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Lifespan estimates of solutions to quasilinear wave equations with damping and negative mass term 具有阻尼和负质量项的拟线性波动方程解的寿命估计
IF 1.2 4区 数学
Mathematical Control and Related Fields Pub Date : 2022-01-01 DOI: 10.3934/mcrf.2022022
Jie Yang, Sen Ming, Wei Han, Xiongmei Fan
{"title":"Lifespan estimates of solutions to quasilinear wave equations with damping and negative mass term","authors":"Jie Yang, Sen Ming, Wei Han, Xiongmei Fan","doi":"10.3934/mcrf.2022022","DOIUrl":"https://doi.org/10.3934/mcrf.2022022","url":null,"abstract":"<p style='text-indent:20px;'>The main goal of this work is to investigate formation of singularities for solutions to the quasilinear wave equations with damping terms, negative mass terms and divergence form nonlinearities in the critical and sub-critical cases. Upper bound lifespan estimates of solutions are derived by applying the rescaled test function method and iteration technique. The results are the same as corresponding wave equation without damping term and mass term. The main new contribution is that lifespan estimates of solutions are associated with the well-known Strauss exponent and Glassey exponent. To the best of our knowledge, the results in Theorems <inline-formula><tex-math id=\"M2\">begin{document}$ 1.1-1.4 $end{document}</tex-math></inline-formula> are new. Moreover, the changing trends of semilinear wave equations are illustrated through numerical simulation.</p>","PeriodicalId":48889,"journal":{"name":"Mathematical Control and Related Fields","volume":"15 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87196298","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Time-consistent lifetime portfolio selection under smooth ambiguity 平滑模糊下的时间一致终身投资组合选择
IF 1.2 4区 数学
Mathematical Control and Related Fields Pub Date : 2022-01-01 DOI: 10.3934/mcrf.2022023
Luyang Yu, Liyuan Lin, Guohui Guan, Jingzhen Liu
{"title":"Time-consistent lifetime portfolio selection under smooth ambiguity","authors":"Luyang Yu, Liyuan Lin, Guohui Guan, Jingzhen Liu","doi":"10.3934/mcrf.2022023","DOIUrl":"https://doi.org/10.3934/mcrf.2022023","url":null,"abstract":"<p style='text-indent:20px;'>This paper studies the optimal consumption, life insurance and investment problem for an income earner with uncertain lifetime under smooth ambiguity model. We assume that risky assets have unknown market prices that result in ambiguity. The individual forms his belief, that is, the distribution of market prices, according to available information. His ambiguity attitude, which is similar to the risk attitude described by utility function <inline-formula><tex-math id=\"M1\">begin{document}$ U $end{document}</tex-math></inline-formula>, is represented by an ambiguity preference function <inline-formula><tex-math id=\"M2\">begin{document}$ phi $end{document}</tex-math></inline-formula>. Under the smooth ambiguity model, the problem becomes time-inconsistent. We derive the extended Hamilton-Jacobi-Bellman (HJB) equation for the equilibrium value function and equilibrium strategy. Then, we obtain the explicit solution for the equilibrium strategy when both <inline-formula><tex-math id=\"M3\">begin{document}$ U $end{document}</tex-math></inline-formula> and <inline-formula><tex-math id=\"M4\">begin{document}$ phi $end{document}</tex-math></inline-formula> are power functions. We find that a more risk- or ambiguity-averse individual will consume less, buy more life insurance and invest less. Moreover, we find that the Tobin-Markowitz separation theorem is no longer applicable when ambiguity attitude is taken into consideration. The investment strategy will change with the characteristics of the decision maker, such as risk attitude, ambiguity attitude and age.</p>","PeriodicalId":48889,"journal":{"name":"Mathematical Control and Related Fields","volume":"121 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86850484","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 1
Identifying a space-dependent source term in distributed order time-fractional diffusion equations 在分布阶时间分数扩散方程中识别与空间相关的源项
IF 1.2 4区 数学
Mathematical Control and Related Fields Pub Date : 2022-01-01 DOI: 10.3934/mcrf.2022025
Dinh Nguyen Duy Hai
{"title":"Identifying a space-dependent source term in distributed order time-fractional diffusion equations","authors":"Dinh Nguyen Duy Hai","doi":"10.3934/mcrf.2022025","DOIUrl":"https://doi.org/10.3934/mcrf.2022025","url":null,"abstract":"The aim of this paper is to investigate an inverse problem of recovering a space-dependent source term governed by distributed order time-fractional diffusion equations in Hilbert scales. Such a problem is ill-posed and has important practical applications. For this problem, we propose a general regularization method based on the idea of the filter method. With a suitable source condition, we prove that the method is of optimal order under various choices of regularization parameter. One is based on the a priori regularization parameter choice rule and another one is the discrepancy principle. Finally, the capabilities of our method are illustrated by both the Tikhonov and the Landweber method.","PeriodicalId":48889,"journal":{"name":"Mathematical Control and Related Fields","volume":"89 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72468860","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 1
First order necessary condition for stochastic evolution control systems with random generators 随机演化控制系统的一阶必要条件
IF 1.2 4区 数学
Mathematical Control and Related Fields Pub Date : 2022-01-01 DOI: 10.3934/mcrf.2022042
Yu Zhang
{"title":"First order necessary condition for stochastic evolution control systems with random generators","authors":"Yu Zhang","doi":"10.3934/mcrf.2022042","DOIUrl":"https://doi.org/10.3934/mcrf.2022042","url":null,"abstract":"The main purpose of this paper is to establish the first order necessary optimality condition for optimal control problems of stochastic evolution systems with random generators. For our controlled system, both the drift and the diffusion terms contain the control variable, and the control region is a nonempty closed subset of a separable Hilbert space. Compared with the existing works, the main difficulties here are to prove the well-posedness of the control and the adjoint systems. We obtain the well-posedness of the adjoint system in the sense of mild solutions and that of the control system by means of the stochastic transposition method. In addition, the variational analysis approach is employed to handle the nonconvexity of the control region when deriving our optimality condition.","PeriodicalId":48889,"journal":{"name":"Mathematical Control and Related Fields","volume":"133 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86229189","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Second-order problems involving time-dependent subdifferential operators and application to control 涉及时变子微分算子的二阶问题及其控制应用
IF 1.2 4区 数学
Mathematical Control and Related Fields Pub Date : 2022-01-01 DOI: 10.3934/mcrf.2022019
S. Saïdi, Fatima Fennour
{"title":"Second-order problems involving time-dependent subdifferential operators and application to control","authors":"S. Saïdi, Fatima Fennour","doi":"10.3934/mcrf.2022019","DOIUrl":"https://doi.org/10.3934/mcrf.2022019","url":null,"abstract":"The paper provides a new result concerning the existence of solutions for second-order evolution problems associated with time-dependent subdifferential operators involving both single-valued and mixed semi-continuous set-valued perturbations. Optimal control problems corresponding to such differential inclusions using relaxation theorems with Young measures are investigated. The existence of solutions for a coupled system governed by a second-order differential equation with an evolution problem is also addressed.","PeriodicalId":48889,"journal":{"name":"Mathematical Control and Related Fields","volume":"82 3 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82884428","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Optimal reinsurance-investment problem for a general insurance company under a generalized dynamic contagion claim model 广义动态传染索赔模型下一般保险公司最优再保险投资问题
IF 1.2 4区 数学
Mathematical Control and Related Fields Pub Date : 2022-01-01 DOI: 10.3934/mcrf.2022030
Fan Wu, Xin Zhang, Zhibin Liang
{"title":"Optimal reinsurance-investment problem for a general insurance company under a generalized dynamic contagion claim model","authors":"Fan Wu, Xin Zhang, Zhibin Liang","doi":"10.3934/mcrf.2022030","DOIUrl":"https://doi.org/10.3934/mcrf.2022030","url":null,"abstract":"In this paper, we study an optimal management problem for a general insurance company which holds shares of an insurance company and a reinsurance company. The general company aims to derive the equilibrium reinsurance-investment strategy under the mean-variance criterion. The claim process described by a generalized compound dynamic contagion process introduced by [18] which allows for self-exciting and externally-exciting clustering effect for the claim arrivals and the processes of the risky assets are described by the jump-diffusion models. Based on practical considerations, we suppose that the externally-exciting clustering effect will simultaneously affect both the price of risky assets and the intensity of claims. To overcome the inconsistency issue caused by the mean-variance criterion, we formulate the optimization problem as an embedded game and solve it via a corresponding extended Hamilton-Jacobi-Bellman equation. The equilibrium reinsurance-investment strategy is obtained, which depends on a solution to an ordinary differential equation. In addition, we demonstrate the derived equilibrium strategy and the economic implications behind it through a large number of mathematical analysis and numerical examples.","PeriodicalId":48889,"journal":{"name":"Mathematical Control and Related Fields","volume":"67 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86873121","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Optimal control of parameterized stationary Maxwell's system: Reduced basis, convergence analysis, and a posteriori error estimates 参数化平稳麦克斯韦系统的最优控制:减少基，收敛分析和后验误差估计
IF 1.2 4区 数学
Mathematical Control and Related Fields Pub Date : 2022-01-01 DOI: 10.3934/mcrf.2022003
Q. Tran, Harbir Antil, Hugo S Díaz
{"title":"Optimal control of parameterized stationary Maxwell's system: Reduced basis, convergence analysis, and a posteriori error estimates","authors":"Q. Tran, Harbir Antil, Hugo S Díaz","doi":"10.3934/mcrf.2022003","DOIUrl":"https://doi.org/10.3934/mcrf.2022003","url":null,"abstract":"We consider an optimal control problem governed by parameterized stationary Maxwell's system with the Gauss's law. The parameters enter through dielectric, magnetic permeability, and charge density. Moreover, the parameter set is assumed to be compact. We discretize the electric field by a finite element method and use variational discretization concept for the control. We present a reduced basis method for the optimal control problem and establish the uniform convergence of the reduced order solutions to that of the original full-dimensional problem provided that the snapshot parameter sample is dense in the parameter set, with an appropriate parameter separability rule. Finally, we establish the absolute a posteriori error estimator for the reduced order solutions and the corresponding cost functions in terms of the state and adjoint residuals.","PeriodicalId":48889,"journal":{"name":"Mathematical Control and Related Fields","volume":"84 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86855076","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Preface special issue on recent advances in mathematical control theory 数学控制理论最新进展特刊序言
IF 1.2 4区 数学
Mathematical Control and Related Fields Pub Date : 2022-01-01 DOI: 10.3934/mcrf.2022044
Qi Lü, Xu Zhang
{"title":"Preface special issue on recent advances in mathematical control theory","authors":"Qi Lü, Xu Zhang","doi":"10.3934/mcrf.2022044","DOIUrl":"https://doi.org/10.3934/mcrf.2022044","url":null,"abstract":"<jats:p xml:lang=\"fr\" />","PeriodicalId":48889,"journal":{"name":"Mathematical Control and Related Fields","volume":"136 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76445689","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
The second-order maximum principle for partially observed optimal controls 部分可观测最优控制的二阶极大值原理
IF 1.2 4区 数学
Mathematical Control and Related Fields Pub Date : 2022-01-01 DOI: 10.3934/mcrf.2022059
Mengzhen Li, Zhanghua Wu
{"title":"The second-order maximum principle for partially observed optimal controls","authors":"Mengzhen Li, Zhanghua Wu","doi":"10.3934/mcrf.2022059","DOIUrl":"https://doi.org/10.3934/mcrf.2022059","url":null,"abstract":"","PeriodicalId":48889,"journal":{"name":"Mathematical Control and Related Fields","volume":"54 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84596324","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Stability analysis for abstract theomoelastic systems with Cattaneo's law and inertial terms 用卡塔尼奥定律和惯性项分析抽象运动弹性系统的稳定性
IF 1.2 4区 数学
Mathematical Control and Related Fields Pub Date : 2022-01-01 DOI: 10.3934/mcrf.2022053
{"title":"Stability analysis for abstract theomoelastic systems with Cattaneo's law and inertial terms","authors":"","doi":"10.3934/mcrf.2022053","DOIUrl":"https://doi.org/10.3934/mcrf.2022053","url":null,"abstract":"","PeriodicalId":48889,"journal":{"name":"Mathematical Control and Related Fields","volume":"07 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86251459","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 2
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