Pub Date : 2024-04-19DOI: 10.1007/s10255-024-1087-6
Ai-fang Qu, Xue-ying Su, Hai-rong Yuan
By considering Radon measure solutions for boundary value problems of stationary non-isentropic compressible Euler equations on hypersonic-limit flows passing ramps with frictions on their boundaries, we construct solutions with density containing Dirac measures supported on the boundaries of the ramps, which represent the infinite-thin shock layers under different assumptions on the skin-frictions. We thus derive corresponding generalizations of the celebrated Newton-Busemann law in hypersonic aerodynamics for distributions of drags/lifts on ramps.
{"title":"Generalized Newton-Busemann Law for Two-dimensional Steady Hypersonic-limit Euler Flows Passing Ramps with Skin-frictions","authors":"Ai-fang Qu, Xue-ying Su, Hai-rong Yuan","doi":"10.1007/s10255-024-1087-6","DOIUrl":"https://doi.org/10.1007/s10255-024-1087-6","url":null,"abstract":"<p>By considering Radon measure solutions for boundary value problems of stationary non-isentropic compressible Euler equations on hypersonic-limit flows passing ramps with frictions on their boundaries, we construct solutions with density containing Dirac measures supported on the boundaries of the ramps, which represent the infinite-thin shock layers under different assumptions on the skin-frictions. We thus derive corresponding generalizations of the celebrated Newton-Busemann law in hypersonic aerodynamics for distributions of drags/lifts on ramps.</p>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140626963","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}
Pub Date : 2024-04-19DOI: 10.1007/s10255-024-1058-y
Dou-dou Li, Wan-lin Shi, Mei Zhang
In this paper, a critical Galton-Watson branching process {Zn} is considered. Large deviation rates of ({S_{{Z_n}}}: = sumlimits_{i = 1}^{{Z_n}} {{X_i}} ) are obtained, where {Xi, i ≥ 1} is a sequence of independent and identically distributed random variables and X1 is in the domain of attraction of an α-stable law with α ∈ (0, 2). One shall see that the convergence rate is determined by the tail index of X1 and the variance of Z1. Our results can be compared with those ones of the supercritical case.
{"title":"Large Deviations for a Critical Galton-Watson Branching Process","authors":"Dou-dou Li, Wan-lin Shi, Mei Zhang","doi":"10.1007/s10255-024-1058-y","DOIUrl":"https://doi.org/10.1007/s10255-024-1058-y","url":null,"abstract":"<p>In this paper, a critical Galton-Watson branching process {<i>Z</i><sub><i>n</i></sub>} is considered. Large deviation rates of <span>({S_{{Z_n}}}: = sumlimits_{i = 1}^{{Z_n}} {{X_i}} )</span> are obtained, where {<i>X</i><sub><i>i</i></sub>, <i>i</i> ≥ 1} is a sequence of independent and identically distributed random variables and <i>X</i><sub>1</sub> is in the domain of attraction of an <i>α</i>-stable law with <i>α</i> ∈ (0, 2). One shall see that the convergence rate is determined by the tail index of <i>X</i><sub>1</sub> and the variance of <i>Z</i><sub>1</sub>. Our results can be compared with those ones of the supercritical case.</p>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140627031","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}
Pub Date : 2024-04-19DOI: 10.1007/s10255-024-1074-y
Jian-wei Dong, Yi-hui Zhang
In this paper, we consider the free boundary value problem for a model of inviscid liquid-gas two-phase flow with cylindrical symmetry. For simplicity, we assume that the gas velocity is always equal to the liquid one and the gas and liquid are both connected continuously to the outer vacuum through the same free boundary. Furthermore, the free boundary is assumed to move in the radial direction with the radial velocity, which will affect the angular velocity but does not affect the axial velocity. We construct two classes of global analytical solutions by using some ansatzs and show that the free boundary will spread outward linearly in time by using some new averaged quantities.
{"title":"Analytical Solutions to a Model of Inviscid Liquid-gas Two-phase Flow with Cylindrical Symmetry and Free Boundary","authors":"Jian-wei Dong, Yi-hui Zhang","doi":"10.1007/s10255-024-1074-y","DOIUrl":"https://doi.org/10.1007/s10255-024-1074-y","url":null,"abstract":"<p>In this paper, we consider the free boundary value problem for a model of inviscid liquid-gas two-phase flow with cylindrical symmetry. For simplicity, we assume that the gas velocity is always equal to the liquid one and the gas and liquid are both connected continuously to the outer vacuum through the same free boundary. Furthermore, the free boundary is assumed to move in the radial direction with the radial velocity, which will affect the angular velocity but does not affect the axial velocity. We construct two classes of global analytical solutions by using some ansatzs and show that the free boundary will spread outward linearly in time by using some new averaged quantities.</p>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140630571","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}
Pub Date : 2024-04-19DOI: 10.1007/s10255-024-1070-2
Ling-hai Zhang
We couple together existing ideas, existing results, special structure and novel ideas to accomplish the exact limits and improved decay estimates with sharp rates for all order derivatives of the global weak solutions of the Cauchy problem for an n-dimensional incompressible Navier-Stokes equations. We also use the global smooth solution of the corresponding heat equation to approximate the global weak solutions of the incompressible Navier-Stokes equations.
我们将现有思想、现有结果、特殊结构和新颖思想结合起来，完成了 n 维不可压缩纳维-斯托克斯方程的考希问题全局弱解的精确极限和改进的衰减估计，并具有尖锐的衰减率。我们还利用相应热方程的全局平稳解来近似不可压缩 Navier-Stokes 方程的全局弱解。
{"title":"The Exact Limits and Improved Decay Estimates for All Order Derivatives of the Global Weak Solutions of n-Dimensional Incompressible Navier-Stokes Equations","authors":"Ling-hai Zhang","doi":"10.1007/s10255-024-1070-2","DOIUrl":"https://doi.org/10.1007/s10255-024-1070-2","url":null,"abstract":"<p>We couple together existing ideas, existing results, special structure and novel ideas to accomplish the exact limits and improved decay estimates with sharp rates for all order derivatives of the global weak solutions of the Cauchy problem for an <i>n</i>-dimensional incompressible Navier-Stokes equations. We also use the global smooth solution of the corresponding heat equation to approximate the global weak solutions of the incompressible Navier-Stokes equations.</p>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140627117","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}
Pub Date : 2024-04-19DOI: 10.1007/s10255-024-1075-x
Ying-hua Li, Yong Wang, Han-bin Cai
We study the initial-boundary value problem of an incompressible Navier-Stokes-Cahn-Hilliard system with variable density. We prove the existence and uniqueness of the local strong solution in two or three dimensions. Moreover, we establish a two-dimensional blow-up criterion in terms of the temporal integral of the square of maximum norm of velocity.
{"title":"Strong Solutions of an Incompressible Phase-field Model with Variable Density","authors":"Ying-hua Li, Yong Wang, Han-bin Cai","doi":"10.1007/s10255-024-1075-x","DOIUrl":"https://doi.org/10.1007/s10255-024-1075-x","url":null,"abstract":"<p>We study the initial-boundary value problem of an incompressible Navier-Stokes-Cahn-Hilliard system with variable density. We prove the existence and uniqueness of the local strong solution in two or three dimensions. Moreover, we establish a two-dimensional blow-up criterion in terms of the temporal integral of the square of maximum norm of velocity.</p>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140630802","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}
Pub Date : 2024-04-19DOI: 10.1007/s10255-024-1046-2
Yan-cheng Lu, Ning Bi, An-hua Wan
The one-bit compressed sensing problem is of fundamental importance in many areas, such as wireless communication, statistics, and so on. However, the optimization of one-bit problem constrained on the unit sphere lacks an algorithm with rigorous mathematical proof of convergence and validity. In this paper, an iteration algorithm is established based on difference-of-convex algorithm for the one-bit compressed sensing problem constrained on the unit sphere, with iterating formula
where C is the convex cone generated by the one-bit measurements and ({eta _1} > {eta _2} > {1 over 2}). The new algorithm is proved to converge as long as the initial point is on the unit sphere and accords with the measurements, and the convergence to the global minimum point of the ℓ1 norm is discussed.
单比特压缩传感问题在无线通信、统计等许多领域都具有重要的基础性意义。然而，受单位球面约束的单比特问题的优化缺乏一种具有严格收敛性和有效性数学证明的算法。本文针对单位球上约束的单比特压缩传感问题，建立了一种基于差分凸算法的迭代算法，迭代公式为 $${x^{k + 1}} = mathop {arg min }limits_{x in ,C}{ ||x|{|_1}+ {eta _1}||{x^k}|{|_1}max (||x||_2^2,1) - 2{eta _2}||{x^k}|{|_1}langle x,{x^k}rangle}$$ 其中 C 是由一位测量和 ({eta _1} > {eta _2} > {1 over 2}) 生成的凸锥。只要初始点在单位球面上并与测量结果一致，新算法就能收敛，并讨论了收敛到 ℓ1 准则全局最小点的问题。
{"title":"A Reliable Iteration Algorithm for One-Bit Compressive Sensing on the Unit Sphere","authors":"Yan-cheng Lu, Ning Bi, An-hua Wan","doi":"10.1007/s10255-024-1046-2","DOIUrl":"10.1007/s10255-024-1046-2","url":null,"abstract":"<div><p>The one-bit compressed sensing problem is of fundamental importance in many areas, such as wireless communication, statistics, and so on. However, the optimization of one-bit problem constrained on the unit sphere lacks an algorithm with rigorous mathematical proof of convergence and validity. In this paper, an iteration algorithm is established based on difference-of-convex algorithm for the one-bit compressed sensing problem constrained on the unit sphere, with iterating formula </p><div><div><span>$${x^{k + 1}} = mathop {arg min }limits_{x in ,C} { ||x|{|_1} + {eta _1}||{x^k}|{|_1}max (||x||_2^2,1) - 2{eta _2}||{x^k}|{|_1}langle x,{x^k}rangle } ,$$</span></div></div><p> where <i>C</i> is the convex cone generated by the one-bit measurements and <span>({eta _1} > {eta _2} > {1 over 2})</span>. The new algorithm is proved to converge as long as the initial point is on the unit sphere and accords with the measurements, and the convergence to the global minimum point of the <i>ℓ</i><sub>1</sub> norm is discussed.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140627113","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}
Pub Date : 2024-04-19DOI: 10.1007/s10255-024-1083-x
Hui Jiang, Qing-shan Yang
In this paper, we study the asymptotic properties for estimators of two parameters in the drift function in the ergodic fractional Ornstein-Uhlenbeck process with Hurst index (H in (0,{1 over 2})). The Cramér-type moderate deviations, as well as the moderation deviations with explicit rate function can be obtained. The main methods consist of the deviation inequalities and Cramér-type moderate deviations for multiple Wiener-Itô integrals, as well as the asymptotic analysis techniques.
本文研究了具有赫斯特指数（H in (0,{1 over 2})）的遍历分数奥恩斯坦-乌伦贝克过程中漂移函数中两个参数的估计值的渐近性质。可以得到克拉梅尔型温和偏差以及具有明确速率函数的温和偏差。主要方法包括多重维纳-伊托积分的偏差不等式和克拉梅尔型温和偏差，以及渐近分析技术。
{"title":"Moderate Deviations for the Parameter Estimation in the Fractional Ornstein-Uhlenbeck Process with $$H in (0,{1 over 2})$$","authors":"Hui Jiang, Qing-shan Yang","doi":"10.1007/s10255-024-1083-x","DOIUrl":"https://doi.org/10.1007/s10255-024-1083-x","url":null,"abstract":"<p>In this paper, we study the asymptotic properties for estimators of two parameters in the drift function in the ergodic fractional Ornstein-Uhlenbeck process with Hurst index <span>(H in (0,{1 over 2}))</span>. The Cramér-type moderate deviations, as well as the moderation deviations with explicit rate function can be obtained. The main methods consist of the deviation inequalities and Cramér-type moderate deviations for multiple Wiener-Itô integrals, as well as the asymptotic analysis techniques.</p>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140626962","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}
Pub Date : 2024-03-27DOI: 10.1007/s10255-024-1109-4
Jin-yan Zhu, Yong Chen
The Gerdjikov-Ivanov (GI) hierarchy is derived via recursion operator, in this article, we mainly investigate the third-order flow GI equation. In the framework of the Riemann-Hilbert method, the soliton matrices of the third-order flow GI equation with simple zeros and elementary high-order zeros of Riemann-Hilbert problem are constructed through the standard dressing process. Taking advantage of this result, some properties and asymptotic analysis of single soliton solution and two soliton solution are discussed, and the simple elastic interaction of two soliton are proved. Compared with soliton solution of the classical second-order flow, we find that the higher-order dispersion term affects the propagation velocity, propagation direction and amplitude of the soliton. Finally, by means of a certain limit technique, the high-order soliton solution matrix for the third-order flow GI equation is derived.
摘要 Gerdjikov-Ivanov（GI）层次结构是通过递归算子推导出来的，本文主要研究三阶流 GI 方程。在黎曼-希尔伯特方法的框架下，通过标准的修整过程，构造了三阶流 GI 方程的具有黎曼-希尔伯特问题简单零点和基本高阶零点的孤子矩阵。利用这一结果，讨论了单孤子解和双孤子解的一些性质和渐近分析，并证明了双孤子的简单弹性相互作用。与经典二阶流的孤子解相比，我们发现高阶分散项会影响孤子的传播速度、传播方向和振幅。最后，通过一定的极限技术，得出了三阶流 GI 方程的高阶孤子解矩阵。
{"title":"High-order Soliton Matrix for the Third-order Flow Equation of the Gerdjikov-Ivanov Hierarchy Through the Riemann-Hilbert Method","authors":"Jin-yan Zhu, Yong Chen","doi":"10.1007/s10255-024-1109-4","DOIUrl":"10.1007/s10255-024-1109-4","url":null,"abstract":"<div><p>The Gerdjikov-Ivanov (GI) hierarchy is derived via recursion operator, in this article, we mainly investigate the third-order flow GI equation. In the framework of the Riemann-Hilbert method, the soliton matrices of the third-order flow GI equation with simple zeros and elementary high-order zeros of Riemann-Hilbert problem are constructed through the standard dressing process. Taking advantage of this result, some properties and asymptotic analysis of single soliton solution and two soliton solution are discussed, and the simple elastic interaction of two soliton are proved. Compared with soliton solution of the classical second-order flow, we find that the higher-order dispersion term affects the propagation velocity, propagation direction and amplitude of the soliton. Finally, by means of a certain limit technique, the high-order soliton solution matrix for the third-order flow GI equation is derived.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140313187","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}
where a > 0, b ≥ 0, ρ > 0 are constants, ({p^ * } = {{Np} over {N - p}}) is the critical Sobolev exponent, μ is a Lagrange multiplier, ( - {Delta _p}u = - {rm{div}}(|nabla u{|^{p - 2}}nabla u)), (2 < p < N < 2p,,,,mu in mathbb{R}) and (s in (2{{N + 2} over N}p - 2,,,,{p^ * })). We demonstrate that the p-Kirchhoff equation has a normalized solution using the mountain pass lemma and some analysis techniques.
在本文中，我们研究了以下 p-Kirchhoff 方程 $$left{ {matrix{{(a + b,int_{mathbb{R}^N}}{(|nabla u{|^p} + |u{|^p})dx),( - {Delta _p}u + |u{|^{p - 2}}u) = |u{|^{s - 2}}u + mu u,,x in {mathbb{R}^N},}}hfill cr {int_{mathbb{R}^N}}{|u{|^2}dx = rho ,}}hfill cr }}right.$$ 其中 a > 0, b ≥ 0, ρ > 0 是常数, ({p^ * } = {{Np} over {N - p}}) 是临界索波列夫指数, μ 是拉格朗日乘数, ( - {Delta _p}u = - {rm{div}}(|nabla u{|^{p - 2}}nabla u)), (2 <；p < N < 2p,,,mu in mathbb{R}) and(s in (2{{N + 2} over N}p - 2,,,,{p^ * })).我们利用山口阶梯和一些分析技术证明 p-Kirchhoff 方程有一个归一化解。
{"title":"Normalized Solution for p-Kirchhoff Equation with a L2-supercritical Growth","authors":"Zhi-min Ren, Yong-yi Lan","doi":"10.1007/s10255-024-1120-9","DOIUrl":"10.1007/s10255-024-1120-9","url":null,"abstract":"<div><p>In this paper, we investigate the following <i>p</i>-Kirchhoff equation </p><div><div><span>$$left{ {matrix{{(a + b,int_{{mathbb{R}^N}} {(|nabla u{|^p} + |u{|^p})dx),( - {Delta _p}u + |u{|^{p - 2}}u) = |u{|^{s - 2}}u + mu u,,,x in {mathbb{R}^N},} } hfill cr {int_{{mathbb{R}^N}} {|u{|^2}dx = rho ,} } hfill cr } } right.$$</span></div></div><p> where <i>a</i> > 0, <i>b</i> ≥ 0, <i>ρ</i> > 0 are constants, <span>({p^ * } = {{Np} over {N - p}})</span> is the critical Sobolev exponent, <i>μ</i> is a Lagrange multiplier, <span>( - {Delta _p}u = - {rm{div}}(|nabla u{|^{p - 2}}nabla u))</span>, <span>(2 < p < N < 2p,,,,mu in mathbb{R})</span> and <span>(s in (2{{N + 2} over N}p - 2,,,,{p^ * }))</span>. We demonstrate that the <i>p</i>-Kirchhoff equation has a normalized solution using the mountain pass lemma and some analysis techniques.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140313255","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}
Pub Date : 2024-03-27DOI: 10.1007/s10255-024-1049-z
Li-li Liu, Hong-gang Wang, Ya-zhi Li
Considering that HBV belongs to the DNA virus family and is hepatotropic, we model the HBV DNA-containing capsids as a compartment. In this paper, a delayed HBV infection model is established, where the general incidence function and two infection routes including cell-virus infection and cell-cell infection are introduced. According to some preliminaries, including well-posedness, basic reproduction number and existence of two equilibria, we obtain the threshold dynamics for the model. We illustrate numerical simulations to verify the above theoretical results, and furthermore explore the impacts of intracellular delay and cell-cell infection on the global dynamics of the model.
考虑到 HBV 属于 DNA 病毒家族且具有肝毒性，我们将含 HBV DNA 的囊壳作为一个区室来建模。本文建立了延迟 HBV 感染模型，其中引入了一般发生函数和两种感染途径，包括细胞-病毒感染和细胞-细胞感染。根据一些预设条件，包括拟合性、基本繁殖数和两个均衡点的存在，我们得到了模型的阈值动力学。我们通过数值模拟验证了上述理论结果，并进一步探讨了细胞内延迟和细胞-细胞感染对模型全局动力学的影响。
{"title":"Mathematical Analysis on a General Delayed HBV Model with Capsids and Two Infection Routes","authors":"Li-li Liu, Hong-gang Wang, Ya-zhi Li","doi":"10.1007/s10255-024-1049-z","DOIUrl":"10.1007/s10255-024-1049-z","url":null,"abstract":"<div><p>Considering that HBV belongs to the DNA virus family and is hepatotropic, we model the HBV DNA-containing capsids as a compartment. In this paper, a delayed HBV infection model is established, where the general incidence function and two infection routes including cell-virus infection and cell-cell infection are introduced. According to some preliminaries, including well-posedness, basic reproduction number and existence of two equilibria, we obtain the threshold dynamics for the model. We illustrate numerical simulations to verify the above theoretical results, and furthermore explore the impacts of intracellular delay and cell-cell infection on the global dynamics of the model.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140313981","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}
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