Pub Date : 2024-10-26DOI: 10.1016/j.aml.2024.109351
Oleg Imanuvilov , Kazufumi Ito , Masahiro Yamamoto
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.
我们通过空间区间一端点的初值和考奇数据，证明了确定一维时间分数扩散方程空间变化零阶系数的唯一性。
{"title":"Inverse coefficient problems for one-dimensional time-fractional diffusion equations","authors":"Oleg Imanuvilov , Kazufumi Ito , Masahiro Yamamoto","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":"160 ","pages":"Article 109351"},"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}
Pub Date : 2024-10-26DOI: 10.1016/j.aml.2024.109346
D. Barrera , S. Eddargani , M.J. Ibáñez , S. Remogna
In this paper we construct new univariate local 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.
{"title":"Local C2-smooth spline quasi-interpolation methods","authors":"D. Barrera , S. Eddargani , M.J. Ibáñez , S. Remogna","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":"160 ","pages":"Article 109346"},"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}
Pub Date : 2024-10-26DOI: 10.1016/j.aml.2024.109349
Yanqing Wang , Yixue Yang , Xue Mei
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 are just in Lions-Shinbrot class.
{"title":"Energy equality of the two-fluid incompressible Navier–Stokes–Maxwell equations","authors":"Yanqing Wang , Yixue Yang , Xue Mei","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":"160 ","pages":"Article 109349"},"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}
Pub Date : 2024-10-24DOI: 10.1016/j.aml.2024.109347
Mingzhan Huang, Shouzong Liu
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.
{"title":"Implementation strategy of insulin therapy under sparse state feedback","authors":"Mingzhan Huang, Shouzong Liu","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":"160 ","pages":"Article 109347"},"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}
Pub Date : 2024-10-24DOI: 10.1016/j.aml.2024.109345
Jiangwei Zhang, Ke Liu, Jianhua Huang
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.
{"title":"Uniform measure attractors for nonautonomous stochastic tamed 3D Navier–Stokes equations with almost periodic forcing","authors":"Jiangwei Zhang, Ke Liu, Jianhua Huang","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":"160 ","pages":"Article 109345"},"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}
Pub Date : 2024-10-24DOI: 10.1016/j.aml.2024.109344
Junsik Bae , Junho Choi , Bongsuk Kwon
We study 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 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.
{"title":"Singularity formation of hydromagnetic waves in cold plasma","authors":"Junsik Bae , Junho Choi , Bongsuk Kwon","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":"160 ","pages":"Article 109344"},"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}
Pub Date : 2024-10-23DOI: 10.1016/j.aml.2024.109343
Di-Kang Lv , Shao-Xia Qiao , Jia-Bing Wang
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.
{"title":"Forced waves of time-delayed nonlocal dispersal equations in shifting habitats","authors":"Di-Kang Lv , Shao-Xia Qiao , Jia-Bing Wang","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":"160 ","pages":"Article 109343"},"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}
Pub Date : 2024-10-22DOI: 10.1016/j.aml.2024.109342
Said El Manouni , Kanishka Perera
We consider a Brézis–Nirenberg type critical growth -Laplacian problem involving a parameter in a smooth bounded domain . We prove the existence of multiple nontrivial solutions if either or the volume of is sufficiently small. The proof is based on an abstract critical point theorem that only assumes a local condition. Our results are new even in the semilinear case .
{"title":"A bifurcation and multiplicity result for a critical growth elliptic problem","authors":"Said El Manouni , Kanishka Perera","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>></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":"160 ","pages":"Article 109342"},"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}
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.
{"title":"A peridynamics approach modeling gas flow in porous media with damaged regions","authors":"Xu Guo , Xiaolin Liao , Xiangcheng Zheng , Suifu Cheng","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":"160 ","pages":"Article 109341"},"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}
Pub Date : 2024-10-18DOI: 10.1016/j.aml.2024.109340
Mingjuan Chen , Nan Liu , Yaqing Wang
The sharp local well-posedness for the one dimensional fourth-order nonlinear Schrödinger equation is established in the Sobolev space for , 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 for . 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.
{"title":"Well-posedness of the Cauchy problem for the fourth-order nonlinear Schrödinger equation","authors":"Mingjuan Chen , Nan Liu , Yaqing Wang","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><</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":"160 ","pages":"Article 109340"},"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}
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