Pub Date : 2025-02-07DOI: 10.1016/j.aml.2025.109496
Dinh Nguyen Duy Hai
Inverse source problems frequently occur in real-world applications, such as pinpointing the location of contaminant sources in areas that are difficult to access. In this paper, we consider an inverse source problem of identifying an unknown source term in an abstract fractional diffusion-wave equation with inexact order. Due to the ill-posed nature of the problem, we propose a truncation method to achieve a stable solution. Under a Hölder-type source condition, we establish an asymptotically optimal convergence estimate by utilizing measurements of both the derivative order and the final time.
{"title":"The inverse source problem for a fractional diffusion-wave equation with inexact order: An asymptotically optimal strategy","authors":"Dinh Nguyen Duy Hai","doi":"10.1016/j.aml.2025.109496","DOIUrl":"10.1016/j.aml.2025.109496","url":null,"abstract":"<div><div>Inverse source problems frequently occur in real-world applications, such as pinpointing the location of contaminant sources in areas that are difficult to access. In this paper, we consider an inverse source problem of identifying an unknown source term in an abstract fractional diffusion-wave equation with inexact order. Due to the ill-posed nature of the problem, we propose a truncation method to achieve a stable solution. Under a Hölder-type source condition, we establish an asymptotically optimal convergence estimate by utilizing measurements of both the derivative order and the final time.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"164 ","pages":"Article 109496"},"PeriodicalIF":2.9,"publicationDate":"2025-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143373111","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 : 2025-02-07DOI: 10.1016/j.aml.2025.109497
Chengzhuo Zhao, Wenjie Tang, Kangshuai Du, Na Liu
In this work, Hamiltonian variational principle is employed to prove that Schrödinger–Maxwell (SM) equations under Lorenz gauge exhibit a symplectic structure. Based on this, symplectic mixed spectral element time domain method () for SM equations under Lorenz gauge is proposed. This method is a structure-preserving geometric algorithm that achieves high accuracy, particularly in long-term simulation. Simultaneously, to address the incompatibility issue between the divergence operator acting on the magnetic vector potential and the edge spectral element method (SEM), an auxiliary variable is introduced. This adjustment allows SM equations under Lorenz gauge to be effectively discretized using mixed SEM (MSEM). Finally, the effectiveness of S-MSETD is validated through numerical simulations.
{"title":"Symplectic mixed spectral element time domain method for 3-D Schrödinger–Maxwell equations under Lorenz gauge","authors":"Chengzhuo Zhao, Wenjie Tang, Kangshuai Du, Na Liu","doi":"10.1016/j.aml.2025.109497","DOIUrl":"10.1016/j.aml.2025.109497","url":null,"abstract":"<div><div>In this work, Hamiltonian variational principle is employed to prove that Schrödinger–Maxwell (SM) equations under Lorenz gauge exhibit a symplectic structure. Based on this, symplectic mixed spectral element time domain method (<span><math><mtext>S-MSETD</mtext></math></span>) for SM equations under Lorenz gauge is proposed. This method is a structure-preserving geometric algorithm that achieves high accuracy, particularly in long-term simulation. Simultaneously, to address the incompatibility issue between the divergence operator acting on the magnetic vector potential <span><math><mi>A</mi></math></span> and the edge spectral element method (SEM), an auxiliary variable <span><math><mrow><mi>p</mi><mo>=</mo><mo>∇</mo><mi>⋅</mi><mi>A</mi></mrow></math></span> is introduced. This adjustment allows SM equations under Lorenz gauge to be effectively discretized using mixed SEM (MSEM). Finally, the effectiveness of S-MSETD is validated through numerical simulations.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"164 ","pages":"Article 109497"},"PeriodicalIF":2.9,"publicationDate":"2025-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143387067","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 : 2025-02-06DOI: 10.1016/j.aml.2025.109484
Minxin Jia, Xianguo Geng
A hierarchy of lattice equations, including a coupled five-point lattice equation, is proposed. By employing the zero-curvature equation, Lax pairs for this hierarchy are derived from a 4 × 4 linear matrix spectral problem. Subsequently, the Hamiltonian structure of the hierarchy is established using the trace identity. Furthermore, infinitely many conservation laws for the coupled five-point lattice equation are presented.
{"title":"Coupled five-point lattices: Lax pairs and Hamiltonian structures","authors":"Minxin Jia, Xianguo Geng","doi":"10.1016/j.aml.2025.109484","DOIUrl":"10.1016/j.aml.2025.109484","url":null,"abstract":"<div><div>A hierarchy of lattice equations, including a coupled five-point lattice equation, is proposed. By employing the zero-curvature equation, Lax pairs for this hierarchy are derived from a 4 × 4 linear matrix spectral problem. Subsequently, the Hamiltonian structure of the hierarchy is established using the trace identity. Furthermore, infinitely many conservation laws for the coupled five-point lattice equation are presented.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"164 ","pages":"Article 109484"},"PeriodicalIF":2.9,"publicationDate":"2025-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143348998","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 : 2025-02-05DOI: 10.1016/j.aml.2025.109480
Wing Pok Lee , Jonathan D. Woo , Luke F. Triplett , Yifan Gu , Sarah C. Burnett , Lingyun Ding , Andrea L. Bertozzi
The dynamics of viscous thin-film particle-laden flows down inclined surfaces are commonly modeled with one of two approaches: a diffusive flux model or a suspension balance model. The diffusive flux model assumes that the particles migrate via a diffusive flux induced by gradients in both the particle concentration and the effective suspension viscosity. The suspension balance model introduces non-Newtonian bulk stress with shear-induced normal stresses, the gradients of which cause particle migration. Both models have appeared in the literature of particle-laden flow with virtually no comparison between the two models. For particle-laden viscous flow on an incline, in a thin-film geometry, one can use lubrication theory to derive a compact dynamic model in the form of a 2 × 2 system of conservation laws. We can then directly compare the two theories side by side by looking at similarities and differences in the flux functions for the conservation laws, and in exact and numerical simulations of the equations. We compare the flux profiles over a range of parameters, showing fairly good agreement between the models, with the biggest difference involving the behavior at the free surface. We also consider less dense suspensions at lower inclination angles where the dynamics involve two shock waves that can be clearly measured in experiments. In this context the solutions differ by no more than about 10%, suggesting that either model could be used for this configuration.
{"title":"A comparative study of dynamic models for gravity-driven particle-laden flows","authors":"Wing Pok Lee , Jonathan D. Woo , Luke F. Triplett , Yifan Gu , Sarah C. Burnett , Lingyun Ding , Andrea L. Bertozzi","doi":"10.1016/j.aml.2025.109480","DOIUrl":"10.1016/j.aml.2025.109480","url":null,"abstract":"<div><div>The dynamics of viscous thin-film particle-laden flows down inclined surfaces are commonly modeled with one of two approaches: a diffusive flux model or a suspension balance model. The diffusive flux model assumes that the particles migrate via a diffusive flux induced by gradients in both the particle concentration and the effective suspension viscosity. The suspension balance model introduces non-Newtonian bulk stress with shear-induced normal stresses, the gradients of which cause particle migration. Both models have appeared in the literature of particle-laden flow with virtually no comparison between the two models. For particle-laden viscous flow on an incline, in a thin-film geometry, one can use lubrication theory to derive a compact dynamic model in the form of a 2 × 2 system of conservation laws. We can then directly compare the two theories side by side by looking at similarities and differences in the flux functions for the conservation laws, and in exact and numerical simulations of the equations. We compare the flux profiles over a range of parameters, showing fairly good agreement between the models, with the biggest difference involving the behavior at the free surface. We also consider less dense suspensions at lower inclination angles where the dynamics involve two shock waves that can be clearly measured in experiments. In this context the solutions differ by no more than about 10%, suggesting that either model could be used for this configuration.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"164 ","pages":"Article 109480"},"PeriodicalIF":2.9,"publicationDate":"2025-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143377632","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 : 2025-02-03DOI: 10.1016/j.aml.2025.109482
Yanglei Li, Ningkui Sun
This paper is devoted to the study of the combined effects of impulsive harvesting and small advection on the dynamical behavior of solutions to a free boundary model. By introducing a one-parameter family of initial data with and being a compactly supported function, under some suitable assumptions, we obtain a threshold value such that spreading happens when , vanishing happens when .
{"title":"A free boundary problem with impulsive harvesting in small advection environment","authors":"Yanglei Li, Ningkui Sun","doi":"10.1016/j.aml.2025.109482","DOIUrl":"10.1016/j.aml.2025.109482","url":null,"abstract":"<div><div>This paper is devoted to the study of the combined effects of impulsive harvesting and small advection on the dynamical behavior of solutions to a free boundary model. By introducing a one-parameter family of initial data <span><math><mrow><mi>σ</mi><mi>ϕ</mi></mrow></math></span> with <span><math><mrow><mi>σ</mi><mo>≥</mo><mn>0</mn></mrow></math></span> and <span><math><mi>ϕ</mi></math></span> being a compactly supported function, under some suitable assumptions, we obtain a threshold value <span><math><msup><mrow><mi>σ</mi></mrow><mrow><mo>∗</mo></mrow></msup></math></span> such that spreading happens when <span><math><mrow><mi>σ</mi><mo>></mo><msup><mrow><mi>σ</mi></mrow><mrow><mo>∗</mo></mrow></msup></mrow></math></span>, vanishing happens when <span><math><mrow><mi>σ</mi><mo>≤</mo><msup><mrow><mi>σ</mi></mrow><mrow><mo>∗</mo></mrow></msup></mrow></math></span>.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"164 ","pages":"Article 109482"},"PeriodicalIF":2.9,"publicationDate":"2025-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143176918","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 : 2025-02-03DOI: 10.1016/j.aml.2025.109483
Meiyun Dai , Jinxia Liu , Yinghui Zhang
We give a new blowup criterion for the strong solution of Cauchy problem for three-dimensional micropolar fluid equations with vacuum. It shows that the strong or smooth solution exists globally if the -norm of the density is bounded, where is a positive constant. Particularly, we succeed in removing the technical condition in Hou and Xu (2024).
{"title":"A blowup criterion for the three-dimensional compressible viscous micropolar fluids","authors":"Meiyun Dai , Jinxia Liu , Yinghui Zhang","doi":"10.1016/j.aml.2025.109483","DOIUrl":"10.1016/j.aml.2025.109483","url":null,"abstract":"<div><div>We give a new blowup criterion for the strong solution of Cauchy problem for three-dimensional micropolar fluid equations with vacuum. It shows that the strong or smooth solution exists globally if the <span><math><mrow><msup><mrow><mi>L</mi></mrow><mrow><mi>∞</mi></mrow></msup><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>:</mo><msup><mrow><mi>L</mi></mrow><mrow><mi>q</mi></mrow></msup><mo>)</mo></mrow></mrow></math></span>-norm of the density is bounded, where <span><math><mi>q</mi></math></span> is a positive constant. Particularly, we succeed in removing the technical condition <span><math><mrow><msub><mrow><mi>ρ</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>∈</mo><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup></mrow></math></span> in Hou and Xu (2024).</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"164 ","pages":"Article 109483"},"PeriodicalIF":2.9,"publicationDate":"2025-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143348997","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 : 2025-02-01DOI: 10.1016/j.aml.2025.109481
X.L. Li , F.Z. Geng , Y.Q. Gao
Taking advantage of the reproducing kernel theory, several effective numerical algorithms have been developed to solve boundary value problems (BVPs) with the exact right side functions. However, these methods have difficulty in solving effectively linear boundary value problems when the right side of the equation has contaminated data. The objective of this letter is to introduce a robust numerical algorithm for linear BVPs with noisy right-hand side functions information. To overcome the challenges of the noisy right-hand side functions, the idea of regularization is used. Numerical simulation is employed to illustrate the superiority of the present method.
{"title":"A kernel function based regularized method for boundary value problems with noisy information","authors":"X.L. Li , F.Z. Geng , Y.Q. Gao","doi":"10.1016/j.aml.2025.109481","DOIUrl":"10.1016/j.aml.2025.109481","url":null,"abstract":"<div><div>Taking advantage of the reproducing kernel theory, several effective numerical algorithms have been developed to solve boundary value problems (BVPs) with the exact right side functions. However, these methods have difficulty in solving effectively linear boundary value problems when the right side of the equation has contaminated data. The objective of this letter is to introduce a robust numerical algorithm for linear BVPs with noisy right-hand side functions information. To overcome the challenges of the noisy right-hand side functions, the idea of regularization is used. Numerical simulation is employed to illustrate the superiority of the present method.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"164 ","pages":"Article 109481"},"PeriodicalIF":2.9,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143176883","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 : 2025-01-30DOI: 10.1016/j.aml.2025.109479
Tingting Luo , Jiayu Liu , Cairong Chen , Qun Wang
In Noor et al. (2011), the second-order Taylor expansion of the objective function is incorrectly used in constructing the descent direction. Thus, the proposed block coordinate descent method is non-monotone and a strict convergence analysis is lack. This motivates us to propose a monotone block coordinate descent method for solving absolute value equations. Under appropriate conditions, we analyze the global convergence of the algorithm and conduct numerical experiments to demonstrate its feasibility and effectiveness.
{"title":"A monotone block coordinate descent method for solving absolute value equations","authors":"Tingting Luo , Jiayu Liu , Cairong Chen , Qun Wang","doi":"10.1016/j.aml.2025.109479","DOIUrl":"10.1016/j.aml.2025.109479","url":null,"abstract":"<div><div>In Noor et al. (2011), the second-order Taylor expansion of the objective function is incorrectly used in constructing the descent direction. Thus, the proposed block coordinate descent method is non-monotone and a strict convergence analysis is lack. This motivates us to propose a monotone block coordinate descent method for solving absolute value equations. Under appropriate conditions, we analyze the global convergence of the algorithm and conduct numerical experiments to demonstrate its feasibility and effectiveness.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"164 ","pages":"Article 109479"},"PeriodicalIF":2.9,"publicationDate":"2025-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143077688","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 : 2025-01-29DOI: 10.1016/j.aml.2025.109477
Liyun Zuo , Guangzhi Du
In this article, we propose and analyze the finite element method for the mixed Stokes–Darcy–Darcy system which involves free flow in conduits coupled with confined flow in fractured porous media. The interactions on the interfaces come from the classical Stokes–Darcy system and the famous bulk-fracture system. Rigorously theoretical results are derived and some numerical results are provided to verify the theoretical findings.
{"title":"Finite element method for the coupled Stokes–Darcy–Darcy system","authors":"Liyun Zuo , Guangzhi Du","doi":"10.1016/j.aml.2025.109477","DOIUrl":"10.1016/j.aml.2025.109477","url":null,"abstract":"<div><div>In this article, we propose and analyze the finite element method for the mixed Stokes–Darcy–Darcy system which involves free flow in conduits coupled with confined flow in fractured porous media. The interactions on the interfaces come from the classical Stokes–Darcy system and the famous bulk-fracture system. Rigorously theoretical results are derived and some numerical results are provided to verify the theoretical findings.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"164 ","pages":"Article 109477"},"PeriodicalIF":2.9,"publicationDate":"2025-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143077658","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 : 2025-01-29DOI: 10.1016/j.aml.2025.109478
Yaqin Huang , Xin Meng , Xia Wang , Libin Rong
In this paper, we investigate an HIV latent infection model that incorporates cell-to-cell transmission and multiple drug classes, extending the model proposed by Areej Alshorman et al. (2022). We derive the basic reproduction number for the model and establish the existence and local stability of its equilibria. By constructing appropriate Lyapunov functions, we analyze the global stability of these equilibria, with serving as the threshold parameter. Specifically, when , the infection-free equilibrium is globally asymptotically stable, whereas when , the infectious equilibrium is globally asymptotically stable.
{"title":"Analysis of an HIV latent infection model with cell-to-cell transmission and multiple drug classes","authors":"Yaqin Huang , Xin Meng , Xia Wang , Libin Rong","doi":"10.1016/j.aml.2025.109478","DOIUrl":"10.1016/j.aml.2025.109478","url":null,"abstract":"<div><div>In this paper, we investigate an HIV latent infection model that incorporates cell-to-cell transmission and multiple drug classes, extending the model proposed by Areej Alshorman et al. (2022). We derive the basic reproduction number <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> for the model and establish the existence and local stability of its equilibria. By constructing appropriate Lyapunov functions, we analyze the global stability of these equilibria, with <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> serving as the threshold parameter. Specifically, when <span><math><mrow><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub><mo><</mo><mn>1</mn></mrow></math></span>, the infection-free equilibrium is globally asymptotically stable, whereas when <span><math><mrow><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>></mo><mn>1</mn></mrow></math></span>, the infectious equilibrium is globally asymptotically stable.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"164 ","pages":"Article 109478"},"PeriodicalIF":2.9,"publicationDate":"2025-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143077689","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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