Acta Applicandae Mathematicae最新文献_第5页

On the Dynamics of Controlled Magnetic Bénard Problem 论受控磁性贝纳德问题的动力学原理

IF 1.2 4区数学

Acta Applicandae Mathematicae Pub Date : 2024-08-02 DOI: 10.1007/s10440-024-00674-x

Dang Thanh Son

引用次数: 0

Global Well-Posedness and Long-Time Asymptotics of a General Nonlinear Non-local Burgers Equation 一般非线性非局部布尔格斯方程的全局拟合性和长期渐近性

IF 1.2 4区数学

Acta Applicandae Mathematicae Pub Date : 2024-07-30 DOI: 10.1007/s10440-024-00672-z

Jin Tan, Francois Vigneron

{"title":"Global Well-Posedness and Long-Time Asymptotics of a General Nonlinear Non-local Burgers Equation","authors":"Jin Tan, Francois Vigneron","doi":"10.1007/s10440-024-00672-z","DOIUrl":"10.1007/s10440-024-00672-z","url":null,"abstract":"<div><p>This paper is concerned with the study of a nonlinear non-local equation that has a commutator structure. The equation reads </p><div><div><span>$$ partial _{t} u-F(u) , (-Delta )^{s/{2}} u+(-Delta )^{s/{2}} (uF(u))=0, quad xin mathbb{T}^{d}, $$</span></div></div><p> with <span>(sin (0, 1])</span>. We are interested in solutions stemming from periodic <i>positive</i> bounded initial data. The given function <span>(Fin mathcal{C}^{infty }(mathbb{R}^{+}))</span> must satisfy <span>(F'>0)</span> a.e. on <span>((0, +infty ))</span>. For instance, all the functions <span>(F(u)=u^{n})</span> with <span>(nin mathbb{N}^{ast })</span> are admissible non-linearities. The local theory can also be developed on the whole space, however the most complete well-posedness result requires the periodic setting. We construct global classical solutions starting from smooth positive data, and global weak solutions starting from positive data in <span>(L^{infty })</span>. We show that any weak solution is instantaneously regularized into <span>(mathcal{C}^{infty })</span>. We also describe the long-time asymptotics of all solutions. Our methods follow several recent advances in the regularity theory of parabolic integro-differential equations, in particular (Ann. Fac. Sci. Toulouse, Math. 25(4):723–758, 2016; Ann. Fac. Sci. Toulouse, Math. 27(4):667–677, 2018).</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"192 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141869216","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

Stability of the Global Weak Axisymmetric Solution to the Quantum Euler System with Vorticity in Dimension (d=2) 具有涡度的量子欧拉系统在维度 $d=2$ 中的全局弱轴对称解的稳定性

IF 1.2 4区数学

Acta Applicandae Mathematicae Pub Date : 2024-07-22 DOI: 10.1007/s10440-024-00663-0

Boris Haspot, Marc-Antoine Vassenet

引用次数: 0

Non-linear Collision-Induced Breakage Equation: Finite Volume and Semi-Analytical Methods 非线性碰撞诱发破损方程：有限体积和半解析方法

IF 1.2 4区数学

Acta Applicandae Mathematicae Pub Date : 2024-07-19 DOI: 10.1007/s10440-024-00671-0

Sanjiv Kumar Bariwal, Saddam Hussain, Rajesh Kumar

{"title":"Non-linear Collision-Induced Breakage Equation: Finite Volume and Semi-Analytical Methods","authors":"Sanjiv Kumar Bariwal, Saddam Hussain, Rajesh Kumar","doi":"10.1007/s10440-024-00671-0","DOIUrl":"10.1007/s10440-024-00671-0","url":null,"abstract":"<div><p>The non-linear collision-induced breakage equation has significant applications in particulate processes. Two semi-analytical techniques, namely homotopy analysis method (HAM) and accelerated homotopy perturbation method (AHPM) are investigated along with the well-known numerical scheme finite volume method (FVM) to comprehend the dynamical behavior of the non-linear system, i.e., the concentration function, the total number, total mass and energy dissipation of the particles in the system. These semi-analytical methods provide approximate analytical solutions by truncating the infinite series form. The theoretical convergence analyses of the series solutions of HAM and AHPM are discussed under some assumptions on the collisional kernels. In addition, the error estimations of the truncated solutions of both methods equip the maximum absolute error bound. Moreover, HAM simulations are computationally costly compared to AHPM because of an additional auxiliary parameter. To justify the applicability and accuracy of these series methods, approximated solutions are compared with the findings of FVM and analytical solutions considering three physical problems.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"192 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141739594","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 Nontrivial Solutions to a Critical Fourth-Order Kirchhoff Type Elliptic Equation 临界四阶基尔霍夫型椭圆方程非微观解的存在性

IF 1.2 4区数学

Acta Applicandae Mathematicae Pub Date : 2024-07-04 DOI: 10.1007/s10440-024-00668-9

Qian Zhang, Yuzhu Han

引用次数: 0

Global Well-Posedness and Exponential Decay of Strong Solution to the Three-Dimensional Nonhomogeneous Bénard System with Density-Dependent Viscosity and Vacuum 具有密度相关粘度和真空的三维非均质贝纳德系统的全局好求和强解的指数衰减

IF 1.2 4区数学

Acta Applicandae Mathematicae Pub Date : 2024-07-04 DOI: 10.1007/s10440-024-00669-8

Huanyuan Li, Jieqiong Liu

引用次数: 0

A New Family of Semi-Norms Between the Berezin Radius and the Berezin Norm 介于贝雷津半径和贝雷津规范之间的新半规范族

IF 1.2 4区数学

Acta Applicandae Mathematicae Pub Date : 2024-07-03 DOI: 10.1007/s10440-024-00667-w

Mojtaba Bakherad, Cristian Conde, Fuad Kittaneh

{"title":"A New Family of Semi-Norms Between the Berezin Radius and the Berezin Norm","authors":"Mojtaba Bakherad, Cristian Conde, Fuad Kittaneh","doi":"10.1007/s10440-024-00667-w","DOIUrl":"10.1007/s10440-024-00667-w","url":null,"abstract":"<div><p>A functional Hilbert space is the Hilbert space ℋ of complex-valued functions on some set <span>(Theta subseteq mathbb{C})</span> such that the evaluation functionals <span>(varphi _{tau }left ( fright ) =fleft ( tau right ) )</span>, <span>(tau in Theta )</span>, are continuous on ℋ. The Berezin number of an operator <span>(X)</span> is defined by <span>(mathbf{ber}(X)=underset{tau in {Theta } }{sup }big vert widetilde{X}(tau )big vert = underset{tau in {Theta } }{sup }big vert langle Xhat{k}_{tau },hat{k}_{tau }rangle big vert )</span>, where the operator <span>(X)</span> acts on the reproducing kernel Hilbert space <span>({mathscr{H}}={mathscr{H}(}Theta ))</span> over some (non-empty) set <span>(Theta )</span>. In this paper, we introduce a new family involving means <span>(Vert cdot Vert _{sigma _{t}})</span> between the Berezin radius and the Berezin norm. Among other results, it is shown that if <span>(Xin {mathscr{L}}({mathscr{H}}))</span> and <span>(f)</span>, <span>(g)</span> are two non-negative continuous functions defined on <span>([0,infty ))</span> such that <span>(f(t)g(t) = t,,(tgeqslant 0))</span>, then </p><div><div><span> $$begin{aligned} Vert XVert ^{2}_{sigma }leqslant textbf{ber}left (frac{1}{4}(f^{4}( vert Xvert )+g^{4}(vert X^{*}vert ))+frac{1}{2}vert Xvert ^{2} right ) end{aligned}$$ </span></div></div><p> and </p><div><div><span> $$begin{aligned} Vert XVert ^{2}_{sigma }leqslant frac{1}{2}sqrt{textbf{ber} left (f^{4}(vert Xvert )+g^{2}(vert Xvert ^{2})right ) textbf{ber}left (f^{2}(vert Xvert ^{2})+g^{4}(vert X^{*}vert ) right )}, end{aligned}$$ </span></div></div><p> where <span>(sigma )</span> is a mean dominated by the arithmetic mean <span>(nabla )</span>.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"192 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141523167","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

Dynamics for a Charge Transfer Model with Cross-Diffusion: Turing Instability of Periodic Solutions 具有交叉扩散的电荷转移模型的动力学：周期解的图灵不稳定性

IF 1.2 4区数学

Acta Applicandae Mathematicae Pub Date : 2024-07-01 DOI: 10.1007/s10440-024-00666-x

Gaihui Guo, Jing You, Xinhuan Du, Yanling Li

引用次数: 0

A New Parallel Algorithm for Solving a Class of Variational Inequalities 求解一类变分不等式的新并行算法

IF 1.2 4区数学

Acta Applicandae Mathematicae Pub Date : 2024-06-19 DOI: 10.1007/s10440-024-00665-y

Nguyen Song Ha, Truong Minh Tuyen, Phan Thi Van Huyen

引用次数: 0

Tumor Growth with a Necrotic Core as an Obstacle Problem in Pressure 带坏死核心的肿瘤生长是压力的一个障碍问题