Nonlinear Analysis-Real World Applications最新文献_第4页

Vanishing viscosity limit for hyperbolic system of Temple class in 1-d with nonlinear viscosity 具有非线性黏度的一维Temple类双曲系统的消失黏度极限

IF 1.8 3区数学

Nonlinear Analysis-Real World Applications Pub Date : 2025-03-10 DOI: 10.1016/j.nonrwa.2025.104346

Boris Haspot , Animesh Jana

引用次数: 0

Analysis of a mathematical model for low-grade gliomas under chemotherapy as a dynamical system 化疗下低级别胶质瘤的动态系统数学模型分析

IF 1.8 3区数学

Nonlinear Analysis-Real World Applications Pub Date : 2025-03-10 DOI: 10.1016/j.nonrwa.2025.104344

Urszula Ledzewicz , Heinz Schättler

{"title":"Analysis of a mathematical model for low-grade gliomas under chemotherapy as a dynamical system","authors":"Urszula Ledzewicz , Heinz Schättler","doi":"10.1016/j.nonrwa.2025.104344","DOIUrl":"10.1016/j.nonrwa.2025.104344","url":null,"abstract":"<div><div>We analyze dynamical system properties of a 3-compartment mathematical model for the cell-cycle under chemotherapy with a phase non-specific drug. It is assumed that the drug damages both proliferating and quiescent cells, but possibly at different rates. While damage to proliferating cells is lethal, damaged quiescent cells may be repaired and can reenter the cell cycle. We prove that there exists a unique dosage <span><math><mover><mrow><mi>u</mi></mrow><mrow><mo>̃</mo></mrow></mover></math></span> (depending only on the parameters of the dynamics of the system) such that the tumor can be eradicated for <span><math><mrow><mi>u</mi><mo>≥</mo><mover><mrow><mi>u</mi></mrow><mrow><mo>̃</mo></mrow></mover></mrow></math></span> as all trajectories converge to the tumor-free equilibrium point (global stability). For lower doses, <span><math><mrow><mn>0</mn><mo>≤</mo><mi>u</mi><mo><</mo><mover><mrow><mi>u</mi></mrow><mrow><mo>̃</mo></mrow></mover></mrow></math></span>, however, there exists a locally asymptotically stable equilibrium point with positive values and such doses are not sufficient to eradicate the tumor. Mathematically, for <span><math><mrow><mi>u</mi><mo>=</mo><mover><mrow><mi>u</mi></mrow><mrow><mo>̃</mo></mrow></mover></mrow></math></span>, the positive and tumor-free equilibrium points are equal and a transcritical or exchange of stability bifurcation occurs. Our theoretical analysis is independent of specific values of the parameters. For the numerical illustration of the results we use clinically validated parameter values for low-grade glioma from Ribba et al., (2012).</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"85 ","pages":"Article 104344"},"PeriodicalIF":1.8,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143580003","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

Bilinear optimal control for chemotaxis model: The case of two-sidedly degenerate diffusion with Volume-Filling Effect 趋化性模型的双线性最优控制：具有体积填充效应的双面退化扩散

IF 1.8 3区数学

Nonlinear Analysis-Real World Applications Pub Date : 2025-03-10 DOI: 10.1016/j.nonrwa.2025.104362

Sarah Serhal , Georges Chamoun , Mazen Saad , Toni Sayah

{"title":"Bilinear optimal control for chemotaxis model: The case of two-sidedly degenerate diffusion with Volume-Filling Effect","authors":"Sarah Serhal , Georges Chamoun , Mazen Saad , Toni Sayah","doi":"10.1016/j.nonrwa.2025.104362","DOIUrl":"10.1016/j.nonrwa.2025.104362","url":null,"abstract":"<div><div>In this paper, we study an optimal control problem for a coupled non-linear system of reaction–diffusion equations with degenerate diffusion, consisting of two partial differential equations representing the density of cells and the concentration of the chemotactic agent. By controlling the concentration of the chemical substrates, this study can guide the optimal growth of cells. The novelty of this work lies on the direct and dual models that remain in a weak setting, which is uncommon in the recent literature for solving optimal control systems. Moreover, it is known that the adjoint problems offer a powerful approach to quantifying the uncertainty associated with model inputs. However, these systems typically lack closed-form solutions, making it challenging to obtain weak solutions. For that, the well-posedness of the direct problem is first well guaranteed. Then, the existence of an optimal control and the first-order optimality conditions are established. Finally, weak solutions for the adjoint system to the non-linear degenerate direct model, are introduced and investigated.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"85 ","pages":"Article 104362"},"PeriodicalIF":1.8,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143580071","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

Dynamic analysis of a class of Insulin-Glucose-Glucocorticoid model with nonlinear pulse 一类非线性脉冲胰岛素-葡萄糖-糖皮质激素模型的动态分析

IF 1.8 3区数学

Nonlinear Analysis-Real World Applications Pub Date : 2025-03-07 DOI: 10.1016/j.nonrwa.2025.104352

Changtong Li, Yuntao Liu, Xiaozhou Feng, Yuzhen Wang

{"title":"Dynamic analysis of a class of Insulin-Glucose-Glucocorticoid model with nonlinear pulse","authors":"Changtong Li, Yuntao Liu, Xiaozhou Feng, Yuzhen Wang","doi":"10.1016/j.nonrwa.2025.104352","DOIUrl":"10.1016/j.nonrwa.2025.104352","url":null,"abstract":"<div><div>Few studies have employed nonlinear processes to characterize treatment strategies in the context of diabetes and combination drug therapy while considering the effects of drug-induced insulin resistance. Based on this, we proposed a nonlinear impulse system to describe the interaction mechanism among insulin, glucose, and glucocorticoids in diabetic patients, with a particular focus on the role of glucocorticoids in diabetes treatment. To investigate the existence of positive periodic solutions in a type 1 diabetes model with double fixed impulses, we employed the properties of the LambertW function and the Floquet multiplier theory, thereby proving the existence, uniqueness, and global asymptotic stability of the periodic solution. Furthermore, for the type 2 diabetes model, we established the permanence of the system. The findings of this study, in conjunction with treatment strategies based on hormonal interactions, provided more scientifically grounded clinical guidance for determining the appropriate dosage of exogenous insulin and glucocorticoid medications.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"85 ","pages":"Article 104352"},"PeriodicalIF":1.8,"publicationDate":"2025-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143562156","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

Asymptotic stability of Plasma-Sheaths to the full Euler–Poisson system 等离子体鞘对全欧拉-泊松系统的渐近稳定性

IF 1.8 3区数学

Nonlinear Analysis-Real World Applications Pub Date : 2025-03-06 DOI: 10.1016/j.nonrwa.2025.104342

Lei Yao , Haiyan Yin , Mengmeng Zhu

{"title":"Asymptotic stability of Plasma-Sheaths to the full Euler–Poisson system","authors":"Lei Yao , Haiyan Yin , Mengmeng Zhu","doi":"10.1016/j.nonrwa.2025.104342","DOIUrl":"10.1016/j.nonrwa.2025.104342","url":null,"abstract":"<div><div>The main concern of this paper is to study large-time behavior of the sheath to the full Euler–Poisson system. As is well known, the monotone stationary solution under the Bohm criterion can be referred to as the sheath which is formed by interactions of plasma with wall. So far, the existence and asymptotic stability of stationary solutions in one-dimensional half space to the full Euler–Poisson system have been proved in Duan et al. (2021). In the present paper, we extend the results in Duan et al. (2021) to <span><math><mi>N</mi></math></span>-dimensional (<span><math><mi>N</mi></math></span>=1,2,3) half space. By assuming that the velocity of the positive ion satisfies the Bohm criterion at the far field, we establish the global unique existence and the large time asymptotic stability of the sheath in some weighted Sobolev spaces by weighted energy method. Moreover, the time-decay rates are also obtained. A key different point from Duan et al. (2021) is to derive some boundary estimates on the derivative of the potential in the <span><math><msub><mrow><mi>x</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>-direction.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"85 ","pages":"Article 104342"},"PeriodicalIF":1.8,"publicationDate":"2025-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143562155","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

Dynamics of competing species in a reaction-diffusive chemostat model with an internal inhibitor 带有内部抑制剂的反应扩散恒温器模型中竞争物种的动态变化

IF 1.8 3区数学

Nonlinear Analysis-Real World Applications Pub Date : 2025-03-05 DOI: 10.1016/j.nonrwa.2025.104347

Wang Zhang, Hongling Jiang

引用次数: 0

Parabolic-scalings on large-time behavior of the incompressible Navier–Stokes flow 不可压缩Navier-Stokes流大时间特性的抛物标度

IF 1.8 3区数学

Nonlinear Analysis-Real World Applications Pub Date : 2025-03-04 DOI: 10.1016/j.nonrwa.2025.104350

Masakazu Yamamoto

引用次数: 0

Leader–follower synchronization of heterogeneous dynamical networks with unknown parameters 未知参数异构动态网络的领导-随从同步

IF 1.8 3区数学

Nonlinear Analysis-Real World Applications Pub Date : 2025-03-04 DOI: 10.1016/j.nonrwa.2025.104341

Xinzhi Liu , Hongtao Zhang

引用次数: 0

Analyticity smoothing effect of the Vlasov–Poisson–Landau system Vlasov-Poisson-Landau系统的分析平滑效应

IF 1.8 3区数学

Nonlinear Analysis-Real World Applications Pub Date : 2025-03-03 DOI: 10.1016/j.nonrwa.2025.104343

LvQiao Liu , Hao Wang

引用次数: 0

Wave-breaking criteria of solution for a Fornberg-Whitham type equation revisited 重新讨论了Fornberg-Whitham型方程解的破波准则

IF 1.8 3区数学

Nonlinear Analysis-Real World Applications Pub Date : 2025-03-03 DOI: 10.1016/j.nonrwa.2025.104348

Xiaofang Dong

{"title":"Wave-breaking criteria of solution for a Fornberg-Whitham type equation revisited","authors":"Xiaofang Dong","doi":"10.1016/j.nonrwa.2025.104348","DOIUrl":"10.1016/j.nonrwa.2025.104348","url":null,"abstract":"<div><div>In this paper, we mainly revisit to a Fornberg-Whitham type equation, which can be derived as a special shallow water wave equation of the Constantin-Lannes-type models proposed by Constantin and Lannes (2009). We focus on some new wave-breaking criteria of the solution for the equation on the line or circle based on the different real-valued intervals in which the dispersive parameter <span><math><mi>m</mi></math></span> being located. A prior estimate of <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>∞</mi></mrow></msup></math></span>-norm of the solution for equation is first obtained by the interval of the dispersive parameter <span><math><mi>m</mi></math></span>. By this estimate and a weaker conserved <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-norm, we then study some sufficient conditions which guarantee the occurrence of wave-breaking of solutions on the line. It is worthy noting that the results we obtained not only supplement the wave-breaking results of classic FW equation on the line in the previous references, but also extend these results to a wider range of dispersive parameters <span><math><mi>k</mi></math></span> and <span><math><mi>m</mi></math></span>. Moreover, we give the wave-breaking criterion of the solution for equation on the circle without utilizing any conservation law.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"85 ","pages":"Article 104348"},"PeriodicalIF":1.8,"publicationDate":"2025-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143552662","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