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Blow up, Growth and Decay of Solutions for Class of a Coupled Nonlinear Viscoelastic Kirchhoff Equations with Variable Exponents and Fractional Boundary Conditions
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2025-04-02 DOI: 10.1007/s10255-024-1150-3
Abdelbaki Choucha, Salah Boulaaras, Djamel Ouchenane, Rashid Jan
{"title":"Blow up, Growth and Decay of Solutions for Class of a Coupled Nonlinear Viscoelastic Kirchhoff Equations with Variable Exponents and Fractional Boundary Conditions","authors":"Abdelbaki Choucha,&nbsp;Salah Boulaaras,&nbsp;Djamel Ouchenane,&nbsp;Rashid Jan","doi":"10.1007/s10255-024-1150-3","DOIUrl":"10.1007/s10255-024-1150-3","url":null,"abstract":"<div><p>We examine a quasilinear system of viscoelastic equations in this study that have fractional boundary conditions, dispersion, source, and variable-exponents. We discovered that the solution of the system is global and constrained under the right assumptions about the relaxation functions and initial conditions. After that, it is demonstrated that the blow-up has negative initial energy. Subsequently, the growth of solutions is demonstrated with positive initial energy, and the general decay result in the absence of the source term is achieved by using an integral inequality due to Komornik.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"41 2","pages":"344 - 374"},"PeriodicalIF":0.9,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143749128","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
The Impact of T-cell Exhaustion Dynamics on Tumour-Immune Interactions and Tumour Growth.
IF 2 4区 数学
Bulletin of Mathematical Biology Pub Date : 2025-04-02 DOI: 10.1007/s11538-025-01433-1
Nicholas Lai, Alexis Farman, Helen M Byrne
{"title":"The Impact of T-cell Exhaustion Dynamics on Tumour-Immune Interactions and Tumour Growth.","authors":"Nicholas Lai, Alexis Farman, Helen M Byrne","doi":"10.1007/s11538-025-01433-1","DOIUrl":"https://doi.org/10.1007/s11538-025-01433-1","url":null,"abstract":"<p><p>Tumours evade immune surveillance through a number of different immunosuppressive mechanisms. One such mechanism causes cytotoxic T-cells, a major driving force of the immune system, to differentiate to a state of 'exhaustion', rendering them less effective at killing tumour cells. We present a structured mathematical model that focuses on T-cell exhaustion and its effect on tumour growth. We compartmentalise cytotoxic T-cells into discrete subgroups based on their exhaustion level, which affects their ability to kill tumour cells. We show that the model reduces to a simpler system of ordinary differential equations (ODEs) that describes the time evolution of the total number of T-cells, their mean exhaustion level and the total number of tumour cells. Numerical simulations of the model equations reveal how the exhaustion distribution of T-cells changes over time and how it influences the tumour's growth dynamics. Complementary bifurcation analysis shows how altering key parameters significantly reduces the tumour burden, highlighting exhaustion as a promising target for immunotherapy. Finally, we derive a continuum approximation of the discrete ODE model, which admits analytical solutions that provide complementary insight into T-cell exhaustion dynamics and their effect on tumour growth.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 5","pages":"61"},"PeriodicalIF":2.0,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143762953","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Low-rank exponential integrators for stiff differential Riccati equations
IF 1.7 3区 数学
Advances in Computational Mathematics Pub Date : 2025-04-02 DOI: 10.1007/s10444-025-10228-w
Hao Chen, Alfio Borzì
{"title":"Low-rank exponential integrators for stiff differential Riccati equations","authors":"Hao Chen,&nbsp;Alfio Borzì","doi":"10.1007/s10444-025-10228-w","DOIUrl":"10.1007/s10444-025-10228-w","url":null,"abstract":"<div><p>Exponential integrators are an efficient alternative to implicit schemes for the time integration of stiff system of differential equations. In this paper, low-rank exponential integrators of orders one and two for stiff differential Riccati equations are proposed and investigated. The error estimates of the proposed schemes are established. The proposed approach allows to overcome the main difficulties that lay in the interplay of time integration and low-rank approximation in the numerical schemes, which is uncommon in standard discretization of differential equations. Results of numerical experiments demonstrate the validity of the convergence analysis and show the performance of the proposed low-rank approximations with different settings.</p></div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"51 2","pages":""},"PeriodicalIF":1.7,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143749225","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}
引用次数: 0
Inverse Scattering Transform and Multi-soliton Solutions for the Sextic Nonlinear Schrödinger Equation
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2025-04-02 DOI: 10.1007/s10255-025-0004-y
Xin Wu, Shou-fu Tian, Jin-Jie Yang
{"title":"Inverse Scattering Transform and Multi-soliton Solutions for the Sextic Nonlinear Schrödinger Equation","authors":"Xin Wu,&nbsp;Shou-fu Tian,&nbsp;Jin-Jie Yang","doi":"10.1007/s10255-025-0004-y","DOIUrl":"10.1007/s10255-025-0004-y","url":null,"abstract":"<div><p>In this work, we consider the inverse scattering transform and multi-soliton solutions of the sextic nonlinear Schrödinger equation. The Jost functions of spectral problem are derived directly, and the scattering data with <i>t</i> = 0 are obtained accordingly to analyze the symmetry and other related properties of the Jost functions. Then we make use of translation transformation to get the relation between potential and kernel, and recover potential according to Gel’fand-Levitan-Marchenko (GLM) integral equations. Furthermore, the time evolution of scattering data is considered, on the basis of that, the multi-soliton solutions are derived. In addition, some solutions of the equation are analyzed and revealed its dynamic behavior via graphical analysis, which could enrich the nonlinear phenomena of the sextic nonlinear Schrödinger equation.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"41 2","pages":"536 - 555"},"PeriodicalIF":0.9,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143749085","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Ramsey and Gallai-Ramsey Numbers of Cycles and Books
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2025-04-02 DOI: 10.1007/s10255-025-0009-6
Mei-qin Wei, Ya-ping Mao, Ingo Schiermeyer, Zhao Wang
{"title":"Ramsey and Gallai-Ramsey Numbers of Cycles and Books","authors":"Mei-qin Wei,&nbsp;Ya-ping Mao,&nbsp;Ingo Schiermeyer,&nbsp;Zhao Wang","doi":"10.1007/s10255-025-0009-6","DOIUrl":"10.1007/s10255-025-0009-6","url":null,"abstract":"<div><p>Given two non-empty graphs <i>G, H</i> and a positive integer <i>k</i>, the Gallai-Ramsey number gr<sub><i>k</i></sub>(<i>G</i>: <i>H</i>) is defined as the minimum integer <i>N</i> such that for all <i>n</i> ≥ <i>N</i>, every exact <i>k</i>-edge-coloring of <i>K</i><sub><i>n</i></sub> contains either a rainbow copy of <i>G</i> or a monochromatic copy of <i>H</i>. Denote gr<sub><i>k</i></sub>′(<i>G</i>: <i>H</i>) as the minimum integer <i>N</i> such that for all <i>n</i> ≥ <i>N</i>, every edge-coloring of <i>K</i><sub><i>n</i></sub> using at most <i>k</i> colors contains either a rainbow copy of <i>G</i> or a monochromatic copy of <i>H</i>. In this paper, we get some exact values or bounds for gr<sub><i>k</i></sub>(<i>P</i><sub>5</sub>: <i>H</i>) and gr<sub><i>k</i></sub>′(<i>P</i><sub>5</sub>: <i>H</i>), where <i>H</i> is a cycle or a book graph. In addition, our results support a conjecture of Li, Besse, Magnant, Wang and Watts in 2020.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"41 2","pages":"425 - 440"},"PeriodicalIF":0.9,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143749086","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Some New Results on Majority Coloring of Digraphs
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2025-04-02 DOI: 10.1007/s10255-025-0002-0
Jian-sheng Cai, Wei-hao Xia, Gui-ying Yan
{"title":"Some New Results on Majority Coloring of Digraphs","authors":"Jian-sheng Cai,&nbsp;Wei-hao Xia,&nbsp;Gui-ying Yan","doi":"10.1007/s10255-025-0002-0","DOIUrl":"10.1007/s10255-025-0002-0","url":null,"abstract":"<div><p>A majority coloring of a directed graph is a vertex-coloring in which every vertex has the same color as at most half of its out-neighbors. Kreutzer et al. conjectured that every digraph is majority 3-colorable. For an integer <i>k</i> ≥ 2, <span>({1 over {k}})</span>-majority coloring of a directed graph is a vertex-coloring in which every vertex <i>v</i> has the same color as at most <span>({1 over {k}}{d^{+}}(v))</span> of its out-neighbors. Girão et al. proved that every digraph admits a <span>({1 over {k}})</span>-majority 2<i>k</i>-coloring. In this paper, we prove that Kreutzer’s conjecture is true for digraphs under some conditions, which improves Kreutzer’s results, also we obtained some results of <span>({1 over {k}})</span>-majority coloring of digraphs. Moreover, we discuss the majority 3-coloring of random digraphs with some conditions.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"41 2","pages":"337 - 343"},"PeriodicalIF":0.9,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143749127","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
The Local Poincaré Inequality of Stochastic Dynamic and Application to the Ising Model
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2025-04-02 DOI: 10.1007/s10255-025-0001-1
Kai-yuan Cui, Fu-zhou Gong
{"title":"The Local Poincaré Inequality of Stochastic Dynamic and Application to the Ising Model","authors":"Kai-yuan Cui,&nbsp;Fu-zhou Gong","doi":"10.1007/s10255-025-0001-1","DOIUrl":"10.1007/s10255-025-0001-1","url":null,"abstract":"<div><p>Inspired by the idea of stochastic quantization proposed by Parisi and Wu, we reconstruct the transition probability function that has a central role in the renormalization group using a stochastic differential equation. From a probabilistic perspective, the renormalization procedure can be characterized by a discrete-time Markov chain. Therefore, we focus on this stochastic dynamic, and establish the local Poincaré inequality by calculating the Bakry-Émery curvature for two point functions. Finally, we choose an appropriate coupling relationship between parameters <i>K</i> and <i>T</i> to obtain the Poincaré inequality of two point functions for the limiting system. Our method extends the classic Bakry-Émery criterion, and the results provide a new perspective to characterize the renormalization procedure.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"41 2","pages":"305 - 336"},"PeriodicalIF":0.9,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143749198","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Existence of solutions for Volterra singular integral equations in the class of differentiable functions
IF 3.5 2区 数学
Applied Mathematics and Computation Pub Date : 2025-04-02 DOI: 10.1016/j.amc.2025.129448
Wenwen Zhang, Pingrun Li
{"title":"Existence of solutions for Volterra singular integral equations in the class of differentiable functions","authors":"Wenwen Zhang,&nbsp;Pingrun Li","doi":"10.1016/j.amc.2025.129448","DOIUrl":"10.1016/j.amc.2025.129448","url":null,"abstract":"<div><div>In this paper, our purpose is to obtain the general solutions of several kinds of Volterra singular integral equations (VSIEs) in the class of differentiable functions. By constructing some operators and using the properties of integral transforms and conformal mappings, we transform VSIEs in the class of differentiable functions into the Riemann-Hilbert problems with discontinuity on a circle. By means of the principle of analytic continuation and Sokhotski-Plemelj formula, we obtain solutions of Riemann-Hilbert problems in the case of non-normal type, and further discuss the asymptotic properties of the solutions at the nodes.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"500 ","pages":"Article 129448"},"PeriodicalIF":3.5,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143747463","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
On the Well-Posedness and Long Time Dynamics for a Coupled Nonlinear Bridge System with Past History
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2025-04-02 DOI: 10.1007/s00245-025-10252-8
Soh Edwin Mukiawa, Salim A. Messaoudi
{"title":"On the Well-Posedness and Long Time Dynamics for a Coupled Nonlinear Bridge System with Past History","authors":"Soh Edwin Mukiawa,&nbsp;Salim A. Messaoudi","doi":"10.1007/s00245-025-10252-8","DOIUrl":"10.1007/s00245-025-10252-8","url":null,"abstract":"<div><p>This work is concerned with a coupled nonlinear mathematical model for a suspension bridge with past history. The vibrations of both the road bed in the vertical plain and main cable from which the road bed is suspended by the tie cables are taken into consideration. Using the semi-group approach, we give a thorough and careful existence and uniqueness result. Also, we prove that the associated solution semi-group has a compact global attractor in an appropriate Hilbert space.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"91 3","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143761692","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
Issue Information-TOC
IF 2.6 2区 数学
Studies in Applied Mathematics Pub Date : 2025-04-02 DOI: 10.1111/sapm.70050
{"title":"Issue Information-TOC","authors":"","doi":"10.1111/sapm.70050","DOIUrl":"https://doi.org/10.1111/sapm.70050","url":null,"abstract":"","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 4","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.70050","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143749867","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
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