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Convergence of Random Attractors for Stochastic Delay p-Laplacian Equation Driven by Nonlinear Colored Noise on Unbounded Thin Domains
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
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
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
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
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
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
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
Mean-Field Partial Information Non-zero Sum Stochastic Differential Games
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2025-02-19 DOI: 10.1007/s00245-025-10233-x
Tianyang Nie, Ke Yan
{"title":"Mean-Field Partial Information Non-zero Sum Stochastic Differential Games","authors":"Tianyang Nie,&nbsp;Ke Yan","doi":"10.1007/s00245-025-10233-x","DOIUrl":"10.1007/s00245-025-10233-x","url":null,"abstract":"<div><p>In this paper, we study a general mean-field partial information non-zero sum stochastic differential game, in which the dynamic of state is described by a stochastic differential equation (SDE) depending on the distribution of the state and the control domain of each player can be non-convex. Moreover, the control variables of both players can enter the diffusion coefficients of the state equation. We establish a necessary condition in the form of Pontryagin’s maximum principle for optimality. Then a verification theorem is obtained for optimal control when the control domain is convex. As an application, our results are applied to studying linear–quadratic (LQ) mean-field game in the type of scalar interaction.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"91 2","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143438720","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: Optimality Conditions for Sparse Optimal Control of Viscous Cahn–Hilliard Systems with Logarithmic Potential
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2025-02-19 DOI: 10.1007/s00245-025-10234-w
Pierluigi Colli, Jürgen Sprekels, Fredi Tröltzsch
{"title":"Correction: Optimality Conditions for Sparse Optimal Control of Viscous Cahn–Hilliard Systems with Logarithmic Potential","authors":"Pierluigi Colli,&nbsp;Jürgen Sprekels,&nbsp;Fredi Tröltzsch","doi":"10.1007/s00245-025-10234-w","DOIUrl":"10.1007/s00245-025-10234-w","url":null,"abstract":"","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"91 2","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00245-025-10234-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143446516","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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