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The Riemann problem for a generalised Burgers equation with spatially decaying sound speed. II General qualitative theory and numerical analysis
IF 1.8 3区 数学
Nonlinear Analysis-Real World Applications Pub Date : 2025-03-11 DOI: 10.1016/j.nonrwa.2025.104349
John Christopher Meyer, David John Needham
{"title":"The Riemann problem for a generalised Burgers equation with spatially decaying sound speed. II General qualitative theory and numerical analysis","authors":"John Christopher Meyer,&nbsp;David John Needham","doi":"10.1016/j.nonrwa.2025.104349","DOIUrl":"10.1016/j.nonrwa.2025.104349","url":null,"abstract":"<div><div>In this paper, we establish the global well-posedness of the Cauchy problem for a generalised viscous Burgers equation with spatially decaying sound speed, continuing from part I of this series of papers. Moreover, we establish qualitative properties, specifically bounds and monotonicity properties of solutions to the Cauchy problem. We also establish a conditional convergence result for an explicit mid-point finite difference scheme used throughout part I to approximate solutions to the Cauchy problem.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"85 ","pages":"Article 104349"},"PeriodicalIF":1.8,"publicationDate":"2025-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143592410","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}
引用次数: 0
Vanishing viscosity limit for hyperbolic system of Temple class in 1-d with nonlinear viscosity
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
{"title":"Vanishing viscosity limit for hyperbolic system of Temple class in 1-d with nonlinear viscosity","authors":"Boris Haspot ,&nbsp;Animesh Jana","doi":"10.1016/j.nonrwa.2025.104346","DOIUrl":"10.1016/j.nonrwa.2025.104346","url":null,"abstract":"<div><div>We consider hyperbolic system with nonlinear viscosity such that the viscosity matrix <span><math><mrow><mi>B</mi><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow></mrow></math></span> is commutating with <span><math><mrow><mi>A</mi><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow></mrow></math></span> the matrix associated to the convective term. The drift matrix is assumed to be Temple class. First we prove the global existence of smooth solutions for initial data with small total variation. We show that the solution to the parabolic equation converges to a semi-group solution of the hyperbolic system as viscosity goes to zero. Furthermore, we prove that the zero diffusion limit coincides with the one obtained in Bianchini and Bressan (2000).</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"85 ","pages":"Article 104346"},"PeriodicalIF":1.8,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143580004","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
Nonlinear mountain waves with active precipitation
IF 1.8 3区 数学
Nonlinear Analysis-Real World Applications Pub Date : 2025-03-10 DOI: 10.1016/j.nonrwa.2025.104351
Tony Lyons
{"title":"Nonlinear mountain waves with active precipitation","authors":"Tony Lyons","doi":"10.1016/j.nonrwa.2025.104351","DOIUrl":"10.1016/j.nonrwa.2025.104351","url":null,"abstract":"<div><div>Exact nonlinear mountain waves described using Lagrangian variables are considered with constant enthalpy of vapourisation in a moist atmosphere. It is shown that if a streamline in the flow with a given temperature is saturated, then the dynamics of the flow are sufficient to deduce the temperature at which any other streamline in the flow becomes saturated. The equation of state for vapour is then applied to deduce the saturation pressure for the water component of the atmospheric flow also. The first law of thermodynamics is then used to deduce the heat gain within a region due to precipitation from the flow. This heat loss is also used to obtain an estimate for the rate of hydrometeor fallout from this region of the flow.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"85 ","pages":"Article 104351"},"PeriodicalIF":1.8,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143580002","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}
引用次数: 0
Analysis of a mathematical model for low-grade gliomas under chemotherapy as a dynamical system
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 ,&nbsp;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>&lt;</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
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 ,&nbsp;Georges Chamoun ,&nbsp;Mazen Saad ,&nbsp;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
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,&nbsp;Yuntao Liu,&nbsp;Xiaozhou Feng,&nbsp;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
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 ,&nbsp;Haiyan Yin ,&nbsp;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
{"title":"Dynamics of competing species in a reaction-diffusive chemostat model with an internal inhibitor","authors":"Wang Zhang,&nbsp;Hongling Jiang","doi":"10.1016/j.nonrwa.2025.104347","DOIUrl":"10.1016/j.nonrwa.2025.104347","url":null,"abstract":"<div><div>This paper investigates the unstirred chemostat model in the presence of an internal inhibitor. The primary objective is to establish the threshold dynamics of this system concerning inhibitor parameters, growth rates and diffusion rates. The theoretical analysis indicates the existence of several critical curves, which categorize the dynamics into three scenarios: (1) extinction of both species; (2) competitive exclusion; and (3) coexistence. Additionally, the numerical results reveal a tradeoff driven coexistence mechanism influenced by relevant parameters. Notably, the bistable phenomenon consistently arises due to the effects of inhibitors. Finally, we examine the impact of diffusion rates on the competitive outcomes of the two species across different competition scenarios. These new findings may have significant biological implications for the interactions between the two species competing in the unstirred chemostat model with an internal inhibitor.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"85 ","pages":"Article 104347"},"PeriodicalIF":1.8,"publicationDate":"2025-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143552661","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
Parabolic-scalings on large-time behavior of the incompressible Navier–Stokes flow
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
{"title":"Parabolic-scalings on large-time behavior of the incompressible Navier–Stokes flow","authors":"Masakazu Yamamoto","doi":"10.1016/j.nonrwa.2025.104350","DOIUrl":"10.1016/j.nonrwa.2025.104350","url":null,"abstract":"<div><div>Through asymptotic expansion, the large-time behavior of incompressible Navier–Stokes flow in <span><math><mi>n</mi></math></span>-dimensional whole space is depicted. Especially, from their parabolic scalings, large-time behaviors of any terms on the expansion are clarified. The parabolic scalings also guarantee the uniqueness of the expansion. In the preceding work, the expansion with the <span><math><mi>n</mi></math></span>th order has already been derived. They also predicted that the flow has some logarithmic evolutions in higher-order decay. In this paper, an asymptotic expansion with <span><math><mrow><mn>2</mn><mi>n</mi></mrow></math></span>th order is presented. Furthermore, logarithmic evolutions are discovered.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"85 ","pages":"Article 104350"},"PeriodicalIF":1.8,"publicationDate":"2025-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143552660","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
Leader–follower synchronization of heterogeneous dynamical networks with unknown parameters
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
{"title":"Leader–follower synchronization of heterogeneous dynamical networks with unknown parameters","authors":"Xinzhi Liu ,&nbsp;Hongtao Zhang","doi":"10.1016/j.nonrwa.2025.104341","DOIUrl":"10.1016/j.nonrwa.2025.104341","url":null,"abstract":"<div><div>This paper studies leader–follower synchronization of a class of heterogeneous dynamical networks with unknown system parameters. Aiming at various unknown parameters, we design the corresponding adaptive controllers and updating laws, respectively. Based on Lyapunov stability theorem, network synchronization criteria are given to guarantee the effectiveness of our adaptive synchronization approaches. Finally, numeral examples, realizing network synchronization in a complex dynamical network including Lorenz system, Chen system and Rössler system with a modified Chua’s circuit, are given to verify the correctness of our main results.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"85 ","pages":"Article 104341"},"PeriodicalIF":1.8,"publicationDate":"2025-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143552663","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}
引用次数: 0
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