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Exact Controllability of Hemivariational Inequalities in Banach spaces Banach空间中半变分不等式的精确可控性
IF 1.7 2区 数学
Applied Mathematics and Optimization Pub Date : 2025-08-04 DOI: 10.1007/s00245-025-10294-y
Bholanath Kumbhakar, Dwijendra Narain Pandey
{"title":"Exact Controllability of Hemivariational Inequalities in Banach spaces","authors":"Bholanath Kumbhakar,&nbsp;Dwijendra Narain Pandey","doi":"10.1007/s00245-025-10294-y","DOIUrl":"10.1007/s00245-025-10294-y","url":null,"abstract":"<div><p>The paper is concerned with the exact controllability of the problems described by an evolution of hemivariational inequalities within the framework of reflexive state spaces and uniformly convex control spaces, where the controls are drawn from the space <span>(L^p(I, U))</span>, <span>(~1&lt;p&lt;infty )</span>. We first introduce an appropriate definition for solutions to the hemivariational inequality problem, as this has not been previously established in the literature. Using this solution framework, we demonstrate that the solutions of the associated differential inclusion problem involving the Clarke subdifferential operator also serve as solutions to the original problem. Consequently, we establish the exact controllability of the original problem through the exact controllability of the corresponding differential inclusion problem. This work presents a novel approach by assuming that the control space <i>U</i> is a uniformly convex Banach space, which helps resolve challenges related to convexity in constructing the necessary control–a difficulty that does not arise when <i>U</i> is a separable Hilbert space.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"92 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2025-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145161768","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
Observability Inequalities of a Semi-discrete Schrödinger Integro-Differential Equation Derived from a Mixed Finite Element Method 由混合有限元法导出的半离散Schrödinger积分-微分方程的可观察性不等式
IF 1.7 2区 数学
Applied Mathematics and Optimization Pub Date : 2025-08-04 DOI: 10.1007/s00245-025-10298-8
Da Xu
{"title":"Observability Inequalities of a Semi-discrete Schrödinger Integro-Differential Equation Derived from a Mixed Finite Element Method","authors":"Da Xu","doi":"10.1007/s00245-025-10298-8","DOIUrl":"10.1007/s00245-025-10298-8","url":null,"abstract":"<div><p>We will consider the use of mixed finite element method for the semi-discretization of the Schrödinger integro-differential systems. We investigate the problem of boundary observability for the semi-discrete models. We show that the semi-discretization based on a mixed finite element method with two different basis functions for the position and its differentiation with respect to time of Schrödinger type integro-differential equation, are uniformly observability as the discretization parameter <i>h</i> goes to zero. Some numerical results are given to illustrate our theoretical finds.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"92 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2025-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145161760","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
Approximation and Characterization of Elastic Relaxed Dirichlet Problems and Shape Optimization 弹性松弛狄利克雷问题的逼近与表征及形状优化
IF 1.7 2区 数学
Applied Mathematics and Optimization Pub Date : 2025-07-31 DOI: 10.1007/s00245-025-10286-y
Mustapha El Jarroudi, Riane Hajjami, Haifa El Jarroudi, Hasan Karjoun, Youness Filali
{"title":"Approximation and Characterization of Elastic Relaxed Dirichlet Problems and Shape Optimization","authors":"Mustapha El Jarroudi,&nbsp;Riane Hajjami,&nbsp;Haifa El Jarroudi,&nbsp;Hasan Karjoun,&nbsp;Youness Filali","doi":"10.1007/s00245-025-10286-y","DOIUrl":"10.1007/s00245-025-10286-y","url":null,"abstract":"<div><p>In this study, we consider a relaxed Dirichlet problem in linear elasticity, which is a generalized Dirichlet problem for homogeneous linear elastic materials involving a potential in the form of a symmetric and positive semi-definite matrix of Borel measures that do not charge polar sets. We present an explicit approximation procedure by means of sequences of classical Dirichlet problems in strongly perturbed domains. Then, we give a characterization of these measures, when the components of the data are nonnegative, in terms of solutions in closed convex sets of particular relaxed Dirichlet problems. Finally, we give some applications to the shape optimization for Dirichlet problems in the linear elasticity framework.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"92 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2025-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145171872","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
Uniform Exponential Stability and Control Convergence of Semi-discrete Scheme for a Timoshenko Beam Timoshenko梁半离散格式的一致指数稳定性和控制收敛性
IF 1.7 2区 数学
Applied Mathematics and Optimization Pub Date : 2025-07-26 DOI: 10.1007/s00245-025-10292-0
Fu Zheng, Zhen Jia, Bao-Zhu Guo
{"title":"Uniform Exponential Stability and Control Convergence of Semi-discrete Scheme for a Timoshenko Beam","authors":"Fu Zheng,&nbsp;Zhen Jia,&nbsp;Bao-Zhu Guo","doi":"10.1007/s00245-025-10292-0","DOIUrl":"10.1007/s00245-025-10292-0","url":null,"abstract":"<div><p>This paper considers numerical approximations of a Timoshenko beam under boundary control. The continuous system under boundary feedback is known to be exponentially stable. Firstly, the continuous system is transformed into an equivalent first-order port-Hamiltonian formulation. A basically order reduction finite difference scheme is applied to derive a family of semi-discretized systems. Secondly, a completely new method which is based on a mixed discrete observability inequality involving final state observability and exact observability is developed to prove the uniform exponential stability of the discrete systems. More interestingly, the proof for the stability of discrete systems is almost parallel to that of the continuous counterpart. Thirdly, the solutions of the semi-discretized systems are shown to be strongly convergent to the solution of the original system through Trotter-Kato theorem. Finally, both exact controllability of continuous system and the discrete systems are proved in light of Russell’s “controllability via stability” principle and the explicit controls are derived. Moreover, the discrete controls are shown in first time to be convergent to the continuous control by proposed approach.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"92 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2025-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145168923","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
Fitted Value Iteration Methods for Bicausal Optimal Transport 双例最优运输的拟合值迭代方法
IF 1.7 2区 数学
Applied Mathematics and Optimization Pub Date : 2025-07-26 DOI: 10.1007/s00245-025-10283-1
Erhan Bayraktar, Bingyan Han
{"title":"Fitted Value Iteration Methods for Bicausal Optimal Transport","authors":"Erhan Bayraktar,&nbsp;Bingyan Han","doi":"10.1007/s00245-025-10283-1","DOIUrl":"10.1007/s00245-025-10283-1","url":null,"abstract":"<div><p>We develop a fitted value iteration (FVI) method to compute bicausal optimal transport (OT) where couplings have an adapted structure. Based on the dynamic programming formulation, FVI adopts a function class to approximate the value functions in bicausal OT. Under the concentrability condition and approximate completeness assumption, we prove the sample complexity using (local) Rademacher complexity. Furthermore, we demonstrate that multilayer neural networks with appropriate structures satisfy the crucial assumptions required in sample complexity proofs. Numerical experiments reveal that FVI outperforms linear programming and adapted Sinkhorn methods in scalability as the time horizon increases, while still maintaining acceptable accuracy.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"92 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2025-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145168924","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
Relationship Between Stochastic Maximum Principle and Dynamic Programming Principle Under Convex Expectation 凸期望下随机极大值原理与动态规划原理的关系
IF 1.7 2区 数学
Applied Mathematics and Optimization Pub Date : 2025-07-22 DOI: 10.1007/s00245-025-10291-1
Xiaojuan Li, Mingshang Hu
{"title":"Relationship Between Stochastic Maximum Principle and Dynamic Programming Principle Under Convex Expectation","authors":"Xiaojuan Li,&nbsp;Mingshang Hu","doi":"10.1007/s00245-025-10291-1","DOIUrl":"10.1007/s00245-025-10291-1","url":null,"abstract":"<div><p>In this paper, we study the relationship between maximum principle (MP) and dynamic programming principle (DPP) for forward–backward control system under consistent convex expectation dominated by <i>G</i> -expectation. Under the smooth assumptions for the value function, we get the relationship between MP and DPP under a reference probability by establishing a useful estimate. If the value function is not smooth, then we obtain the first-order sub-jet and super-jet of the value function at any <i>t</i>. However, the processing method in this case is much more difficult than that when <i>t</i> equals 0.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"92 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2025-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145167465","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
Numerical Solution by Shape Optimization Method to an Inverse Shape Problem in Multi-dimensional Advection–Diffusion Problem with Space Dependent Coefficients 具有空间相关系数的多维平流扩散问题中反形状问题的形状优化数值解
IF 1.7 2区 数学
Applied Mathematics and Optimization Pub Date : 2025-07-18 DOI: 10.1007/s00245-025-10290-2
Elmehdi Cherrat, Lekbir Afraites, Julius Fergy T. Rabago
{"title":"Numerical Solution by Shape Optimization Method to an Inverse Shape Problem in Multi-dimensional Advection–Diffusion Problem with Space Dependent Coefficients","authors":"Elmehdi Cherrat,&nbsp;Lekbir Afraites,&nbsp;Julius Fergy T. Rabago","doi":"10.1007/s00245-025-10290-2","DOIUrl":"10.1007/s00245-025-10290-2","url":null,"abstract":"<div><p>This work focuses on numerically solving a shape identification problem related to advection–diffusion processes with space-dependent coefficients using shape optimization techniques. Two boundary-type cost functionals are considered, and their corresponding variations with respect to shapes are derived using the adjoint method, employing the chain rule approach. This involves firstly utilizing the material derivative of the state system and secondly using its shape derivative. Subsequently, an alternating direction method of multipliers (ADMM) combined with the Sobolev-gradient-descent algorithm is applied to stably solve the shape reconstruction problem. Numerical experiments in two and three dimensions are conducted to demonstrate the feasibility of the methods.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"92 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2025-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145167362","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
Concentration Phenomena of Sign-Changing Solutions for the Planar Schrödinger-Poisson Systems 平面Schrödinger-Poisson系统变符号解的集中现象
IF 1.7 2区 数学
Applied Mathematics and Optimization Pub Date : 2025-07-18 DOI: 10.1007/s00245-025-10289-9
Yiqing Li, Patrizia Pucci, Binlin Zhang
{"title":"Concentration Phenomena of Sign-Changing Solutions for the Planar Schrödinger-Poisson Systems","authors":"Yiqing Li,&nbsp;Patrizia Pucci,&nbsp;Binlin Zhang","doi":"10.1007/s00245-025-10289-9","DOIUrl":"10.1007/s00245-025-10289-9","url":null,"abstract":"<div><p>This paper investigates the existence and concentration behavior of nodal solutions for the planar Schrödinger-Poisson system with subcritical exponential growth </p><div><div><span>$$begin{aligned} left{ begin{array}{l} -Delta u+V(varepsilon x)u+mu phi u= f(u) text{ in } {mathbb {R}}^2, Delta phi =u^2 text{ in } {mathbb {R}}^2, end{array}right. qquad qquad qquad ({mathcal {S}}) end{aligned}$$</span></div></div><p>where <span>(varepsilon, mu &gt;0)</span> are parameters, <i>V</i> and <i>f</i> are continuous functions. Under suitable assumptions, the existence of nodal solutions is established, using variational methods. Furthermore, we prove that the nodal solutions of (<span>({mathcal {S}})</span>) concentrate around the minimum point of <i>V</i> and exhibit exponential decay at infinity.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"92 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2025-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145167365","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
Multi-parameter Robustness of Random Attractors for Non-autonomous Stochastic Lamé Systems 非自治随机lam<s:1>系统随机吸引子的多参数鲁棒性
IF 1.7 2区 数学
Applied Mathematics and Optimization Pub Date : 2025-07-17 DOI: 10.1007/s00245-025-10285-z
Taís Saito Tavares, Mirelson M. Freitas, Xin-Guang Yang, Jinyun Yuan
{"title":"Multi-parameter Robustness of Random Attractors for Non-autonomous Stochastic Lamé Systems","authors":"Taís Saito Tavares,&nbsp;Mirelson M. Freitas,&nbsp;Xin-Guang Yang,&nbsp;Jinyun Yuan","doi":"10.1007/s00245-025-10285-z","DOIUrl":"10.1007/s00245-025-10285-z","url":null,"abstract":"<div><p>In this work, the multi-parameter robustness of pullback random attractors for Lamé systems is investigated. More precisely, this robustness reveals how smooth is the transition from the non-autonomous stochastic setting to the autonomous deterministic one. This is achieved by establishing the upper semicontinuity for a three-parameter family of pullback random attractors.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"92 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2025-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145166395","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
Finite-Time Blowup in a Parabolic-Parabolic-Elliptic Chemotaxis Model Involving Indirect Signal Production 含间接信号产生的抛物-抛物-椭圆趋化性模型的有限时间爆破
IF 1.7 2区 数学
Applied Mathematics and Optimization Pub Date : 2025-07-08 DOI: 10.1007/s00245-025-10287-x
Xuan Mao, Yuxiang Li
{"title":"Finite-Time Blowup in a Parabolic-Parabolic-Elliptic Chemotaxis Model Involving Indirect Signal Production","authors":"Xuan Mao,&nbsp;Yuxiang Li","doi":"10.1007/s00245-025-10287-x","DOIUrl":"10.1007/s00245-025-10287-x","url":null,"abstract":"<div><p>This paper is concerned with a three-component chemotaxis model accounting for indirect signal production, reading as <span>(u_t = nabla cdot (nabla u - unabla v))</span>, <span>(v_t = Delta v - v + w)</span> and <span>(0 = Delta w - w + u)</span>, posed in a ball of <span>(mathbb {R}^n)</span> with <span>(nge 5)</span>, subject to homogeneous Neumann boundary conditions. The system is a Nagai-type variant of its fully parabolic version that has a four-dimensional critical mass phenomenon concerning blowup in finite or infinite time according to the seminal works of Fujie and Senba [J. Differential Equations, 263 (2017), 88–148; 266 (2019), 942–976]. We prove that for any prescribed mass <span>(m &gt; 0)</span>, there exist radially symmetric and positive initial data <span>((u_0,v_0)in C^0(overline{Omega })times C^2(overline{Omega }))</span> with <span>(int _Omega u_0 = m)</span> such that the corresponding solutions blow up in finite time.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"92 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2025-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145163359","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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