Pub Date : 2024-11-01DOI: 10.1016/j.aml.2024.109360
Jing Wang, Hongyong Zhao
This work examines the global dynamics of a two-strain malaria model proposed in a recent paper (Agusto, 2014). The global stability of the disease-free equilibrium when the basic reproduction number equals one, as well as the global stability of the resistant strain-only boundary equilibrium and coexistence equilibrium, have not been addressed in Agusto (2014). In fact, the model incorporates a factor that individuals infected with sensitive strain can transform into individuals infected with resistant strain, posing substantial challenges to global stability analysis. Notably, a key characteristic of this model is that the dynamics of humans and mosquitoes operate on different time scales. Consequently, we utilize the geometric singular perturbation theory to separate fast and slow dynamics, thereby obtaining global dynamics. Our results may offer deeper insights into the competitive exclusion and coexistence of two strains.
{"title":"Global dynamics of a multiscale malaria model with two strains","authors":"Jing Wang, Hongyong Zhao","doi":"10.1016/j.aml.2024.109360","DOIUrl":"10.1016/j.aml.2024.109360","url":null,"abstract":"<div><div>This work examines the global dynamics of a two-strain malaria model proposed in a recent paper (Agusto, 2014). The global stability of the disease-free equilibrium when the basic reproduction number equals one, as well as the global stability of the resistant strain-only boundary equilibrium and coexistence equilibrium, have not been addressed in Agusto (2014). In fact, the model incorporates a factor that individuals infected with sensitive strain can transform into individuals infected with resistant strain, posing substantial challenges to global stability analysis. Notably, a key characteristic of this model is that the dynamics of humans and mosquitoes operate on different time scales. Consequently, we utilize the geometric singular perturbation theory to separate fast and slow dynamics, thereby obtaining global dynamics. Our results may offer deeper insights into the competitive exclusion and coexistence of two strains.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"160 ","pages":"Article 109360"},"PeriodicalIF":2.9,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142586533","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 : 2024-11-01DOI: 10.1016/j.aml.2024.109358
Guiping Liu, Haiyan Yin
In this paper, the inflow problem for the thermally radiative magnetohydrodynamics in a half line is investigated by using an -energy method in the case that we consider the effects of high temperature radiation (pressure , internal energy ).
{"title":"Stability of stationary solutions for inflow problem on the thermally radiative magnetohydrodynamics","authors":"Guiping Liu, Haiyan Yin","doi":"10.1016/j.aml.2024.109358","DOIUrl":"10.1016/j.aml.2024.109358","url":null,"abstract":"<div><div>In this paper, the inflow problem for the thermally radiative magnetohydrodynamics in a half line is investigated by using an <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-energy method in the case that we consider the effects of high temperature radiation (pressure <span><math><mrow><mi>p</mi><mo>=</mo><mi>R</mi><mi>ρ</mi><mi>θ</mi><mo>+</mo><mfrac><mrow><mi>a</mi></mrow><mrow><mn>3</mn></mrow></mfrac><msup><mrow><mi>θ</mi></mrow><mrow><mn>4</mn></mrow></msup></mrow></math></span>, internal energy <span><math><mrow><mi>e</mi><mo>=</mo><msub><mrow><mi>C</mi></mrow><mrow><mi>v</mi></mrow></msub><mi>θ</mi><mo>+</mo><mfrac><mrow><mi>a</mi></mrow><mrow><mi>ρ</mi></mrow></mfrac><msup><mrow><mi>θ</mi></mrow><mrow><mn>4</mn></mrow></msup></mrow></math></span>).</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"160 ","pages":"Article 109358"},"PeriodicalIF":2.9,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142593029","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 : 2024-10-31DOI: 10.1016/j.aml.2024.109357
Wenlong Zeng , Qing-Wen Wang
The -eigenvalues of piezoelectric-type tensors are crucial for understanding both the piezoelectric and converse piezoelectric effects. He et al. (2021) introduced an -type inclusion set to locate all -eigenvalues of such tensors. However, a straightforward counterexample demonstrates that this method can occasionally be inaccurate. In this paper, we propose an improved -type localization sets for the -eigenvalues of piezoelectric-type tensors. Additionally, we demonstrate that the proposed eigenvalue localization sets improve upon a recent result. Finally, numerical experiments are conducted to validate the effectiveness of our main results.
压电型张量的 C 特征值对于理解压电效应和反压电效应至关重要。He 等人（2021 年）引入了一种 S 型包含集来定位此类张量的所有 C 特征值。然而，一个直接的反例表明，这种方法偶尔会不准确。在本文中，我们为压电型张量的 C 特征值提出了一种改进的 S 型定位集。此外，我们还证明了所提出的特征值定位集改进了最近的一个结果。最后，我们通过数值实验验证了主要结果的有效性。
{"title":"Improvement of S-type localization sets of C-eigenvalues for piezoelectric-type tensors","authors":"Wenlong Zeng , Qing-Wen Wang","doi":"10.1016/j.aml.2024.109357","DOIUrl":"10.1016/j.aml.2024.109357","url":null,"abstract":"<div><div>The <span><math><mi>C</mi></math></span>-eigenvalues of piezoelectric-type tensors are crucial for understanding both the piezoelectric and converse piezoelectric effects. He et al. (2021) introduced an <span><math><mi>S</mi></math></span>-type inclusion set to locate all <span><math><mi>C</mi></math></span>-eigenvalues of such tensors. However, a straightforward counterexample demonstrates that this method can occasionally be inaccurate. In this paper, we propose an improved <span><math><mi>S</mi></math></span>-type localization sets for the <span><math><mi>C</mi></math></span>-eigenvalues of piezoelectric-type tensors. Additionally, we demonstrate that the proposed eigenvalue localization sets improve upon a recent result. Finally, numerical experiments are conducted to validate the effectiveness of our main results.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"160 ","pages":"Article 109357"},"PeriodicalIF":2.9,"publicationDate":"2024-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142586534","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 : 2024-10-31DOI: 10.1016/j.aml.2024.109356
Liangwei Wang , Fengying Wei , Zhen Jin , Xuerong Mao
We propose a stochastic HCV model with protection awareness and exposed-acute-chronic phases in this study. First of all, we show that the stochastic HCV model admits a unique global positive solution for any given positive initial values. Then, we verify that HCV model has a unique stationary distribution under the sufficient criterion , which indicates that HCV transmission undergoes the persistence in the long term. Furthermore, we derive the sufficient conditions for HCV extinction under the condition . As a consequence, we derive the relationships among the stochastic persistence index , the stochastic extinction index and the threshold (the basic reproduction number ) of the model without fluctuations. The condition reveals that the existence of the white noises triggers the less stochastic persistence index. While, the condition reveals that, when the intensities of the white noises are enhanced, the value triggers the stochastic extinction.
{"title":"Stationary distribution and extinction of an HCV transmission model with protection awareness and environmental fluctuations","authors":"Liangwei Wang , Fengying Wei , Zhen Jin , Xuerong Mao","doi":"10.1016/j.aml.2024.109356","DOIUrl":"10.1016/j.aml.2024.109356","url":null,"abstract":"<div><div>We propose a stochastic HCV model with protection awareness and exposed-acute-chronic phases in this study. First of all, we show that the stochastic HCV model admits a unique global positive solution for any given positive initial values. Then, we verify that HCV model has a unique stationary distribution under the sufficient criterion <span><math><mrow><msubsup><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow><mrow><mi>s</mi></mrow></msubsup><mo>></mo><mn>1</mn></mrow></math></span>, which indicates that HCV transmission undergoes the persistence in the long term. Furthermore, we derive the sufficient conditions for HCV extinction under the condition <span><math><mrow><msubsup><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow><mrow><mi>e</mi></mrow></msubsup><mo><</mo><mn>1</mn></mrow></math></span>. As a consequence, we derive the relationships among the stochastic persistence index <span><math><msubsup><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow><mrow><mi>s</mi></mrow></msubsup></math></span>, the stochastic extinction index <span><math><msubsup><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow><mrow><mi>e</mi></mrow></msubsup></math></span> and the threshold (the basic reproduction number <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>) of the model without fluctuations. The condition <span><math><mrow><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>></mo><msubsup><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow><mrow><mi>s</mi></mrow></msubsup><mo>></mo><mn>1</mn></mrow></math></span> reveals that the existence of the white noises triggers the less stochastic persistence index. While, the condition <span><math><mrow><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub><mo><</mo><msubsup><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow><mrow><mi>e</mi></mrow></msubsup><mo><</mo><mn>1</mn></mrow></math></span> reveals that, when the intensities of the white noises are enhanced, the value <span><math><msubsup><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow><mrow><mi>e</mi></mrow></msubsup></math></span> triggers the stochastic extinction.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"160 ","pages":"Article 109356"},"PeriodicalIF":2.9,"publicationDate":"2024-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142586537","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 : 2024-10-30DOI: 10.1016/j.aml.2024.109355
Kai Chen, Yuanchao Si
This paper explores the Ulam type stability of second-order linear Hahn difference equations, beginning with the analysis of general solution for linear homogeneous cases, as well as the Ulam type stability of non-homogeneous equations. Additionally, an example is given to demonstrate the theoretical results.
{"title":"Ulam type stability for the second-order linear Hahn difference equations","authors":"Kai Chen, Yuanchao Si","doi":"10.1016/j.aml.2024.109355","DOIUrl":"10.1016/j.aml.2024.109355","url":null,"abstract":"<div><div>This paper explores the Ulam type stability of second-order linear Hahn difference equations, beginning with the analysis of general solution for linear homogeneous cases, as well as the Ulam type stability of non-homogeneous equations. Additionally, an example is given to demonstrate the theoretical results.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"160 ","pages":"Article 109355"},"PeriodicalIF":2.9,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142593030","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 : 2024-10-30DOI: 10.1016/j.aml.2024.109354
Zhengguang Guo , Chol-Jun O
In this article, we prove an extension criterion for a local strong solution to the 3D Navier–Stokes equations that only require control of the positive part of middle eigenvalue of strain tensor in the critical endpoint Besov space, i.e., . This gives a positive answer to the problem proposed by Miller [1] and improves the results by Wu [2], [3], [4]. The proof relies on the identity for enstrophy growth and -norm estimate of the gradient of .
{"title":"Extension criterion involving the middle eigenvalue of the strain tensor on local strong solutions to the 3D Navier–Stokes equations","authors":"Zhengguang Guo , Chol-Jun O","doi":"10.1016/j.aml.2024.109354","DOIUrl":"10.1016/j.aml.2024.109354","url":null,"abstract":"<div><div>In this article, we prove an extension criterion for a local strong solution to the 3D Navier–Stokes equations that only require control of the positive part of middle eigenvalue of strain tensor in the critical endpoint Besov space, i.e., <span><math><mrow><msubsup><mrow><mi>λ</mi></mrow><mrow><mn>2</mn></mrow><mrow><mo>+</mo></mrow></msubsup><mo>∈</mo><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>;</mo><msubsup><mrow><mover><mrow><mi>B</mi></mrow><mrow><mo>̇</mo></mrow></mover></mrow><mrow><mi>∞</mi><mo>,</mo><mi>∞</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msubsup><mo>)</mo></mrow></mrow></math></span>. This gives a positive answer to the problem proposed by Miller <span><span>[1]</span></span> and improves the results by Wu <span><span>[2]</span></span>, <span><span>[3]</span></span>, <span><span>[4]</span></span>. The proof relies on the identity for enstrophy growth and <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span>-norm estimate of the gradient of <span><math><msubsup><mrow><mi>λ</mi></mrow><mrow><mn>2</mn></mrow><mrow><mo>+</mo></mrow></msubsup></math></span>.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"160 ","pages":"Article 109354"},"PeriodicalIF":2.9,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142577807","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 : 2024-10-28DOI: 10.1016/j.aml.2024.109348
Yu-Qiang Yuan , Xiang Luo , Zhong Du
Investigated in this paper is the resonant soliton interactions for the ()-dimensional Date–Jimbo–Kashiwara–Miwa equation. A comprehensive classification of these interactions is presented, based on the exact expression of resonant soliton branches derived from asymptotic analysis. Two types of resonant interactions between two solitons are identified, characterized by the parameter , which directly determines the phase shift. One-resonant and two-resonant three-soliton interactions are discussed, in which certain new soliton branches are revealed. Some graphical analyses are provided to illustrate these resonant interactions.
{"title":"Resonant soliton interaction for the Date–Jimbo–Kashiwara–Miwa equation","authors":"Yu-Qiang Yuan , Xiang Luo , Zhong Du","doi":"10.1016/j.aml.2024.109348","DOIUrl":"10.1016/j.aml.2024.109348","url":null,"abstract":"<div><div>Investigated in this paper is the resonant soliton interactions for the (<span><math><mrow><mn>2</mn><mo>+</mo><mn>1</mn></mrow></math></span>)-dimensional Date–Jimbo–Kashiwara–Miwa equation. A comprehensive classification of these interactions is presented, based on the exact expression of resonant soliton branches derived from asymptotic analysis. Two types of resonant interactions between two solitons are identified, characterized by the parameter <span><math><msub><mrow><mi>A</mi></mrow><mrow><mi>i</mi><mi>j</mi></mrow></msub></math></span>, which directly determines the phase shift. One-resonant and two-resonant three-soliton interactions are discussed, in which certain new soliton branches are revealed. Some graphical analyses are provided to illustrate these resonant interactions.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"160 ","pages":"Article 109348"},"PeriodicalIF":2.9,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142553253","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 : 2024-10-28DOI: 10.1016/j.aml.2024.109352
Hejin Wang, Xiaoqun Wang
Importance Sampling (IS), a variance reduction technique of significant efficacy in Monte Carlo (MC) simulation, is frequently utilized for Bayesian inference and other statistical challenges. Quasi-Monte Carlo (QMC) replaces the random samples in MC with low discrepancy points and has the potential to substantially enhance error rates. In this paper, we integrate IS with a randomly shifted rank-1 lattice rule, a widely used QMC method. Within the framework of Reproducing Kernel Hilbert spaces (RKHS), we establish the convergence rate of the lattice rule for a class of exponential growth unbounded integrands. Besides, we give the convergence order of IS combined with QMC on this class, which provides a reference for us to choose the importance density later.
重要度采样（IS）是蒙特卡罗（MC）模拟中一种显著降低方差的技术，经常用于贝叶斯推理和其他统计挑战。准蒙特卡罗（QMC）用低差异点取代了蒙特卡罗模拟中的随机样本，有可能大幅提高误差率。在本文中，我们将 IS 与随机移动的秩-1 网格规则（一种广泛使用的 QMC 方法）相结合。在重现核希尔伯特空间（RKHS）框架内，我们建立了一类指数增长无约束积分的网格规则收敛率。此外，我们还给出了 IS 结合 QMC 对该类积分的收敛阶数，这为我们以后选择重要度密度提供了参考。
{"title":"On the convergence rate of Quasi Monte Carlo method with importance sampling for unbounded functions in RKHS","authors":"Hejin Wang, Xiaoqun Wang","doi":"10.1016/j.aml.2024.109352","DOIUrl":"10.1016/j.aml.2024.109352","url":null,"abstract":"<div><div>Importance Sampling (IS), a variance reduction technique of significant efficacy in Monte Carlo (MC) simulation, is frequently utilized for Bayesian inference and other statistical challenges. Quasi-Monte Carlo (QMC) replaces the random samples in MC with low discrepancy points and has the potential to substantially enhance error rates. In this paper, we integrate IS with a randomly shifted rank-1 lattice rule, a widely used QMC method. Within the framework of Reproducing Kernel Hilbert spaces (RKHS), we establish the convergence rate of the lattice rule for a class of exponential growth unbounded integrands. Besides, we give the convergence order of IS combined with QMC on this class, which provides a reference for us to choose the importance density later.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"160 ","pages":"Article 109352"},"PeriodicalIF":2.9,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142572383","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 : 2024-10-28DOI: 10.1016/j.aml.2024.109350
Anmin Mao, Changchang Yan, Xiaoxu Zhang
We consider the following mass-constrained elliptic problem with and is fractional Laplacian. We get a sharp description of the existence and non-existence of the global minimizer on the mass constraint, which is called energy ground state. More specifically, we show that there exists a constant such that there exists an energy ground state if and there exists no energy ground state if . Our results extends some related works.
{"title":"Sharp existence results on fractional elliptic equation","authors":"Anmin Mao, Changchang Yan, Xiaoxu Zhang","doi":"10.1016/j.aml.2024.109350","DOIUrl":"10.1016/j.aml.2024.109350","url":null,"abstract":"<div><div>We consider the following mass-constrained elliptic problem <span><span><span><math><mfenced><mrow><mtable><mtr><mtd><msup><mrow><mrow><mo>(</mo><mo>−</mo><mi>Δ</mi><mo>)</mo></mrow></mrow><mrow><mi>s</mi></mrow></msup><mi>u</mi><mo>+</mo><mi>V</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mi>u</mi><mo>+</mo><mi>λ</mi><mi>u</mi><mo>=</mo><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>u</mi><mo>)</mo></mrow><mspace></mspace><mi>i</mi><mi>n</mi><mspace></mspace><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup><mo>,</mo><mspace></mspace></mtd></mtr><mtr><mtd><msub><mrow><mo>∫</mo></mrow><mrow><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></mrow></msub><msup><mrow><mrow><mo>|</mo><mi>u</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>|</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup><mi>d</mi><mi>x</mi><mo>=</mo><mi>c</mi><mo>,</mo><mspace></mspace></mtd></mtr></mtable></mrow></mfenced></math></span></span></span>with <span><math><mrow><mn>0</mn><mo><</mo><mi>s</mi><mo><</mo><mn>1</mn></mrow></math></span> and <span><math><msup><mrow><mrow><mo>(</mo><mo>−</mo><mi>Δ</mi><mo>)</mo></mrow></mrow><mrow><mi>s</mi></mrow></msup></math></span> is fractional Laplacian. We get a sharp description of the existence and non-existence of the global minimizer on the mass constraint, which is called energy ground state. More specifically, we show that there exists a constant <span><math><msub><mrow><mi>c</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> such that there exists an energy ground state if <span><math><mrow><mi>c</mi><mo>></mo><msub><mrow><mi>c</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow></math></span> and there exists no energy ground state if <span><math><mrow><mn>0</mn><mo><</mo><mi>c</mi><mo><</mo><msub><mrow><mi>c</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow></math></span>. Our results extends some related works.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"160 ","pages":"Article 109350"},"PeriodicalIF":2.9,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142553182","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 : 2024-10-28DOI: 10.1016/j.aml.2024.109353
Chunlong Sun , Wenlong Zhang
In this work, we investigate the Tikhonov-type regularized solutions and their finite element solutions to the time-domain fluorescence diffuse optical tomography. Firstly, we analyze the finite element method for solving the direct problem and give its error estimates. With the classical source condition, we further establish the convergence estimates of the regularized solutions and their finite element solutions. The error estimates present explicit dependence on the critical parameters like noise level, regularization parameter, mesh size and time step size.
{"title":"Convergence estimates of the Tikhonov-type regularized solutions for the time-domain fluorescence diffuse optical tomography","authors":"Chunlong Sun , Wenlong Zhang","doi":"10.1016/j.aml.2024.109353","DOIUrl":"10.1016/j.aml.2024.109353","url":null,"abstract":"<div><div>In this work, we investigate the Tikhonov-type regularized solutions and their finite element solutions to the time-domain fluorescence diffuse optical tomography. Firstly, we analyze the finite element method for solving the direct problem and give its error estimates. With the classical source condition, we further establish the convergence estimates of the regularized solutions and their finite element solutions. The error estimates present explicit dependence on the critical parameters like noise level, regularization parameter, mesh size and time step size.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"160 ","pages":"Article 109353"},"PeriodicalIF":2.9,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142572384","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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