SIAM Journal on Control and Optimization, Volume 62, Issue 1, Page 630-649, February 2024. Abstract. We consider a beam equation in the presence of a leading degenerate operator which is not in divergence form. We impose clamped conditions where the degeneracy occurs and dissipative conditions at the other endpoint. We provide some conditions for the uniform exponential decay of solutions for the associated problem.
{"title":"A Stability Result for a Degenerate Beam Equation","authors":"Alessandro Camasta, Genni Fragnelli","doi":"10.1137/23m1565668","DOIUrl":"https://doi.org/10.1137/23m1565668","url":null,"abstract":"SIAM Journal on Control and Optimization, Volume 62, Issue 1, Page 630-649, February 2024. <br/> Abstract. We consider a beam equation in the presence of a leading degenerate operator which is not in divergence form. We impose clamped conditions where the degeneracy occurs and dissipative conditions at the other endpoint. We provide some conditions for the uniform exponential decay of solutions for the associated problem.","PeriodicalId":49531,"journal":{"name":"SIAM Journal on Control and Optimization","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139758463","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}
Charalambos D. Charalambous, Christos K. Kourtellaris, Ioannis Tzortzis
SIAM Journal on Control and Optimization, Volume 62, Issue 1, Page 600-629, February 2024. Abstract. We investigate the control-coding (CC) capacity of general dynamical decision models (DMs) that involve nonlinear filtering, which is absent in the specific DMs investigated in [C. K. Kourtellaris and C. D. Charalambous, IEEE Trans. Inform. Theory, 64 (2018), pp. 4962–4992]. We derive characterizations of CC capacity and we show their equivalence to extremum problems of maximizing the information theoretic measure of directed information from the input process to the output process of the DM over randomized strategies. Due to the generality of the DMs, the CC capacity is shown to be equivalent to partially observable Markov decision problems, contrary to the DMs in the above mentioned paper, which give rise to fully observable Markov decision problems. Subsequently, the CC capacity is transformed, using nonlinear filtering theory, to fully observable Markov decision problems. For the application example of a Gaussian DM with past dependence on inputs and outputs, we prove a decentralized separation principle that states optimal inputs are Gaussian and consist of (i) a control, (ii) an estimation, and (iii) an information transmission part, which interact in a specific order. The optimal control and estimation parts are related to linear-quadratic Gaussian stochastic optimal control problems with partial information. Various degenerated cases are discussed, including examples from the above mentioned paper, which do not involve estimation.
SIAM 控制与优化期刊》，第 62 卷第 1 期，第 600-629 页，2024 年 2 月。 摘要我们研究了涉及非线性滤波的一般动态决策模型（DM）的控制编码（CC）能力，这在 [C. K. Kourtellaris 和 C. D. Charalambous] 研究的特定 DM 中是不存在的。K. Kourtellaris 和 C. D. Charalambous, IEEE Trans.Inform.Theory, 64 (2018), pp.］我们推导出 CC 容量的特征，并证明它们等价于在随机策略上最大化从 DM 的输入过程到输出过程的有向信息的信息论度量的极值问题。由于 DM 的普遍性，CC 容量被证明等价于部分可观测的马尔可夫决策问题，这与上述论文中的 DM 相反，后者引起的是完全可观测的马尔可夫决策问题。随后，利用非线性滤波理论将 CC 容量转换为完全可观测的马尔可夫决策问题。对于输入和输出具有过去依赖性的高斯DM应用实例，我们证明了一种分散分离原理，即最优输入是高斯的，由(i) 控制、(ii) 估计和(iii) 信息传输部分组成，它们以特定顺序相互作用。最优控制和估计部分与具有部分信息的线性-二次高斯随机最优控制问题相关。本文讨论了各种退化情况，包括上述论文中不涉及估计的例子。
{"title":"Optimal Control and Signaling Strategies of Control-Coding Capacity of General Decision Models: Applications to Gaussian Models and Decentralized Strategies","authors":"Charalambos D. Charalambous, Christos K. Kourtellaris, Ioannis Tzortzis","doi":"10.1137/22m1518700","DOIUrl":"https://doi.org/10.1137/22m1518700","url":null,"abstract":"SIAM Journal on Control and Optimization, Volume 62, Issue 1, Page 600-629, February 2024. <br/> Abstract. We investigate the control-coding (CC) capacity of general dynamical decision models (DMs) that involve nonlinear filtering, which is absent in the specific DMs investigated in [C. K. Kourtellaris and C. D. Charalambous, IEEE Trans. Inform. Theory, 64 (2018), pp. 4962–4992]. We derive characterizations of CC capacity and we show their equivalence to extremum problems of maximizing the information theoretic measure of directed information from the input process to the output process of the DM over randomized strategies. Due to the generality of the DMs, the CC capacity is shown to be equivalent to partially observable Markov decision problems, contrary to the DMs in the above mentioned paper, which give rise to fully observable Markov decision problems. Subsequently, the CC capacity is transformed, using nonlinear filtering theory, to fully observable Markov decision problems. For the application example of a Gaussian DM with past dependence on inputs and outputs, we prove a decentralized separation principle that states optimal inputs are Gaussian and consist of (i) a control, (ii) an estimation, and (iii) an information transmission part, which interact in a specific order. The optimal control and estimation parts are related to linear-quadratic Gaussian stochastic optimal control problems with partial information. Various degenerated cases are discussed, including examples from the above mentioned paper, which do not involve estimation.","PeriodicalId":49531,"journal":{"name":"SIAM Journal on Control and Optimization","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139758434","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}
SIAM Journal on Control and Optimization, Volume 62, Issue 1, Page 563-580, February 2024. Abstract. In this paper, we obtain the exact controllability for a refined stochastic wave equation with three controls by establishing a novel Carleman estimate for a backward hyperbolic-like operator. Compared with the known result [Q. Lü and X Zhang, Mathematical Control Theory for Stochastic Partial Differential Equations, Springer, Cham, Switzerland, 2021], the novelty of this paper is twofold: (1) Our model contains the effects in the drift terms when we put controls directly in the diffusion terms, which is more sensible for practical applications; (2) We provide an explicit description of the waiting time which is sharp in the case of dimension one and is independent of the coefficents of lower terms.
SIAM 控制与优化期刊》第 62 卷第 1 期第 563-580 页，2024 年 2 月。 摘要本文通过建立后向双曲样算子的新颖卡勒曼估计，得到了具有三个控制的精炼随机波方程的精确可控性。与已知结果 [Q.Lü and X Zhang, Mathematical Control Theory for Stochastic Partial Differential Equations, Springer, Cham, Switzerland, 2021]相比，本文的新颖之处有两点：(1) 当我们直接在扩散项中加入控制时，我们的模型包含了漂移项中的效应，这对实际应用更有意义；(2) 我们提供了等待时间的显式描述，该描述在维数为一的情况下是尖锐的，且与较低项的系数无关。
{"title":"Exact Controllability for a Refined Stochastic Wave Equation","authors":"Zhonghua Liao, Qi Lü","doi":"10.1137/22m1537680","DOIUrl":"https://doi.org/10.1137/22m1537680","url":null,"abstract":"SIAM Journal on Control and Optimization, Volume 62, Issue 1, Page 563-580, February 2024. <br/> Abstract. In this paper, we obtain the exact controllability for a refined stochastic wave equation with three controls by establishing a novel Carleman estimate for a backward hyperbolic-like operator. Compared with the known result [Q. Lü and X Zhang, Mathematical Control Theory for Stochastic Partial Differential Equations, Springer, Cham, Switzerland, 2021], the novelty of this paper is twofold: (1) Our model contains the effects in the drift terms when we put controls directly in the diffusion terms, which is more sensible for practical applications; (2) We provide an explicit description of the waiting time which is sharp in the case of dimension one and is independent of the coefficents of lower terms.","PeriodicalId":49531,"journal":{"name":"SIAM Journal on Control and Optimization","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139758534","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}
SIAM Journal on Control and Optimization, Volume 62, Issue 1, Page 581-599, February 2024. Abstract. We consider an interconnection of a one-dimensional ODE and an infinite dimensional abstract differential equation in view of the asymptotic stability. Sufficient stability conditions are obtained under the assumption that the whole system is positive with respect to the Minkowski cone. The decoupled ODE subsystem is not required to be stable. We illustrate our results by means of examples demonstrating the advantages of the developed approach over the existing results. As well we compare our results with the known small-gain theory.
{"title":"Stability of Abstract Interconnected Systems with a Possibly Unstable Component","authors":"Ivan Atamas, Sergey Dashkovskiy, Vitalii Slynko","doi":"10.1137/23m1572350","DOIUrl":"https://doi.org/10.1137/23m1572350","url":null,"abstract":"SIAM Journal on Control and Optimization, Volume 62, Issue 1, Page 581-599, February 2024. <br/> Abstract. We consider an interconnection of a one-dimensional ODE and an infinite dimensional abstract differential equation in view of the asymptotic stability. Sufficient stability conditions are obtained under the assumption that the whole system is positive with respect to the Minkowski cone. The decoupled ODE subsystem is not required to be stable. We illustrate our results by means of examples demonstrating the advantages of the developed approach over the existing results. As well we compare our results with the known small-gain theory.","PeriodicalId":49531,"journal":{"name":"SIAM Journal on Control and Optimization","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139758453","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}
SIAM Journal on Control and Optimization, Volume 62, Issue 1, Page 539-562, February 2024. Abstract. The moment method is used to prove the exact controllability of a wide class of bidimensional linear dispersive PDE’s posed on the two-dimensional torus [math]. The control function is considered to be acting on a small vertical and horizontal strip of the torus. Our results apply to several well-known models including some bidimesional extensions of the Benajamin–Ono and Korteweg–de Vries equations. As a by product, the exponential stabilizability with any given decay rate is also established in the Sobolev space [math], with [math], by constructing an appropriated feedback control law.
{"title":"Exact Controllability and Stabilization for Linear Dispersive PDE’s on the Two-Dimensional Torus","authors":"Francisco J. Vielma-Leal, Ademir Pastor","doi":"10.1137/22m1529361","DOIUrl":"https://doi.org/10.1137/22m1529361","url":null,"abstract":"SIAM Journal on Control and Optimization, Volume 62, Issue 1, Page 539-562, February 2024. <br/> Abstract. The moment method is used to prove the exact controllability of a wide class of bidimensional linear dispersive PDE’s posed on the two-dimensional torus [math]. The control function is considered to be acting on a small vertical and horizontal strip of the torus. Our results apply to several well-known models including some bidimesional extensions of the Benajamin–Ono and Korteweg–de Vries equations. As a by product, the exponential stabilizability with any given decay rate is also established in the Sobolev space [math], with [math], by constructing an appropriated feedback control law.","PeriodicalId":49531,"journal":{"name":"SIAM Journal on Control and Optimization","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139758351","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}
SIAM Journal on Control and Optimization, Volume 62, Issue 1, Page 509-538, February 2024. Abstract. In this paper we study the stochastic control problem of a partially observed (multidimensional) stochastic system driven by both Brownian motions and fractional Brownian motions. In the absence of the powerful tool of Girsanov transformation, we introduce and study new stochastic processes which are used to transform the original problem to a “classical one”. The adjoint backward stochastic differential equations and the necessary condition satisfied by the optimal control (maximum principle) are obtained.
{"title":"The Global Maximum Principle for Optimal Control of Partially Observed Stochastic Systems Driven by Fractional Brownian Motion","authors":"Yueyang Zheng, Yaozhong Hu","doi":"10.1137/22m1543203","DOIUrl":"https://doi.org/10.1137/22m1543203","url":null,"abstract":"SIAM Journal on Control and Optimization, Volume 62, Issue 1, Page 509-538, February 2024. <br/> Abstract. In this paper we study the stochastic control problem of a partially observed (multidimensional) stochastic system driven by both Brownian motions and fractional Brownian motions. In the absence of the powerful tool of Girsanov transformation, we introduce and study new stochastic processes which are used to transform the original problem to a “classical one”. The adjoint backward stochastic differential equations and the necessary condition satisfied by the optimal control (maximum principle) are obtained.","PeriodicalId":49531,"journal":{"name":"SIAM Journal on Control and Optimization","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139758462","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}
SIAM Journal on Control and Optimization, Volume 62, Issue 1, Page 466-486, February 2024. Abstract. We study Jeffreys-type overdamped second order linear systems with observed outputs in the setting of Hilbert spaces. The state equation comes from an overdamped second order linear partial differential equation which is wave-like but was proposed to describe heat conduction. It results from adopting the Jeffreys law of constitutive relation for heat flux, rather than the usual Fourier law. Sufficient conditions for infinite-time admissibility of the system observation operator and system observability are obtained. In the general case, we obtain the infinite-time admissibility from that of the first order Cauchy system, which is done by employing the Hardy space approach. In the special case when the operator in the state equation is negative definite, we derive the infinite-time admissibility and system observability using a semigroup approach. Illustrative examples are given.
{"title":"Admissibility and Observability of Jeffreys Type of Overdamped Second Order Linear Systems","authors":"Jian-Hua Chen, Xian-Feng Zhao, Hua-Cheng Zhou","doi":"10.1137/22m1511680","DOIUrl":"https://doi.org/10.1137/22m1511680","url":null,"abstract":"SIAM Journal on Control and Optimization, Volume 62, Issue 1, Page 466-486, February 2024. <br/> Abstract. We study Jeffreys-type overdamped second order linear systems with observed outputs in the setting of Hilbert spaces. The state equation comes from an overdamped second order linear partial differential equation which is wave-like but was proposed to describe heat conduction. It results from adopting the Jeffreys law of constitutive relation for heat flux, rather than the usual Fourier law. Sufficient conditions for infinite-time admissibility of the system observation operator and system observability are obtained. In the general case, we obtain the infinite-time admissibility from that of the first order Cauchy system, which is done by employing the Hardy space approach. In the special case when the operator in the state equation is negative definite, we derive the infinite-time admissibility and system observability using a semigroup approach. Illustrative examples are given.","PeriodicalId":49531,"journal":{"name":"SIAM Journal on Control and Optimization","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139666348","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}
SIAM Journal on Control and Optimization, Volume 62, Issue 1, Page 487-508, February 2024. Abstract. We explore the dual approach to nonlocal optimal control in the coefficients, specifically for a classical min-max problem which in this study is associated with a nonlocal scalar diffusion equation. We reformulate the optimal control problem utilizing a dual variational principle, which is expressed in terms of nonlocal two-point fluxes. We introduce the proper functional space framework to deal with this formulation and establish its well-posedness. The key ingredient is the inf-sup (Ladyzhenskaya–Babuška–Brezzi) condition, which holds uniformly with respect to small nonlocal horizons. As a by-product of this fact, we are able to prove convergence of nonlocal optimal control problems toward their local counterparts in a straightforward fashion.
{"title":"The Nonlocal Kelvin Principle and the Dual Approach to Nonlocal Control in the Conduction Coefficients","authors":"Anton Evgrafov, José C. Bellido","doi":"10.1137/22m1522127","DOIUrl":"https://doi.org/10.1137/22m1522127","url":null,"abstract":"SIAM Journal on Control and Optimization, Volume 62, Issue 1, Page 487-508, February 2024. <br/> Abstract. We explore the dual approach to nonlocal optimal control in the coefficients, specifically for a classical min-max problem which in this study is associated with a nonlocal scalar diffusion equation. We reformulate the optimal control problem utilizing a dual variational principle, which is expressed in terms of nonlocal two-point fluxes. We introduce the proper functional space framework to deal with this formulation and establish its well-posedness. The key ingredient is the inf-sup (Ladyzhenskaya–Babuška–Brezzi) condition, which holds uniformly with respect to small nonlocal horizons. As a by-product of this fact, we are able to prove convergence of nonlocal optimal control problems toward their local counterparts in a straightforward fashion.","PeriodicalId":49531,"journal":{"name":"SIAM Journal on Control and Optimization","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139666311","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}
SIAM Journal on Control and Optimization, Volume 62, Issue 1, Page 415-440, February 2024. Abstract. We address the problem of existence and uniqueness of solutions [math] to ergodic Hamilton–Jacobi–Bellman (HJB) equations of the form [math] in the whole space [math] with unbounded and merely measurable data and where [math] is a Bellman Hamiltonian. The method we use is different from classical approaches. It relies on duality theory and optimization in abstract Banach spaces together with maximal dissipativity of the diffusion operator.
{"title":"A Viscous Ergodic Problem with Unbounded and Measurable Ingredients, Part 1: HJB Equation","authors":"Hicham Kouhkouh","doi":"10.1137/22m1478069","DOIUrl":"https://doi.org/10.1137/22m1478069","url":null,"abstract":"SIAM Journal on Control and Optimization, Volume 62, Issue 1, Page 415-440, February 2024. <br/> Abstract. We address the problem of existence and uniqueness of solutions [math] to ergodic Hamilton–Jacobi–Bellman (HJB) equations of the form [math] in the whole space [math] with unbounded and merely measurable data and where [math] is a Bellman Hamiltonian. The method we use is different from classical approaches. It relies on duality theory and optimization in abstract Banach spaces together with maximal dissipativity of the diffusion operator.","PeriodicalId":49531,"journal":{"name":"SIAM Journal on Control and Optimization","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139666159","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}
SIAM Journal on Control and Optimization, Volume 62, Issue 1, Page 441-465, February 2024. Abstract. In this paper, we study the stabilization issue for a multidimensional wave equation with localized Kelvin–Voigt damping on a cuboidal domain, in which the damping region does not satisfy the geometric control condition (GCC). The variable damping coefficient is assumed to be degenerate near the interface. We prove that the system is polynomially stable with a decay rate depending on the degree of the degeneration [math]. A relationship between the decay order and [math] is identified. In particular, this decay rate is consistent with the optimal one for the corresponding system with constant damping coefficient (i.e., [math]) obtained in [K. Yu and Z.-J. Han, SIAM J. Control Optim., 59 (2021), pp. 1973–1988]. Moreover, it is the first result on the decay rates of the solutions to multidimensional wave equations with localized degenerate Kelvin–Voigt damping when GCC is not satisfied.
SIAM 控制与优化期刊》第 62 卷第 1 期第 441-465 页，2024 年 2 月。 摘要本文研究了在立方体域上具有局部 Kelvin-Voigt 阻尼的多维波方程的稳定问题，其中阻尼区域不满足几何控制条件 (GCC)。假设可变阻尼系数在界面附近是退化的。我们证明该系统是多项式稳定的，其衰减率取决于退化程度[math]。我们确定了衰减阶数与[math]之间的关系。特别是，该衰减率与 [K. Yu and Z.-J. Han, SIAM J. Control Optim.此外，这是第一个关于不满足 GCC 时具有局部退化开尔文-沃依格阻尼的多维波方程解的衰减率的结果。
{"title":"Stabilization for Wave Equation with Localized Kelvin–Voigt Damping on Cuboidal Domain: A Degenerate Case","authors":"Zhong-Jie Han, Zhuangyi Liu, Kai Yu","doi":"10.1137/22m153210x","DOIUrl":"https://doi.org/10.1137/22m153210x","url":null,"abstract":"SIAM Journal on Control and Optimization, Volume 62, Issue 1, Page 441-465, February 2024. <br/> Abstract. In this paper, we study the stabilization issue for a multidimensional wave equation with localized Kelvin–Voigt damping on a cuboidal domain, in which the damping region does not satisfy the geometric control condition (GCC). The variable damping coefficient is assumed to be degenerate near the interface. We prove that the system is polynomially stable with a decay rate depending on the degree of the degeneration [math]. A relationship between the decay order and [math] is identified. In particular, this decay rate is consistent with the optimal one for the corresponding system with constant damping coefficient (i.e., [math]) obtained in [K. Yu and Z.-J. Han, SIAM J. Control Optim., 59 (2021), pp. 1973–1988]. Moreover, it is the first result on the decay rates of the solutions to multidimensional wave equations with localized degenerate Kelvin–Voigt damping when GCC is not satisfied.","PeriodicalId":49531,"journal":{"name":"SIAM Journal on Control and Optimization","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139666153","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}
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