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Exponential Stabilization of a Semi Linear Third Order in Time Equation with Memory 带记忆的半线性三阶时间方程的指数稳定
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2024-05-27 DOI: 10.1007/s00245-024-10144-3
M. Barbosa da Silva, V. N. Domingos Cavalcanti, E. H. Gomes Tavares, T. Saito Tavares
{"title":"Exponential Stabilization of a Semi Linear Third Order in Time Equation with Memory","authors":"M. Barbosa da Silva,&nbsp;V. N. Domingos Cavalcanti,&nbsp;E. H. Gomes Tavares,&nbsp;T. Saito Tavares","doi":"10.1007/s00245-024-10144-3","DOIUrl":"10.1007/s00245-024-10144-3","url":null,"abstract":"<div><p>We are concerned with a third order in time equation in the presence of viscoelastic effects given by the memory term and with a semi linear source term, posed on a bounded domain <span>(Omega subset mathbb {R}^3 )</span>. Considering three different types of memory in the past history framework, we prove the well-posedness of its solutions as well as the exponential stability of the energy functional. Relaxing some hypotheses on the memory kernel, we improve and extend the results established in the existing literature.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"90 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141170411","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 Explicit Abstract Neutral Differential Equations with State-Dependent Delay 论状态相关延迟的显式抽象中性微分方程
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2024-05-24 DOI: 10.1007/s00245-024-10146-1
Eduardo Hernandez, Michelle Pierri
{"title":"On Explicit Abstract Neutral Differential Equations with State-Dependent Delay","authors":"Eduardo Hernandez,&nbsp;Michelle Pierri","doi":"10.1007/s00245-024-10146-1","DOIUrl":"10.1007/s00245-024-10146-1","url":null,"abstract":"<div><p>We study the local and global existence and uniqueness of a strict solution for a general class of abstract explicit neutral equations with state-dependent delay. Some examples on explicit partial neutral differential equations with state dependent delay are presented.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"89 3","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141102227","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
Inverse Coefficient Problem for the Coupled System of Fourth and Second Order Partial Differential Equations 四阶和二阶偏微分方程耦合系统的反系数问题
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2024-05-21 DOI: 10.1007/s00245-024-10142-5
Navaneetha Krishnan Murugesan, Kumarasamy Sakthivel, Alemdar Hasanov, Barani Balan Natesan
{"title":"Inverse Coefficient Problem for the Coupled System of Fourth and Second Order Partial Differential Equations","authors":"Navaneetha Krishnan Murugesan,&nbsp;Kumarasamy Sakthivel,&nbsp;Alemdar Hasanov,&nbsp;Barani Balan Natesan","doi":"10.1007/s00245-024-10142-5","DOIUrl":"10.1007/s00245-024-10142-5","url":null,"abstract":"<div><p>The study of the paper mainly focuses on recovering the dissipative parameter in a coupled system formed by coupling a bilaplacian operator to a heat equation from final time measured output data via a quasi-solution approach with optimization. The inverse coefficient problem is expressed as a minimization problem. We establish the existence of a minimizer and extract the necessary optimality condition, which is essential in proving the requisite stability result for the inverse coefficient problem. The effectiveness of the proposed approach is demonstrated through an analysis of numerical results using the conjugate gradient approach.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"89 3","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141113475","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 Nonconvex Perturbed Fractional Sweeping Processes 关于非凸扰动分数扫频过程
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2024-05-21 DOI: 10.1007/s00245-024-10139-0
Shengda Zeng, Abderrahim Bouach, Tahar Haddad
{"title":"On Nonconvex Perturbed Fractional Sweeping Processes","authors":"Shengda Zeng,&nbsp;Abderrahim Bouach,&nbsp;Tahar Haddad","doi":"10.1007/s00245-024-10139-0","DOIUrl":"10.1007/s00245-024-10139-0","url":null,"abstract":"<div><p>This paper is devoted to the existence and uniqueness of solution for a large class of perturbed sweeping processes formulated by fractional differential inclusions in infinite dimensional setting. The normal cone to the (mildly non-convex) prox-regular moving set <i>C</i>(<i>t</i>) is supposed to have a Hölder continuous variation, is perturbed by a continuous mapping, which is both time and state dependent. Using an explicit catching-up algorithm, we show that the fractional perturbed sweeping process has one and only one Hölder continuous solution. Then this abstract result is applied to provide a theorem on the weak solvability of a fractional viscoelastic frictionless contact problem. The process is quasistatic and the constitutive relation is modeled with the fractional Kelvin–Voigt law. This application represents an additional novelty of our paper.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"89 3","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141114009","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
An Optimal Control Problem Related to a Parabolic–Elliptic Chemo-repulsion System in 2D Domains 二维域中与抛物线-椭圆化合推进系统相关的优化控制问题
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2024-05-20 DOI: 10.1007/s00245-024-10120-x
Jinxia Cen, Julio Huayta-Centeno, Exequiel Mallea-Zepeda, Shengda Zeng
{"title":"An Optimal Control Problem Related to a Parabolic–Elliptic Chemo-repulsion System in 2D Domains","authors":"Jinxia Cen,&nbsp;Julio Huayta-Centeno,&nbsp;Exequiel Mallea-Zepeda,&nbsp;Shengda Zeng","doi":"10.1007/s00245-024-10120-x","DOIUrl":"10.1007/s00245-024-10120-x","url":null,"abstract":"<div><p>In this paper we study an optimal control problem associated to a parabolic–elliptic chemo-repulsion system with a linear production term in a two-dimensional domain. Under the injection/extract chemical substance on a control subdomain <span>(varOmega _c)</span>, we prove the existence and uniqueness of global-in-time strong solutions. Afterwards, for the optimal control problem, we prove the existence of at least one global optimal solution, and derive an optimality system via using a Lagrange multipliers theorem.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"89 3","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00245-024-10120-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141122778","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
Actor-Critic Reinforcement Learning Algorithms for Mean Field Games in Continuous Time, State and Action Spaces 连续时间、状态和行动空间中平均场博弈的行为批判强化学习算法
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2024-05-20 DOI: 10.1007/s00245-024-10138-1
Hong Liang, Zhiping Chen, Kaili Jing
{"title":"Actor-Critic Reinforcement Learning Algorithms for Mean Field Games in Continuous Time, State and Action Spaces","authors":"Hong Liang,&nbsp;Zhiping Chen,&nbsp;Kaili Jing","doi":"10.1007/s00245-024-10138-1","DOIUrl":"10.1007/s00245-024-10138-1","url":null,"abstract":"<div><p>This paper investigates mean field games in continuous time, state and action spaces with an infinite number of agents, where each agent aims to maximize its expected cumulative reward. Using the technique of randomized policies, we show policy evaluation and policy gradient are equivalent to the martingale conditions of a process by focusing on a representative agent. Then combined with fictitious game, we propose online and offline actor-critic algorithms for solving continuous mean field games that update the value function and policy alternatively under the given population state and action distributions. We demonstrate through two numerical experiments that our proposed algorithms can converge to the mean field equilibrium quickly and stably.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"89 3","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141119120","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
Stochastic Optimal Transport with at Most Quadratic Growth Cost 增长成本最多为二次方的随机优化运输
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2024-05-15 DOI: 10.1007/s00245-024-10141-6
Toshio Mikami
{"title":"Stochastic Optimal Transport with at Most Quadratic Growth Cost","authors":"Toshio Mikami","doi":"10.1007/s00245-024-10141-6","DOIUrl":"10.1007/s00245-024-10141-6","url":null,"abstract":"<div><p>We consider a class of stochastic optimal transport, SOT for short, with given two endpoint marginals in the case where a cost function exhibits at most quadratic growth. We first study the upper and lower estimates, the short-time asymptotics, the zero-noise limits, and the explosion rate as time goes to infinity of SOT. We also show that the value function of SOT is equal to zero or infinity in the case where a cost function exhibits less than linear growth. As a by-product, we characterize the finiteness of the value function of SOT by that of the Monge–Kantorovich problem. As an application, we show the existence of a continuous semimartingale, with given initial and terminal distributions, of which the drift vector is <i>r</i>th integrable for <span>(rin [1,2))</span>. We also consider the same problem for Schrödinger’s problem where <span>(r=2)</span>. This paper is a continuation of our previous work.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"89 3","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141063430","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
Limit Invariant Measures for the Modified Stochastic Swift–Hohenberg Equation in a 3D Thin Domain 三维薄域中修正随机斯威夫特-霍恩伯格方程的极限不变量
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2024-05-13 DOI: 10.1007/s00245-024-10140-7
Guanggan Chen, Wenhu Zhong, Yunyun Wei
{"title":"Limit Invariant Measures for the Modified Stochastic Swift–Hohenberg Equation in a 3D Thin Domain","authors":"Guanggan Chen,&nbsp;Wenhu Zhong,&nbsp;Yunyun Wei","doi":"10.1007/s00245-024-10140-7","DOIUrl":"10.1007/s00245-024-10140-7","url":null,"abstract":"<div><p>This work is concerned with the modified stochastic Swift–Hohenberg equation in a 3D thin domain. Although the diffusion motion of molecules is irregular with the interference of the film-fluid fluctuation, the invariant measure on the trajectory space reveals delicate transition of the dynamical behavior when the interior forces change. We therefore prove that the invariant measure of the system converges weakly to the unique counterpart of the stochastic Swift–Hohenberg equation in a 2D bounded domain with a concrete convergence rate, as the modified parameter and the thickness of the thin domain tend to zero. Furthermore, we address that the smooth density of the limit invariant measure fulfills a Fokker–Planck equation.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"89 3","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140984011","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
Controlling a Nonlinear Fokker–Planck Equation via Inputs with Nonlocal Action 通过非局部作用输入控制非线性福克-普朗克方程
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2024-04-26 DOI: 10.1007/s00245-024-10135-4
Ştefana-Lucia Aniţa
{"title":"Controlling a Nonlinear Fokker–Planck Equation via Inputs with Nonlocal Action","authors":"Ştefana-Lucia Aniţa","doi":"10.1007/s00245-024-10135-4","DOIUrl":"10.1007/s00245-024-10135-4","url":null,"abstract":"<div><p>This paper concerns an optimal control problem (<i>P</i>) associated to a nonlinear Fokker–Planck equation via inputs with nonlocal action. The Fokker–Planck equation describes the dynamics of the probability density of a population under a control that produces a repellent vector field which displaces the population. Actually, problem (<i>P</i>) asks to optimally displace a population via the repellent action produced by the control. The problem is deeply related to a stochastic optimal control problem <span>((P_S))</span> for a McKean–Vlasov equation. The existence of an optimal control is obtained for the deterministic problem (<i>P</i>). The existence of an optimal control is established and necessary optimality conditions are derived for a penalized optimal control problem <span>((P_h))</span> related to a backward Euler approximation of the nonlinear Fokker–Planck equation (with a constant discretization step <i>h</i>). Using a passing-to-the-limit-like argument (as <span>(hrightarrow 0)</span>) one derives the necessary optimality conditions for problem (<i>P</i>). Some possible extensions are discussed as well.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"89 3","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140887600","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
Linear-Quadratic Stochastic Stackelberg Games of N Players for Time-Delay Systems and Related FBSDEs 时延系统的 N 人线性-二次随机斯塔克尔伯格博弈及相关 FBSDEs
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2024-04-20 DOI: 10.1007/s00245-024-10132-7
Na Li, Shujun Wang
{"title":"Linear-Quadratic Stochastic Stackelberg Games of N Players for Time-Delay Systems and Related FBSDEs","authors":"Na Li,&nbsp;Shujun Wang","doi":"10.1007/s00245-024-10132-7","DOIUrl":"10.1007/s00245-024-10132-7","url":null,"abstract":"<div><p>Motivated by the multi-scheme supply chain problem, a linear-quadratic generalized Stackelberg game for time-delay is studied, in which the multi-level hierarchy structure with delay is involved. With the help of the continuity method, we first establish the unique solvability of nonlinear anticipated forward–backward stochastic delayed differential equations with a multi-level self-similar domination-monotonicity structure. Based on it, we derive the Stackelberg equilibrium in this framework. By the theoretical results, a corporate social responsibility problem is studied in the view of a multi-scheme supply chain problem, some simulations are also presented to illustrate the Stackelberg equilibrium in a special case.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"89 3","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140681000","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
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