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Analytical Solutions to a Model of Inviscid Liquid-gas Two-phase Flow with Cylindrical Symmetry and Free Boundary 具有圆柱对称性和自由边界的无粘性液气两相流模型的解析解
IF 0.8 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-04-19 DOI: 10.1007/s10255-024-1074-y
Jian-wei Dong, Yi-hui Zhang
{"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":"78 1","pages":""},"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}
引用次数: 0
Strong Solutions of an Incompressible Phase-field Model with Variable Density 密度可变的不可压缩相场模型的强解
IF 0.8 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-04-19 DOI: 10.1007/s10255-024-1075-x
Ying-hua Li, Yong Wang, Han-bin Cai
{"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":"101 1","pages":""},"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}
引用次数: 0
The Exact Limits and Improved Decay Estimates for All Order Derivatives of the Global Weak Solutions of n-Dimensional Incompressible Navier-Stokes Equations n 维不可压缩纳维-斯托克斯方程全局弱解的所有阶衍生物的精确极限和改进衰减估计值
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-04-19 DOI: 10.1007/s10255-024-1070-2
Ling-hai Zhang
{"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":"10.1007/s10255-024-1070-2","url":null,"abstract":"<div><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></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"41 1","pages":"27 - 83"},"PeriodicalIF":0.9,"publicationDate":"2024-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10255-024-1070-2.pdf","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":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Reliable Iteration Algorithm for One-Bit Compressive Sensing on the Unit Sphere 单位球上一位压缩传感的可靠迭代算法
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-04-19 DOI: 10.1007/s10255-024-1046-2
Yan-cheng Lu, Ning Bi, An-hua Wan
{"title":"A Reliable Iteration Algorithm for One-Bit Compressive Sensing on the Unit Sphere","authors":"Yan-cheng Lu,&nbsp;Ning Bi,&nbsp;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} &gt; {eta _2} &gt; {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":"40 3","pages":"801 - 822"},"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}
引用次数: 0
Moderate Deviations for the Parameter Estimation in the Fractional Ornstein-Uhlenbeck Process with $$H in (0,{1 over 2})$$ 分式奥恩斯坦-乌伦贝克过程中参数估计的适度偏差与 $$H in (0,{1over 2})$$
IF 0.8 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-04-19 DOI: 10.1007/s10255-024-1083-x
Hui Jiang, Qing-shan Yang
{"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":"34 1","pages":""},"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}
引用次数: 0
High-order Soliton Matrix for the Third-order Flow Equation of the Gerdjikov-Ivanov Hierarchy Through the Riemann-Hilbert Method 通过黎曼-希尔伯特方法计算格尔吉科夫-伊万诺夫层次三阶流动方程的高阶孤子矩阵
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-03-27 DOI: 10.1007/s10255-024-1109-4
Jin-yan Zhu, Yong Chen
{"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,&nbsp;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":"40 2","pages":"358 - 378"},"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}
引用次数: 0
Normalized Solution for p-Kirchhoff Equation with a L2-supercritical Growth 具有 L2 超临界增长的 p-Kirchhoff 方程的归一化解法
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-03-27 DOI: 10.1007/s10255-024-1120-9
Zhi-min Ren, Yong-yi Lan
{"title":"Normalized Solution for p-Kirchhoff Equation with a L2-supercritical Growth","authors":"Zhi-min Ren,&nbsp;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> &gt; 0, <i>b</i> ≥ 0, <i>ρ</i> &gt; 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 &lt; p &lt; N &lt; 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":"40 2","pages":"414 - 429"},"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}
引用次数: 0
Asymptotic Inference in the Random Coefficient Autoregressive Model with Time-functional Variance Noises 具有时间函数方差噪声的随机系数自回归模型的渐近推理
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-03-27 DOI: 10.1007/s10255-024-1072-0
En-wen Zhu, Zi-wei Deng, Han-jun Zhang, Jun Cao, Xiao-hui Liu
{"title":"Asymptotic Inference in the Random Coefficient Autoregressive Model with Time-functional Variance Noises","authors":"En-wen Zhu,&nbsp;Zi-wei Deng,&nbsp;Han-jun Zhang,&nbsp;Jun Cao,&nbsp;Xiao-hui Liu","doi":"10.1007/s10255-024-1072-0","DOIUrl":"10.1007/s10255-024-1072-0","url":null,"abstract":"<div><p>This paper considers the random coefficient autoregressive model with time-functional variance noises, hereafter the RCA-TFV model. We first establish the consistency and asymptotic normality of the conditional least squares estimator for the constant coefficient. The semiparametric least squares estimator for the variance of the random coefficient and the nonparametric estimator for the variance function are constructed, and their asymptotic results are reported. A simulation study is presented along with an analysis of real data to assess the performance of our method in finite samples.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"40 2","pages":"320 - 346"},"PeriodicalIF":0.9,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140313810","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
Mathematical Analysis on a General Delayed HBV Model with Capsids and Two Infection Routes 带有囊壳和两种感染途径的一般延迟型 HBV 模型的数学分析
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-03-27 DOI: 10.1007/s10255-024-1049-z
Li-li Liu, Hong-gang Wang, Ya-zhi Li
{"title":"Mathematical Analysis on a General Delayed HBV Model with Capsids and Two Infection Routes","authors":"Li-li Liu,&nbsp;Hong-gang Wang,&nbsp;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":"40 2","pages":"508 - 525"},"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}
引用次数: 0
Local Hamilton type Gradient Estimates and Harnack Inequalities for Nonlinear Parabolic Equations on Riemannian Manifolds 黎曼曲面上非线性抛物方程的局部汉密尔顿型梯度估计和哈纳克不等式
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-03-27 DOI: 10.1007/s10255-024-1041-7
Wen Wang, Da-peng Xie, Hui Zhou
{"title":"Local Hamilton type Gradient Estimates and Harnack Inequalities for Nonlinear Parabolic Equations on Riemannian Manifolds","authors":"Wen Wang,&nbsp;Da-peng Xie,&nbsp;Hui Zhou","doi":"10.1007/s10255-024-1041-7","DOIUrl":"10.1007/s10255-024-1041-7","url":null,"abstract":"<div><p>In this paper, we prove a local Hamilton type gradient estimate for positive solution of the nonlinear parabolic equation </p><div><div><span>$${u_t}(x,t) = Delta u(x,t) + au(x,t)ln ,u(x,t) + b{u^alpha }(x,t),$$</span></div></div><p> on <b>M</b> × (−∞, ∞) with <i>α</i> ∈ <b>R</b>, where <i>a</i> and <i>b</i> are constants. As application, the Harnack inequalities are derived.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"40 2","pages":"539 - 546"},"PeriodicalIF":0.9,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140314101","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
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