&lt;mml:mn&gt;1&lt;/mml:mn&gt;&lt;/mml:mrow&gt;&lt;/mml:msub&gt;&lt;mml:mo&gt;+&lt;/mml:mo&gt;&lt;mml:munderover&gt;&lt;mml:mrow&gt;&lt;mml:mo linebreak=\"badbreak\"&gt;∑&lt;/mml:mo&gt;&lt;/mml:mrow&gt;&lt;mml:mrow&gt;&lt;mml:mi&gt;i&lt;/mml:mi&gt;&lt;mml:mo linebreak=\"badbreak\"&gt;=&lt;/mml:mo&gt;&lt;mml:mn&gt;1&lt;/mml:mn&gt;&lt;/mml:mrow&gt;&lt;mml:mrow&gt;&lt;mml:mi&gt;d&lt;/mml:mi&gt;&lt;/mml:mrow&gt;&lt;/mml:munderover&gt;&lt;mml:msub&gt;&lt;mml:mrow&gt;&lt;mml:mi&gt;c&lt;/mml:mi&gt;&lt;/mml:mrow&gt;&lt;mml:mrow&gt;&lt;mml:mi&gt;i&lt;/mml:mi&gt;&lt;/mml:mrow&gt;&lt;/mml:msub&gt;&lt;mml:msub&gt;&lt;mml:mrow&gt;&lt;mml:mi&gt;x&lt;/mml:mi&gt;&lt;/mml:mrow&gt;&lt;mml:mrow&gt;&lt;mml:mi&gt;i&lt;/mml:mi&gt;&lt;/mml:mrow&gt;&lt;/mml:msub&gt;&lt;/mml:mrow&gt;&lt;mml:mo fence=\"true\"&gt;)&lt;/mml:mo&gt;&lt;/mml:mrow&gt;&lt;mml:mspace width=\"0.16667em\"&gt;&lt;/mml:mspace&gt;&lt;mml:mi mathvariant=\"normal\"&gt;d&lt;/mml:mi&gt;&lt;mml:msub&gt;&lt;mml:mrow&gt;&lt;mml:mi&gt;x&lt;/mml:mi&gt;&lt;/mml:mrow&gt;&lt;mml:mrow&gt;&lt;mml:mi&gt;d&lt;/mml:mi&gt;&lt;/mml:mrow&gt;&lt;/mml:msub&gt;&lt;mml:mo linebreak=\"goodbreak\"&gt;⋯&lt;/mml:mo&gt;&lt;mml:mspace width=\"0.16667em\"&gt;&lt;/mml:mspace&gt;&lt;mml:mi mathvariant=\"normal\"&gt;d&lt;/mml:mi&gt;&lt;mml:msub&gt;&lt;mml:mrow&gt;&lt;mml:mi&gt;x&lt;/mml:mi&gt;&lt;/mml:mrow&gt;&lt;mml:mrow&gt;&lt;mml:mn&gt;1&lt;/mml:mn&gt;&lt;/mml:mrow&gt;&lt;/mml:msub&gt;&lt;mml:mo linebreak=\"goodbreak\"&gt;=&lt;/mml:mo&gt;&lt;mml:msup&gt;&lt;mml:mrow&gt;&lt;mml:mn&gt;2&lt;/mml:mn&gt;&lt;/mml:mrow&gt;&lt;mml:mrow&gt;&lt;mml:mi&gt;d&lt;/mml:mi&gt;&lt;/mml:mrow&gt;&lt;/mml:msup&gt;&lt;mml:mo&gt;cos&lt;/mml:mo&gt;&lt;mml:mrow&gt;&lt;mml:mo fence=\"true\"&gt;(&lt;/mml:mo&gt;&lt;mml:mrow&gt;&lt;mml:mn&gt;2&lt;/mml:mn&gt;&lt;mml:mi&gt;π&lt;/mml:mi&gt;&lt;mml:msub&gt;&lt;mml:mrow&gt;&lt;mml:mi&gt;w&lt;/mml:mi&gt;&lt;/mml:mrow&gt;&lt;mml:mrow&gt;&lt;mml:mn&gt;1&lt;/mml:mn&gt;&lt;/mml:mrow&gt;&lt;/mml:msub&gt;&lt;mml:mo&gt;+&lt;/mml:mo&gt;&lt;mml:mfrac&gt;&lt;mml:mrow&gt;&lt;mml:mn&gt;1&lt;/mml:mn&gt;&lt;/mml:mrow&gt;&lt;mml:mrow&gt;&lt;mml:mn&gt;2&lt;/mml:mn&gt;&lt;/mml:mrow&gt;&lt;/mml:mfrac&gt;&lt;mml:munderover&gt;&lt;mml:mrow&gt;&lt;mml:mo linebreak=\"badbreak\"&gt;∑&lt;/mml:mo&gt;&lt;/mml:mrow&gt;&lt;mml:mrow&gt;&lt;mml:mi&gt;i&lt;/mml:mi&gt;&lt;mml:mo linebreak=\"badbreak\"&gt;=&lt;/mml:mo&gt;&lt;mml:mn&gt;1&lt;/mml:mn&gt;&lt;/mml:mrow&gt;&lt;mml:mrow&gt;&lt;mml:mi&gt;d&lt;/mml:mi&gt;&lt;/mml:mrow&gt;&lt;/mml:munderover&gt;&lt;mml:msub&gt;&lt;mml:mrow&gt;&lt;mml:mi&gt;c&lt;/mml:mi&gt;&lt;/mml:mrow&gt;&lt;mml:mrow&gt;&lt;mml:mi&gt;i&lt;/mml:mi&gt;&lt;/mml:mrow&gt;&lt;/mml:msub&gt;&lt;/mml:mrow&gt;&lt;mml:mo fence=\"true\"&gt;)&lt;/mml:mo&gt;&lt;/mml:mrow&gt;&lt;mml:munderover&gt;&lt;mml:mrow&gt;&lt;mml:mo linebreak=\"badbreak\"&gt;∏&lt;/mml:mo&gt;&lt;/mml:mrow&gt;&lt;mml:mrow&gt;&lt;mml:mi&gt;i&lt;/mml:mi&gt;&lt;mml:mo line","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"20 1","pages":""},"PeriodicalIF":3.7,"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":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Finite time blow-up for a heat equation in [formula omitted]","authors":"Kaiqiang Zhang","doi":"10.1016/j.aml.2024.109441","DOIUrl":"https://doi.org/10.1016/j.aml.2024.109441","url":null,"abstract":"We consider the semilinear heat equation <ce:display><ce:formula><mml:math altimg=\"si1.svg\" display=\"block\"><mml:mrow><mml:msub><mml:mrow><mml:mi>u</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo linebreak=\"goodbreak\">−</mml:mo><mml:mi>Δ</mml:mi><mml:mi>u</mml:mi><mml:mo linebreak=\"goodbreak\">=</mml:mo><mml:msup><mml:mrow><mml:mrow><mml:mo>|</mml:mo><mml:mi>u</mml:mi><mml:mo>|</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mi>p</mml:mi><mml:mo linebreak=\"badbreak\">−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:mi>u</mml:mi><mml:mo linebreak=\"goodbreak\">+</mml:mo><mml:mi>λ</mml:mi><mml:mi>u</mml:mi><mml:mo>,</mml:mo><mml:mspace width=\"1em\"></mml:mspace><mml:mspace width=\"1em\"></mml:mspace><mml:mtext>on</mml:mtext><mml:mspace width=\"1em\"></mml:mspace><mml:msup><mml:mrow><mml:mi mathvariant=\"double-struck\">R</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math></ce:formula></ce:display>where <mml:math altimg=\"si2.svg\" display=\"inline\"><mml:mrow><mml:mi>p</mml:mi><mml:mo linebreak=\"goodbreak\" linebreakstyle=\"after\">&gt;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math>, and <mml:math altimg=\"si3.svg\" display=\"inline\"><mml:mrow><mml:mi>λ</mml:mi><mml:mo linebreak=\"goodbreak\" linebreakstyle=\"after\">∈</mml:mo><mml:mi mathvariant=\"double-struck\">R</mml:mi></mml:mrow></mml:math> is a parameter. When <mml:math altimg=\"si4.svg\" display=\"inline\"><mml:mrow><mml:mi>λ</mml:mi><mml:mo linebreak=\"goodbreak\" linebreakstyle=\"after\">=</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math>, the equation reduces to the classical heat equation. We reveal that the parameter <mml:math altimg=\"si5.svg\" display=\"inline\"><mml:mi>λ</mml:mi></mml:math> 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 <mml:math altimg=\"si6.svg\" display=\"inline\"><mml:mrow><mml:mi>λ</mml:mi><mml:mo linebreak=\"goodbreak\" linebreakstyle=\"after\">&gt;</mml:mo><mml:mfrac><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:mfrac></mml:mrow></mml:math>, all non-negative solutions blow up in finite time, which shows that the Fujita exponent is equal to <mml:math altimg=\"si7.svg\" display=\"inline\"><mml:mrow><mml:mo>+</mml:mo><mml:mi>∞</mml:mi></mml:mrow></mml:math>. Our result extends the Theorem 17.1 in Quittner and Souplet (2007). In addition, for <mml:math altimg=\"si8.svg\" display=\"inline\"><mml:mrow><mml:mi>λ</mml:mi><mml:mo linebreak=\"goodbreak\" linebreakstyle=\"after\">&lt;</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math>, we provide a new sufficient condition for the finite time blow-up solution.","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"4 1","pages":""},"PeriodicalIF":3.7,"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":"Local-in-space blow-up of a weakly dissipative generalized Dullin–Gottwald–Holm equation","authors":"Wenguang Cheng, Bingqi Li","doi":"10.1016/j.aml.2024.109445","DOIUrl":"https://doi.org/10.1016/j.aml.2024.109445","url":null,"abstract":"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 <ce:cross-ref ref>[1]</ce:cross-ref>.","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"123 1","pages":""},"PeriodicalIF":3.7,"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":"Dynamics of a weak-kernel distributed memory-based diffusion model with nonlocal delay effect","authors":"Quanli Ji, Ranchao Wu, Federico Frascoli, Zhenzhen Chen","doi":"10.1016/j.aml.2024.109442","DOIUrl":"https://doi.org/10.1016/j.aml.2024.109442","url":null,"abstract":"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.","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"83 1","pages":""},"PeriodicalIF":3.7,"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":"Constructing solutions of the ‘bad’ Jaulent–Miodek equation based on a relationship with the Burgers equation","authors":"Jing-Jing Su, Yu-Long He, Bo Ruan","doi":"10.1016/j.aml.2024.109440","DOIUrl":"https://doi.org/10.1016/j.aml.2024.109440","url":null,"abstract":"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.","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"41 1","pages":""},"PeriodicalIF":3.7,"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, Qing Xia, Binhu Xia, Yibao Li","doi":"10.1016/j.aml.2024.109439","DOIUrl":"https://doi.org/10.1016/j.aml.2024.109439","url":null,"abstract":"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.","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"26 1","pages":""},"PeriodicalIF":3.7,"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}

{"title":"An unstructured algorithm for the singular value decomposition of biquaternion matrices","authors":"Gang Wang","doi":"10.1016/j.aml.2024.109436","DOIUrl":"https://doi.org/10.1016/j.aml.2024.109436","url":null,"abstract":"With the modeling of the biquaternion algebra in multidimensional signal processing, it has become possible to address issues such as data separation, denoising, and anomaly detection. This paper investigates the singular value decomposition of biquaternion matrices (SVDBQ), establishing an SVDBQ theorem that ensures unitary matrices formed by the left and right singular vectors, while also introducing a new form for singular values. Additionally, the non-uniqueness of SVDBQ is proven, expanding the theoretical framework of the biquaternion algebra. Building on this foundation, the paper presents a novel, fast, unstructured algorithm based on the isomorphic representation matrices of biquaternion matrices. Unlike existing methods, which are often complex and computationally expensive, the proposed algorithm is structurally simple and significantly faster, making it ideal for real-time signal processing. Numerical experiments validate the efficiency and effectiveness of this new algorithm, demonstrating its potential to advance both research and practical applications in signal processing.","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"14 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142889256","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 identifying multiple parameters in a time-fractional Cattaneo equation","authors":"Yun Zhang, Xiaoli Feng","doi":"10.1016/j.aml.2024.109438","DOIUrl":"https://doi.org/10.1016/j.aml.2024.109438","url":null,"abstract":"This paper addresses an inverse problem involving the simultaneous identification of the fractional order, potential coefficient, initial value and source term in a time-fractional Cattaneo equation. Utilizing the method of Laplace transformation, we demonstrate that the multiple unknowns can be uniquely determined from observational data collected at two boundary points.","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"33 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142889362","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 trapped lee waves with centripetal forces","authors":"Tao Li, JinRong Wang","doi":"10.1016/j.aml.2024.109435","DOIUrl":"https://doi.org/10.1016/j.aml.2024.109435","url":null,"abstract":"This paper firstly studies exact solutions to the atmospheric equations of motion in the <mml:math altimg=\"si209.svg\" display=\"inline\"><mml:mi>f</mml:mi></mml:math>-plane and <mml:math altimg=\"si213.svg\" display=\"inline\"><mml:mi>β</mml:mi></mml:math>-plane approximations while considering centripetal forces. The obtained solutions are shown in Lagrangian coordinates. Additionally, we derive the dispersion relations and perform a qualitative analysis of density, pressure, and vorticity.","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"93 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142889363","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}