Applied Mathematics and Optimization最新文献

Modelling of Poro-Acoustic Media 多孔声介质的建模

IF 1.7 2区数学

Applied Mathematics and Optimization Pub Date : 2025-10-10 DOI: 10.1007/s00245-025-10338-3

Isabelle Gruais

引用次数: 0

Prescribed Signal Concentration on the Boundary: Radial Solutions to a Chemotaxis System with Proliferation and Nonlinear Consumption 边界上的规定信号浓度：具有扩散和非线性消耗的趋化系统的径向解

IF 1.7 2区数学

Applied Mathematics and Optimization Pub Date : 2025-10-10 DOI: 10.1007/s00245-025-10315-w

Zhan Jiao, Irena Jadlovská, Tongxing Li

{"title":"Prescribed Signal Concentration on the Boundary: Radial Solutions to a Chemotaxis System with Proliferation and Nonlinear Consumption","authors":"Zhan Jiao, Irena Jadlovská, Tongxing Li","doi":"10.1007/s00245-025-10315-w","DOIUrl":"10.1007/s00245-025-10315-w","url":null,"abstract":"<div>The chemotaxis model <div><div>$$begin{aligned} left{ begin{array}{l} begin{aligned} & u_t = Delta u-chi nabla cdot (g(u)nabla v)+ku-mu u^l, & xin Omega , t>0& , & v_t=Delta v-g(u)v, & xin Omega , t>0& end{aligned} end{array} right. end{aligned}$$</div></div>is considered under the boundary conditions (frac{partial u}{partial nu }-chi g(u)frac{partial v}{partial nu }=0) and (v=v_*) on (partial Omega), where (Omega subset {mathbb {R}}^n) ((nin {2,3})) is a ball and (v_*) is a given positive constant. Here, the parameters (chi ,k,mu) are positive and the function (gin C^1([0,infty ))) satisfies (0le g(u)le u^{beta }) with (frac{5}{6}le beta <1). For all suitably regular initial data, the present work provides a result on global boundedness of the radially symmetric classical solution in two dimensions when (beta =chi) and (1<l<frac{5}{3}), while the global existence of the radially symmetric weak solution is established in three-dimensional settings.</div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"92 2","pages":""},"PeriodicalIF":1.7,"publicationDate":"2025-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145256138","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Correction: Constructive approximate transport maps with normalizing flows 更正：具有正规化流的建设性近似运输图

IF 1.7 2区数学

Applied Mathematics and Optimization Pub Date : 2025-10-08 DOI: 10.1007/s00245-025-10340-9

Antonio Álvarez-López, Borjan Geshkovski, Domènec Ruiz-Balet

引用次数: 0

Exact Controllability for Wave Equation on General Metric Graphs with Non-smooth Controls 具有非光滑控制的一般度量图上波动方程的精确可控性

IF 1.7 2区数学

Applied Mathematics and Optimization Pub Date : 2025-10-08 DOI: 10.1007/s00245-025-10329-4

Avdonin Sergei, Edward Julian

引用次数: 0

Well-Posedness and Asymptotic Analysis of Wave Equation with Nonlocal Boundary Damping 非局部边界阻尼波动方程的适定性及渐近分析

IF 1.7 2区数学

Applied Mathematics and Optimization Pub Date : 2025-09-30 DOI: 10.1007/s00245-025-10327-6

Marcelo M. Cavalcanti, Adel M. Al-Mahdi, Mohammad M. Al-Gharabli, Cintya A. Okawa

引用次数: 0

Generalized exponential ({mathfrak {D}}_{mathcal {C}^*})–pullback attractor for a nonautonomous wave equation 非自治波动方程的广义指数({mathfrak {D}}_{mathcal {C}^*}) -回拉吸引子

IF 1.7 2区数学

Applied Mathematics and Optimization Pub Date : 2025-09-30 DOI: 10.1007/s00245-025-10330-x

Matheus C. Bortolan, Tomás Caraballo, Carlos Pecorari Neto

{"title":"Generalized exponential ({mathfrak {D}}_{mathcal {C}^*})–pullback attractor for a nonautonomous wave equation","authors":"Matheus C. Bortolan, Tomás Caraballo, Carlos Pecorari Neto","doi":"10.1007/s00245-025-10330-x","DOIUrl":"10.1007/s00245-025-10330-x","url":null,"abstract":"<div>In this work we introduce the concept of generalized exponential ({mathfrak {D}}_{mathcal {C}^*})–pullback attractors for evolution processes, which are compact and positively invariant families that pullback attract all elements of a universe of families ({mathfrak {D}}_{mathcal {C}^*}), with an exponential rate. Such concept, within the pullback framework for nonautonomous problems, was introduced in Bortolan et al. (Appl Math Optim 89(62):1–52, 2024) for more general decay functions (which include the exponential decay), but for fixed bounded sets rather than for a universe of families, and was inspired by Zhao et al. (Estimate of the attractive velocity of attractors for some dynamical systems, http://arxiv.org/abs/2108.07410, 2021), which dealt with the autonomous case. We prove a result that ensures the existence of a generalized exponential ({mathfrak {D}}_{mathcal {C}^*})–pullback attractor for an evolution process, using the concept of pullback (kappa )–dissipativity for evolution processes with respect to a general universe ({mathfrak {D}}). This required an adaptation of the results presented in Bortolan et al. (Appl Math Optim 89(62):1–52, 2024), which only covered the case of a polynomial rate of attraction for fixed bounded sets. Later, we prove that a nonautonomous wave equation has a generalized exponential ({mathfrak {D}}_{mathcal {C}^*})–pullback attractor. This, in turn, also implies the existence of the ({mathfrak {D}}_{mathcal {C}^*})–pullback attractor for such problem.</div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"92 2","pages":""},"PeriodicalIF":1.7,"publicationDate":"2025-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145210950","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

A Control Theoretical Approach to Mean Field Games: Part I—Global Equilibrium Solution 平均场博弈的控制理论方法：第1部分：全局均衡解

IF 1.7 2区数学

Applied Mathematics and Optimization Pub Date : 2025-09-30 DOI: 10.1007/s00245-025-10324-9

Alain Bensoussan, Ho Man Tai, Tak Kwong Wong, Sheung Chi Phillip Yam

{"title":"A Control Theoretical Approach to Mean Field Games: Part I—Global Equilibrium Solution","authors":"Alain Bensoussan, Ho Man Tai, Tak Kwong Wong, Sheung Chi Phillip Yam","doi":"10.1007/s00245-025-10324-9","DOIUrl":"10.1007/s00245-025-10324-9","url":null,"abstract":"<div>We establish the global-in-time well-posedness for a broad class of mean field games including those with the small mean field sensitivity and the linear-quadratic setting as special cases. Instead of using the master equation approach, we adopt the maximum principle to investigate the unique existence of the equilibrium strategy by solving the corresponding forward-backward stochastic differential equations (FBSDEs), whose global existence is shown by controlling the sensitivity of the backward solutions with respect to the initial data via new a priori estimates for the corresponding Jacobian flows. Besides, we provide the state-of-the-art study with general cost functions having both quadratic growth and non-convexity in the state variable. We also impose the structural conditions on the cost functions but not on the Hamiltonian. The advantages of this framework are threefold: (i) the structural conditions can be easily verified; (ii) reduced regularity of cost functions suffices for the unique existence of equilibrium solutions compared to solving the master equations; and (iii) when the mean field effect is not small, the cost functions are not convex in the state variable, or there is lack of monotonicity of cost functions, an accurate lifespan for the local existence of the FBSDEs is still given, which is not small in general. Finally, we provide a counterexample to illustrate the ill-posedness of the mean field games when the small mean field effect and the contemporary monotonicity conditions are violated, this demonstrates numerically that our assumptions should be sharp.</div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"92 2","pages":""},"PeriodicalIF":1.7,"publicationDate":"2025-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145210951","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

On the Improvement of the Barzilai–Borwein Step Size in Variance Reduction Methods 方差缩减方法中Barzilai-Borwein步长的改进

IF 1.7 2区数学

Applied Mathematics and Optimization Pub Date : 2025-09-27 DOI: 10.1007/s00245-025-10316-9

Hai Liu, Yan Liu, Tiande Guo, Congying Han

{"title":"On the Improvement of the Barzilai–Borwein Step Size in Variance Reduction Methods","authors":"Hai Liu, Yan Liu, Tiande Guo, Congying Han","doi":"10.1007/s00245-025-10316-9","DOIUrl":"10.1007/s00245-025-10316-9","url":null,"abstract":"<div>We propose several modifications of the Barzilai–Borwein (BB) step size in the variance reduction (VR) methods for finite-sum optimization problems. Our first approach relies on a scalar function, which we call the TaiL Function (TLF). The TLF maps the computed BB step size to some positive real number, which will be used as the step size instead. The computational overhead is almost negligible and the functional forms of TLFs in this work don’t involve any problem-dependent parameters. In the strongly convex setting, due to the undesirable appearance of the condition number (kappa ) in the linear convergence rate, the IFO complexity of VR methods with BB step size has the form (mathcal {O}((n+kappa ^a)kappa log (1/epsilon ))), (ain mathbb {R}_{+}). With the utilization of the TLF, the aforementioned complexity is improved to (mathcal {O}((n+kappa ^{tilde{a}})log (1/epsilon ))), (tilde{a}in mathbb {R}_{+}, tilde{a}<a). In the non-convex setting, we improve (mathcal {O}(n+nepsilon ^{-1})) of SVRG-SBB to (mathcal {O}(n+n^{beta }epsilon ^{-1})), where (beta in mathbb {R}_{+}) can take any value in (2/3, 1). Specifically, the constant step size regime is recovered by taking the TLF as a constant function, whose function value relies on problem-dependent parameters. As a counterpart of the constant step size regime, we also propose a BB-based vibration technique to set step sizes for VR methods, leading to methods with novel one-parameter step sizes. These methods have the same complexities compared to their constant step size versions. Meanwhile, they are more robust w.r.t. the sole step size parameter empirically. Moreover, a novel analysis is proposed for SARAH-I-type methods in the strongly convex setting. Numerical tests corroborate the proposed methods.</div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"92 2","pages":""},"PeriodicalIF":1.7,"publicationDate":"2025-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145210836","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Correction: Two-Player Diffusion Control Games with Private Information 修正：带有私人信息的二人扩散控制博弈

IF 1.7 2区数学

Applied Mathematics and Optimization Pub Date : 2025-09-27 DOI: 10.1007/s00245-025-10339-2

Julian Wendt

引用次数: 0

Mathematical and Numerical Investigation of the Exponential Stability of Piezoelectric Beams Under Magnetic and Microtemperature Effects 磁和微温度作用下压电梁指数稳定性的数学和数值研究

IF 1.7 2区数学

Applied Mathematics and Optimization Pub Date : 2025-09-20 DOI: 10.1007/s00245-025-10308-9

Carlos A. S. Nonato, Vinicius S. Paula, Jorge A. J. Avila, Flávio A. F. Nascimento

引用次数: 0