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Entropic Mean-Field Min–Max Problems via Best Response Flow 基于最佳响应流的熵平均场最小-最大问题
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2025-03-09 DOI: 10.1007/s00245-025-10246-6
Razvan-Andrei Lascu, Mateusz B. Majka, Łukasz Szpruch
{"title":"Entropic Mean-Field Min–Max Problems via Best Response Flow","authors":"Razvan-Andrei Lascu,&nbsp;Mateusz B. Majka,&nbsp;Łukasz Szpruch","doi":"10.1007/s00245-025-10246-6","DOIUrl":"10.1007/s00245-025-10246-6","url":null,"abstract":"<div><p>We investigate the convergence properties of a continuous-time optimization method, the <i>Mean-Field Best Response</i> flow, for solving convex-concave min-max games with entropy regularization. We introduce suitable Lyapunov functions to establish exponential convergence to the unique mixed Nash equilibrium. Additionally, we demonstrate the convergence of the fictitious play flow as a by-product of our analysis.\u0000</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"91 2","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00245-025-10246-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143581128","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Strong Convergence of Solutions and Attractors for Reaction-Diffusion Equations Governed by a Fractional Laplacian 分数阶拉普拉斯控制的反应扩散方程解和吸引子的强收敛性
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2025-03-08 DOI: 10.1007/s00245-025-10242-w
Jiaohui Xu, Tomás Caraballo, José Valero
{"title":"Strong Convergence of Solutions and Attractors for Reaction-Diffusion Equations Governed by a Fractional Laplacian","authors":"Jiaohui Xu,&nbsp;Tomás Caraballo,&nbsp;José Valero","doi":"10.1007/s00245-025-10242-w","DOIUrl":"10.1007/s00245-025-10242-w","url":null,"abstract":"<div><p>A nonlocal reaction-diffusion equation governed by a fractional Laplace operator on a bounded domain is studied in this paper. First, the strong convergence of solutions of the equations governed by fractional Laplacian to the solutions of the classical equations governed by a standard Laplace operator is proved, when the fractional parameter grows to <span>(1)</span>. Second, for the autonomous case, the upper semicontinuity of global attractors with respect to the attractors of the limit problem is established. Apparently, these are the first results for this kind of problems on bounded domains.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"91 2","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00245-025-10242-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143581009","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Convergence of Random Attractors for Stochastic Delay p-Laplacian Equation Driven by Nonlinear Colored Noise on Unbounded Thin Domains 无界薄域上非线性有色噪声驱动的随机延迟p-拉普拉斯方程随机吸引子的收敛性
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2025-03-08 DOI: 10.1007/s00245-025-10244-8
Fuzhi Li, Mirelson M. Freitas
{"title":"Convergence of Random Attractors for Stochastic Delay p-Laplacian Equation Driven by Nonlinear Colored Noise on Unbounded Thin Domains","authors":"Fuzhi Li,&nbsp;Mirelson M. Freitas","doi":"10.1007/s00245-025-10244-8","DOIUrl":"10.1007/s00245-025-10244-8","url":null,"abstract":"<div><p>We study the limiting behavior of solutions for stochastic delay <i>p</i>-Laplacian equation with nonlinear multiplicative colored noise on unbounded thin domains. There are three major ingredients. The first ingredient is to prove the existence and uniqueness of tempered random attractors for these equations. Secondly, the upper semi-continuity of these attractors when a family of <span>((n+1))</span>-dimensional thin domains degenerates onto an <i>n</i>-dimensional domain as the thinness measure approaches zero is established. The final ingredient is to show the upper semi-continuity of these delay random attractors when the length of time delay tends to zero.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"91 2","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00245-025-10244-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143581008","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Observability of the Linear Zakharov–Kuznetsov Equation 线性Zakharov-Kuznetsov方程的可观测性
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2025-03-08 DOI: 10.1007/s00245-025-10248-4
Roberto de A. Capistrano–Filho, Vilmos Komornik, Ademir F. Pazoto
{"title":"Observability of the Linear Zakharov–Kuznetsov Equation","authors":"Roberto de A. Capistrano–Filho,&nbsp;Vilmos Komornik,&nbsp;Ademir F. Pazoto","doi":"10.1007/s00245-025-10248-4","DOIUrl":"10.1007/s00245-025-10248-4","url":null,"abstract":"<div><p>We study the linear Zakharov–Kuznetsov equation with periodic boundary conditions. Employing some tools from the nonharmonic Fourier series we obtain several internal observability theorems. Then we prove various exact controllability and rapid uniform stabilization results by applying a duality principle and a general feedback construction. The method presented here introduces a new insight into the control of dispersive equations in two-dimensional cases and may be adapted to more general equations.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"91 2","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00245-025-10248-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143581007","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Rough Data in an Evolution System Generalizing 1D Thermoviscoelasticity with Temperature-Dependent Parameters 演化系统中的粗略数据泛化了随温度变化的参数的一维热可塑性
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2025-03-06 DOI: 10.1007/s00245-025-10243-9
Michael Winkler
{"title":"Rough Data in an Evolution System Generalizing 1D Thermoviscoelasticity with Temperature-Dependent Parameters","authors":"Michael Winkler","doi":"10.1007/s00245-025-10243-9","DOIUrl":"10.1007/s00245-025-10243-9","url":null,"abstract":"<div><p>A Neumann-type initial-boundary value problem for </p><div><div><span>$$begin{aligned} left{ begin{array}{l} u_{tt} = nabla cdot (gamma (Theta ) nabla u_t) + a nabla cdot (gamma (Theta ) nabla u) + nabla cdot f(Theta ), Theta _t = DDelta Theta + Gamma (Theta ) |nabla u_t|^2 + F(Theta )cdot nabla u_t, end{array} right. end{aligned}$$</span></div></div><p>is considered in a smoothly bounded domain <span>(Omega subset mathbb {R}^n)</span>, <span>(nge 1)</span>. In the case when <span>(n=1)</span>, <span>(gamma equiv Gamma )</span> and <span>(fequiv F)</span>, this system coincides with the standard model for heat generation in a viscoelastic material of Kelvin-Voigt type, well-understood in situations in which <span>(gamma =const)</span>. Covering scenarios in which all key ingredients <span>(gamma ,Gamma ,f)</span> and <i>F</i> may depend on the temperature <span>(Theta )</span> here, for initial data which merely satisfy <span>(u_0in W^{1,p+2}(Omega ))</span>, <span>(u_{0t}in W^{1,p}(Omega ))</span> and <span>(Theta _0in W^{1,p}(Omega ))</span> with some <span>(pge 2)</span> such that <span>(p&gt;n)</span>, a result on local-in-time existence and uniqueness is derived in a natural framework of weak solvability.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"91 2","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00245-025-10243-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143564455","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Stochastic Linear-Quadratic Optimal Control Problems with Multi-dimensional State, Random Coefficients and Regime Switching 具有多维状态、随机系数和状态切换的随机线性二次最优控制问题
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2025-03-05 DOI: 10.1007/s00245-025-10235-9
Yuyang Chen, Peng Luo
{"title":"Stochastic Linear-Quadratic Optimal Control Problems with Multi-dimensional State, Random Coefficients and Regime Switching","authors":"Yuyang Chen,&nbsp;Peng Luo","doi":"10.1007/s00245-025-10235-9","DOIUrl":"10.1007/s00245-025-10235-9","url":null,"abstract":"<div><p>This paper investigates the stochastic linear-quadratic (LQ, for short) optimal control problems with random coefficients and regime switching in a finite time horizon where the state equation is multi-dimensional. Similar to the classical stochastic LQ problems, we establish the relationship between the stochastic LQ optimal control problems with regime switching and the related extended stochastic Riccati equations. To solve the extended stochastic Riccati equations, we construct a monotone Piccard iterative sequence and present the link between this sequence and solutions of a family of forward-backward stochastic differential equations. Relying on <span>(L^p)</span> estimates for FBSDEs, we show that the extended stochastic Riccati equation has a solution. This partially addresses one question left in Hu et al. (Ann. Appl. Probab. 32(1): 426-460, 2022). Finally, the stochastic LQ optimal control problems with regime switching is solved.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"91 2","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143553939","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
Boundary Controllability for Degenerate/Singular Hyperbolic Equations in Nondivergence Form with Drift 具有漂移的退化/奇异双曲型非散型方程的边界可控性
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2025-03-05 DOI: 10.1007/s00245-025-10236-8
Genni Fragnelli, Dimitri Mugnai, Amine Sbai
{"title":"Boundary Controllability for Degenerate/Singular Hyperbolic Equations in Nondivergence Form with Drift","authors":"Genni Fragnelli,&nbsp;Dimitri Mugnai,&nbsp;Amine Sbai","doi":"10.1007/s00245-025-10236-8","DOIUrl":"10.1007/s00245-025-10236-8","url":null,"abstract":"<div><p>We study the null controllability for a degenerate/singular wave equation with drift in non divergence form. In particular, considering a control localized on the non degenerate boundary point, we provide some conditions for the boundary controllability via energy methods and boundary observability.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"91 2","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00245-025-10236-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143553938","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 Generalization of Hoffman’s Lemma in Banach Spaces and Applications Banach空间中Hoffman引理的推广及其应用
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2025-02-24 DOI: 10.1007/s00245-025-10238-6
Nguyen Quang Huy, Hoang Ngoc Tuan, Nguyen Dong Yen
{"title":"A Generalization of Hoffman’s Lemma in Banach Spaces and Applications","authors":"Nguyen Quang Huy,&nbsp;Hoang Ngoc Tuan,&nbsp;Nguyen Dong Yen","doi":"10.1007/s00245-025-10238-6","DOIUrl":"10.1007/s00245-025-10238-6","url":null,"abstract":"<div><p>A generalized version of an important theorem called Hoffman’s lemma in the book by Bonnans and Shapiro (Perturbation analysis of optimization problems, Springer, Berlin, 2000), which deals with generalized polyhedral convex multifunctions, is obtained in this paper. Under a mild assumption, the result allows us to demonstrate that the domain of a generalized polyhedral convex multifunction is closed and the multifunction is Lipschitz continuous on its effective domain. As concrete applications of the results, we prove some local error bounds for generalized affine variational inequalities and a theorem on the (strong) convergence of feasible descent methods for solving generalized quadratic programming problems.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"91 2","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143475282","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
Systematic Design of Compliant Morphing Structures: A Phase-Field Approach 柔性变形结构的系统设计：相场法
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2025-02-24 DOI: 10.1007/s00245-025-10237-7
Jamal Shabani, Kaushik Bhattacharya, Blaise Bourdin
{"title":"Systematic Design of Compliant Morphing Structures: A Phase-Field Approach","authors":"Jamal Shabani,&nbsp;Kaushik Bhattacharya,&nbsp;Blaise Bourdin","doi":"10.1007/s00245-025-10237-7","DOIUrl":"10.1007/s00245-025-10237-7","url":null,"abstract":"<div><p>We investigate the systematic design of compliant morphing structures composed of materials reacting to an external stimulus. We add a perimeter penalty term to ensure existence of solutions. We propose a phase-field approximation of this sharp interface problem, prove its convergence as the regularization length approaches 0 and present an efficient numerical implementation. We illustrate the strengths of our approach through a series of numerical examples.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"91 2","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143475283","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 Nonlocal Cahn–Hilliard–Darcy System with Singular Potential, Degenerate Mobility, and Sources 具有奇异势、简并迁移率和源的非局部Cahn-Hilliard-Darcy系统
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2025-02-21 DOI: 10.1007/s00245-025-10239-5
Cecilia Cavaterra, Sergio Frigeri, Maurizio Grasselli
{"title":"A Nonlocal Cahn–Hilliard–Darcy System with Singular Potential, Degenerate Mobility, and Sources","authors":"Cecilia Cavaterra,&nbsp;Sergio Frigeri,&nbsp;Maurizio Grasselli","doi":"10.1007/s00245-025-10239-5","DOIUrl":"10.1007/s00245-025-10239-5","url":null,"abstract":"<div><p>We consider a Cahn–Hilliard–Darcy system for an incompressible mixture of two fluids we already analyzed in [9]. In this system, the relative concentration difference <span>(varphi )</span> obeys a convective nonlocal Cahn–Hilliard equation with degenerate mobility and singular (e.g., logarithmic) potential, while the volume averaged fluid velocity <span>(varvec{u})</span> is given by a Darcy’s law subject to the Korteweg force <span>(mu nabla varphi )</span>, where the chemical potential <span>(mu )</span> is defined by means of a nonlocal Helmholtz free energy. The kinematic viscosity <span>(eta )</span> depends on <span>(varphi )</span>. With respect to the quoted contribution, here we assume that the Darcy’s law is subject to gravity and to a given additional source. Moreover, we suppose that the Cahn–Hilliard equation and the chemical potential contain source terms. Our main goal is to establish the existence of two notions of weak solutions. The first, called “generalized” weak solution, is based a convenient splitting of <span>(mu )</span> so that the entropy derivative does not need to be integrable. The second is slightly stronger and allows to reconstruct <span>(mu )</span> and to prove the validity of a canonical energy identity. For this reason, the latter is called “natural” weak solution. The rigorous relation between the two notions of weak solution is also analyzed. The existence of a global attractor for generalized weak solutions and time independent sources is then demonstrated via the theory of generalized semiflows introduced by J.M. Ball.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"91 2","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00245-025-10239-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143455656","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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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