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Inverse coefficient problems for one-dimensional time-fractional diffusion equations 一维时间分数扩散方程的反系数问题
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2024-10-26 DOI: 10.1016/j.aml.2024.109351
{"title":"Inverse coefficient problems for one-dimensional time-fractional diffusion equations","authors":"","doi":"10.1016/j.aml.2024.109351","DOIUrl":"10.1016/j.aml.2024.109351","url":null,"abstract":"<div><div>We prove the uniqueness in determining a spatially varying zeroth-order coefficient of a one-dimensional time-fractional diffusion equation by initial value and Cauchy data at one end point of the spatial interval.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142577806","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}
引用次数: 0
Local C2-smooth spline quasi-interpolation methods 局部 C2 平滑样条准插值法
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2024-10-26 DOI: 10.1016/j.aml.2024.109346
{"title":"Local C2-smooth spline quasi-interpolation methods","authors":"","doi":"10.1016/j.aml.2024.109346","DOIUrl":"10.1016/j.aml.2024.109346","url":null,"abstract":"<div><div>In this paper we construct new univariate local <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> quasi-interpolating splines having specific polynomial reproduction properties. The splines are directly determined by setting their Bernstein-Bézier coefficients to appropriate combinations of the given data values. In certain cases we obtain a family of quasi-interpolating operators satisfying the required conditions, so we fix some extra properties (interpolation of the vertices, extra locality, extra polynomial reproduction) in order to compute unique approximants. We also provide numerical results confirming the theoretical ones.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142586535","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}
引用次数: 0
Energy equality of the two-fluid incompressible Navier–Stokes–Maxwell equations 双流体不可压缩纳维-斯托克斯-麦克斯韦方程的能量相等问题
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2024-10-26 DOI: 10.1016/j.aml.2024.109349
{"title":"Energy equality of the two-fluid incompressible Navier–Stokes–Maxwell equations","authors":"","doi":"10.1016/j.aml.2024.109349","DOIUrl":"10.1016/j.aml.2024.109349","url":null,"abstract":"<div><div>In this paper, we are concerned with the energy equality of weak solutions of the two-fluid incompressible Navier–Stokes–Maxwell equations. It is shown that the energy equality of weak solutions of this system is valid provided the velocities <span><math><mrow><msup><mrow><mi>u</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>,</mo><msup><mrow><mi>u</mi></mrow><mrow><mo>−</mo></mrow></msup></mrow></math></span> are just in Lions-Shinbrot class.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142572382","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}
引用次数: 0
Implementation strategy of insulin therapy under sparse state feedback 稀疏状态反馈下的胰岛素治疗实施策略
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2024-10-24 DOI: 10.1016/j.aml.2024.109347
{"title":"Implementation strategy of insulin therapy under sparse state feedback","authors":"","doi":"10.1016/j.aml.2024.109347","DOIUrl":"10.1016/j.aml.2024.109347","url":null,"abstract":"<div><div>Traditional continuous glucose monitoring is often costly and inconvenient, necessitating more efficient methods. This paper proposes a novel approach to diabetes management by utilizing sparse monitoring data for insulin injection decisions. A differential equation-based model is developed to estimate plasma glucose levels and optimize insulin dosages and injection intervals using limited feedback data. This method ensures that glucose levels remain within a safe range. Numerical simulations demonstrate the effectiveness of this approach, offering a viable alternative for improving diabetes management.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142553181","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}
引用次数: 0
Uniform measure attractors for nonautonomous stochastic tamed 3D Navier–Stokes equations with almost periodic forcing 具有几乎周期性强迫的非自主随机驯服三维纳维-斯托克斯方程的均匀量吸引子
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2024-10-24 DOI: 10.1016/j.aml.2024.109345
{"title":"Uniform measure attractors for nonautonomous stochastic tamed 3D Navier–Stokes equations with almost periodic forcing","authors":"","doi":"10.1016/j.aml.2024.109345","DOIUrl":"10.1016/j.aml.2024.109345","url":null,"abstract":"<div><div>This article provides a characterization of uniform measure attractors for non-autonomous stochastic tamed 3D Navier–Stokes equations, specifically with a almost-periodic external force term. The existing literature has primarily focused on measure attractors within an autonomous framework; however, when the forcing function is almost periodic, the solution process generated by the corresponding equations behaves as a non-autonomous Markov process, rendering the existing framework inapplicable. Therefore, it is crucial to investigate this within a new framework, which is the motivation behind the study of uniform measure attractors in this paper.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142553180","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}
引用次数: 0
Singularity formation of hydromagnetic waves in cold plasma 冷等离子体中水磁波奇点的形成
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2024-10-24 DOI: 10.1016/j.aml.2024.109344
{"title":"Singularity formation of hydromagnetic waves in cold plasma","authors":"","doi":"10.1016/j.aml.2024.109344","DOIUrl":"10.1016/j.aml.2024.109344","url":null,"abstract":"<div><div>We study <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> blow-up of the compressible fluid model introduced by Gardner and Morikawa, which describes the dynamics of a magnetized cold plasma. We propose sufficient conditions that lead to <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> blow-up. In particular, we find that smooth solutions can break down in finite time even if the gradient of initial velocity is identically zero. The density and the gradient of the velocity become unbounded as time approaches the lifespan of the smooth solution. The Lagrangian formulation reduces the singularity formation problem to finding a zero of the associated second-order ODE.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142553184","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}
引用次数: 0
Forced waves of time-delayed nonlocal dispersal equations in shifting habitats 移动栖息地中时延非局部扩散方程的强迫波
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2024-10-23 DOI: 10.1016/j.aml.2024.109343
{"title":"Forced waves of time-delayed nonlocal dispersal equations in shifting habitats","authors":"","doi":"10.1016/j.aml.2024.109343","DOIUrl":"10.1016/j.aml.2024.109343","url":null,"abstract":"<div><div>To investigate the combined effects of time delay, nonlocal dispersal and climate change on population dynamics, we consider a time-delayed nonlocal dispersal equations in shifting habitats. Firstly, with the construction of appropriate lower and upper solutions, the existence of forced waves is established via the monotone iteration scheme. Furthermore, we show that the forced wave profile is unique in the classic sense, i.e., NOT up to a shift in the co-moving frame coordinate, by applying the sliding technique. Our result shows that time delay does not prevent the occurrence of forced extinction waves for non-locally diffusive populations in degraded habitats.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142532522","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}
引用次数: 0
A bifurcation and multiplicity result for a critical growth elliptic problem 临界增长椭圆问题的分岔和多重性结果
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2024-10-22 DOI: 10.1016/j.aml.2024.109342
{"title":"A bifurcation and multiplicity result for a critical growth elliptic problem","authors":"","doi":"10.1016/j.aml.2024.109342","DOIUrl":"10.1016/j.aml.2024.109342","url":null,"abstract":"<div><div>We consider a Brézis–Nirenberg type critical growth <span><math><mi>p</mi></math></span>-Laplacian problem involving a parameter <span><math><mrow><mi>μ</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span> in a smooth bounded domain <span><math><mi>Ω</mi></math></span>. We prove the existence of multiple nontrivial solutions if either <span><math><mi>μ</mi></math></span> or the volume of <span><math><mi>Ω</mi></math></span> is sufficiently small. The proof is based on an abstract critical point theorem that only assumes a local <span><math><msub><mrow><mrow><mo>(</mo><mtext>PS</mtext><mo>)</mo></mrow></mrow><mrow></mrow></msub></math></span> condition. Our results are new even in the semilinear case <span><math><mrow><mi>p</mi><mo>=</mo><mn>2</mn></mrow></math></span>.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142532521","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}
引用次数: 0
A peridynamics approach modeling gas flow in porous media with damaged regions 用周动力学方法模拟多孔介质中带有损伤区域的气体流动
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2024-10-20 DOI: 10.1016/j.aml.2024.109341
{"title":"A peridynamics approach modeling gas flow in porous media with damaged regions","authors":"","doi":"10.1016/j.aml.2024.109341","DOIUrl":"10.1016/j.aml.2024.109341","url":null,"abstract":"<div><div>The study of gas flow within porous media, particularly those characterized by complex pore-fracture networks, is critical for applications in fields such as shale gas engineering, gas extraction, and hydrogeology. This paper proposes a convenient and novel peridynamics approach to describe gas flow behavior in fracture regions and transition regions between fractured and intact regions in porous media, where the bonds naturally describe the interactions between material points in damaged areas. For implementation, we interpolate the permeability of the bonds in the transition region by using local damage values, and adopt a meshfree discretization approach that does not require additional mesh refinement for damaged or fractured regions. Numerical examples are provided and compared with the traditional finite element method to verify the accuracy and effectiveness of the proposed method.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142532520","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}
引用次数: 0
Well-posedness of the Cauchy problem for the fourth-order nonlinear Schrödinger equation 四阶非线性薛定谔方程的考奇问题的良好提出性
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2024-10-18 DOI: 10.1016/j.aml.2024.109340
{"title":"Well-posedness of the Cauchy problem for the fourth-order nonlinear Schrödinger equation","authors":"","doi":"10.1016/j.aml.2024.109340","DOIUrl":"10.1016/j.aml.2024.109340","url":null,"abstract":"<div><div>The sharp local well-posedness for the one dimensional fourth-order nonlinear Schrödinger equation is established in the Sobolev space <span><math><mrow><msup><mrow><mi>H</mi></mrow><mrow><mi>s</mi></mrow></msup><mrow><mo>(</mo><mi>R</mi><mo>)</mo></mrow></mrow></math></span> for <span><math><mrow><mi>s</mi><mo>≥</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></math></span>, which improves the results in Huo and Jia (2007). In addition, we prove that this equation cannot be solved by an iteration scheme based on the Duhamel formula in <span><math><mrow><msup><mrow><mi>H</mi></mrow><mrow><mi>s</mi></mrow></msup><mrow><mo>(</mo><mi>R</mi><mo>)</mo></mrow></mrow></math></span> for <span><math><mrow><mi>s</mi><mo>&lt;</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></math></span>. Our method relies upon the Bourgain space and a crucial bilinear estimate, which avoids the tedious classification of the location to the highest dispersion modulation.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142532519","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}
引用次数: 0
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