Mathematical Methods in the Applied Sciences最新文献

{"title":"Multiplicity and concentration of nontrivial solutions for Kirchhoff–Schrödinger–Poisson system with steep potential well","authors":"Liuyang Shao,&nbsp;Haibo Chen,&nbsp;Yingmin Wang","doi":"10.1002/mma.10422","DOIUrl":"https://doi.org/10.1002/mma.10422","url":null,"abstract":"<p>This article is about the following Kirchhoff–Schrödinger–Poisson system with steep potential well \u0000\u0000 </p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 2","pages":"2022-2038"},"PeriodicalIF":2.1,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142862006","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Stabilization of solutions of marine riser equations","authors":"S.Z. Ahmedov,&nbsp;V.K. Kalantarov,&nbsp;A.A. Namazov","doi":"10.1002/mma.10432","DOIUrl":"https://doi.org/10.1002/mma.10432","url":null,"abstract":"<p>We study the problem of stabilization to zero stationary state of nonlinear fourth-order wave equation with nonlinear damping term modelling dynamics of marine riser by feedback control terms that employ finitely many Fourier modes. Additionally, we demonstrate that the corresponding equation with linear damping, which represents the dynamics of pipes conveying fluids, can be exponentially stabilized by a feedback controller employing a finite number of Fourier modes.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 2","pages":"2224-2234"},"PeriodicalIF":2.1,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142862005","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The soliton solutions for the higher-order nonlinear Schrödinger equation with nonzero boundary conditions: Riemann–Hilbert method","authors":"Yuxia Wang,&nbsp;Lin Huang","doi":"10.1002/mma.10430","DOIUrl":"https://doi.org/10.1002/mma.10430","url":null,"abstract":"<p>This paper explores the Riemann–Hilbert method for deriving exact N-soliton solutions of the sixth-order nonlinear Schrödinger (6th-NLS) equation with nonzero boundary condition. The analytical process comprises three fundamental steps. First, transformations are used to simplify the nonzero boundaries. Next, the inverse scattering method establishes a crucial link between the solutions of the 6th-NLS equation and the corresponding Riemann–Hilbert problem. Finally, this Riemann–Hilbert problem is systematically solved. Additionally, selected parameter values in the solutions generate graphical representations, vividly illustrating the solutions to the 6th-NLS equation.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 2","pages":"2179-2193"},"PeriodicalIF":2.1,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142862004","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Existence of ground state solutions for a biharmonic Choquard equation with critical exponential growth in \u0000ℝ4","authors":"Wenjing Chen,&nbsp;Yumei Li,&nbsp;Zexi Wang","doi":"10.1002/mma.10428","DOIUrl":"https://doi.org/10.1002/mma.10428","url":null,"abstract":"<p>In this paper, we study the following singularly perturbed biharmonic Choquard equation: \u0000\u0000 </p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 2","pages":"2141-2163"},"PeriodicalIF":2.1,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142862007","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Utilizing the Caputo fractional derivative for the flux tube close to the neutral points","authors":"Hasan Durmaz,&nbsp;Hazal Ceyhan,&nbsp;Zehra Özdemir,&nbsp;Ameth Ndiaye","doi":"10.1002/mma.10410","DOIUrl":"https://doi.org/10.1002/mma.10410","url":null,"abstract":"<p>This study examines how fractional derivatives affect the theory of curves and related surfaces, an application area that is expanding daily. There has been limited research on the geometric interpretation of fractional calculus. The present study applied the Caputo fractional calculation method, which has the most suitable structure for geometric computations, to examine the effect of fractional calculus on differential geometry. The Caputo fractional derivative of a constant is zero, enabling the geometric solution and understanding of many fractional physical problems. We examined flux tubes, which are magnetic surfaces that incorporate these lines of magnetic fields as parameter curves. Examples are visualized using mathematical programs for various values of Caputo fractional analysis, employing theory-related examples. Fractional derivatives and integrals are widely utilized in various disciplines, including mathematics, physics, engineering, biology, and fluid dynamics, as they yield more numerical results than classical solutions. Also, many problems outside the scope of classical analysis methods can be solved using the Caputo fractional calculation approach. In this context, applying the Caputo fractional analytic calculation method in differential geometry yields physically and mathematically relevant findings, particularly in the theory of curves and surfaces.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 2","pages":"1792-1808"},"PeriodicalIF":2.1,"publicationDate":"2024-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mma.10410","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142862009","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Mathematical modeling of poliomyelitis virus with vaccination and post-paralytic syndrome dynamics using Caputo and ABC fractional derivatives","authors":"Elhoussine Azroul,&nbsp;Sara Bouda","doi":"10.1002/mma.10406","DOIUrl":"https://doi.org/10.1002/mma.10406","url":null,"abstract":"<p>In this study, using Caputo and ABC derivatives, we present a mathematical analysis of two fractional models for poliomyelitis, considering the presence of vaccination (V) and a post-paralytic class (A). The existence and uniqueness of solutions are proved. The basic reproduction number \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mi>R</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>$$ {mathcal{R}}_0 $$</annotation>\u0000 </semantics></math> is computed. Local and global stability of the disease-free stationary state, depending on the threshold \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mi>R</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>$$ {mathcal{R}}_0 $$</annotation>\u0000 </semantics></math>, is provided, along with conditions for the existence of an endemic stationary state. Moreover, we performed a sensitivity analysis to study the influence of all biological parameters on \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mi>R</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>$$ {mathcal{R}}_0 $$</annotation>\u0000 </semantics></math>. We concluded our study with numerical simulations to illustrate the models' dynamics and to compare the trajectories of Caputo and ABC solutions. We found that the Caputo and ABC operators are both convenient for the modelization of the poliomyelitis disease. However, the ABC operator not only refined the Caputo operator by removing singularity from the kernel expression but also brought out heredity and memory in the model's characteristics.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 2","pages":"1725-1749"},"PeriodicalIF":2.1,"publicationDate":"2024-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142862011","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Modeling the dynamics of user adoption and abandonment in online social networks","authors":"Noah Kimmel,&nbsp;Lingju Kong,&nbsp;Min Wang","doi":"10.1002/mma.10413","DOIUrl":"https://doi.org/10.1002/mma.10413","url":null,"abstract":"<p>We introduce a new compartmental model aimed at examining the dynamics of user adoption and abandonment within online social networks. Our model encompasses two abandonment dynamics: infectious abandonment caused by internal influences from individuals who have already left the network and noninfectious abandonment triggered by mass media, advertisements, or the introduction of new products. We verify the model's validity and explore the existence and stability of its equilibria. To confirm our theoretical framework, we conduct extensive numerical simulations. We demonstrate the model's effectiveness by fitting it to historical data on Facebook's daily active users. Finally, we utilize the derived model parameters to forecast the future numbers of active users on Facebook.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 2","pages":"1853-1868"},"PeriodicalIF":2.1,"publicationDate":"2024-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142862010","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An improved Dai-Liao-style hybrid conjugate gradient-based method for solving unconstrained nonconvex optimization and extension to constrained nonlinear monotone equations","authors":"Zihang Yuan,&nbsp;Hu Shao,&nbsp;Xiaping Zeng,&nbsp;Pengjie Liu,&nbsp;Xianglin Rong,&nbsp;Jianhao Zhou","doi":"10.1002/mma.10396","DOIUrl":"https://doi.org/10.1002/mma.10396","url":null,"abstract":"<p>In this work, for unconstrained optimization, we introduce an improved Dai-Liao-style hybrid conjugate gradient method based on the hybridization-based self-adaptive technique, and the search direction generated fulfills the sufficient descent and trust region properties regardless of any line search. The global convergence is established under standard Wolfe line search and common assumptions. Then, combining the hyperplane projection technique and a new self-adaptive line search, we extend the proposed conjugate gradient method and obtain an improved Dai-Liao-style hybrid conjugate gradient projection method to solve constrained nonlinear monotone equations. Under mild conditions, we obtain its global convergence without Lipschitz continuity. In addition, the convergence rates for the two proposed methods are analyzed, respectively. Finally, numerical experiments are conducted to demonstrate the effectiveness of the proposed methods.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 2","pages":"1563-1588"},"PeriodicalIF":2.1,"publicationDate":"2024-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mma.10396","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142861733","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Finite-time extinction of a fractional rumor model","authors":"Xiaohuan Wang,&nbsp;Xinyao Wang,&nbsp;Wanli Yang","doi":"10.1002/mma.10414","DOIUrl":"https://doi.org/10.1002/mma.10414","url":null,"abstract":"<p>Rumors often exist in real life. If rumors are not controlled, they usually do not disappear for a limited time. Meanwhile, everyone has memories and time-fractional derivative can describe the memories. Thus, in this paper, a new time-fractional rumor model is introduced, and moreover, the finite time extinction of rumor is obtained under a distributed controller is added. What's more, both the ordinary differential equations model and partial differential equations model are studied. Numerical examples verify our results.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 2","pages":"1869-1876"},"PeriodicalIF":2.1,"publicationDate":"2024-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142861527","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Logarithmic convexity of non-symmetric time-fractional diffusion equations","authors":"Salah-Eddine Chorfi,&nbsp;Lahcen Maniar,&nbsp;Masahiro Yamamoto","doi":"10.1002/mma.10421","DOIUrl":"https://doi.org/10.1002/mma.10421","url":null,"abstract":"<p>We consider a class of diffusion equations with the Caputo time-fractional derivative \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msubsup>\u0000 <mrow>\u0000 <mi>∂</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>t</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>α</mi>\u0000 </mrow>\u0000 </msubsup>\u0000 <mi>u</mi>\u0000 <mo>=</mo>\u0000 <mi>L</mi>\u0000 <mi>u</mi>\u0000 </mrow>\u0000 <annotation>$$ {partial}_t&amp;amp;amp;#x0005E;{alpha }u&amp;amp;amp;#x0003D; Lu $$</annotation>\u0000 </semantics></math> subject to the homogeneous Dirichlet boundary conditions. Here, we consider a fractional order \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>0</mn>\u0000 <mo>&lt;</mo>\u0000 <mi>α</mi>\u0000 <mo>&lt;</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <annotation>$$ 0&amp;amp;lt;alpha &amp;amp;lt;1 $$</annotation>\u0000 </semantics></math> and a second-order operator \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>L</mi>\u0000 </mrow>\u0000 <annotation>$$ L $$</annotation>\u0000 </semantics></math> which is elliptic and non-symmetric. In this paper, we show that the logarithmic convexity extends to this non-symmetric case provided that the drift coefficient is given by a gradient vector field. Next, we perform some numerical experiments to validate the theoretical results in both symmetric and non-symmetric cases. Finally, some conclusions and open problems will be mentioned.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 2","pages":"2011-2021"},"PeriodicalIF":2.1,"publicationDate":"2024-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142861526","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}