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Evolution Equations and Control Theory最新文献

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Controllability of a backward stochastic cascade system of coupled parabolic heat equations by one control force 一个控制力对耦合抛物热方程的倒向随机级联系统的可控性
IF 1.5 4区 数学
Evolution Equations and Control Theory Pub Date : 2022-01-01 DOI: 10.3934/eect.2022037
Mohamed Fadili
{"title":"Controllability of a backward stochastic cascade system of coupled parabolic heat equations by one control force","authors":"Mohamed Fadili","doi":"10.3934/eect.2022037","DOIUrl":"https://doi.org/10.3934/eect.2022037","url":null,"abstract":"<p style='text-indent:20px;'>This paper is devoted to the null controllability of a cascade system of <inline-formula><tex-math id=\"M1\">begin{document}$ m $end{document}</tex-math></inline-formula> coupled backward stochastic heat equations governed by a unique distributed control force, where <inline-formula><tex-math id=\"M2\">begin{document}$ mgeq 2 $end{document}</tex-math></inline-formula>. This task is obtained by means of proving a suitable observability estimate for the dual system of the controlled system.</p>","PeriodicalId":48833,"journal":{"name":"Evolution Equations and Control Theory","volume":"25 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74689836","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
Existence and regularity in inverse source problem for fractional reaction-subdiffusion equation perturbed by locally Lipschitz sources 局部Lipschitz源摄动分数阶反应-扩散方程逆源问题的存在性和正则性
IF 1.5 4区 数学
Evolution Equations and Control Theory Pub Date : 2022-01-01 DOI: 10.3934/eect.2022032
T. Tuan
{"title":"Existence and regularity in inverse source problem for fractional reaction-subdiffusion equation perturbed by locally Lipschitz sources","authors":"T. Tuan","doi":"10.3934/eect.2022032","DOIUrl":"https://doi.org/10.3934/eect.2022032","url":null,"abstract":"In this paper, we consider an inverse problem of determining a space-dependent source in the time fractional reaction-subdiffusion equation involving locally Lipschitz perturbations, where the additional measurements take place at the terminal time which are allowed to be nonlinearly dependent on the state. By providing regularity estimates on both time and space of resolvent operator and using local estimates on Hilbert scales, we establish some results on the existence and uniqueness of solutions and the Lipschitz type stability of solution map of the problem under consideration. In addition, when the input data take more regular values, we obtain results on regularity in time of solution for both the direct linear problem and the inverse problem above.","PeriodicalId":48833,"journal":{"name":"Evolution Equations and Control Theory","volume":"10 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90287504","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
Decay estimates for a perturbed two-terms space-time fractional diffusive problem 摄动两项时空分数扩散问题的衰减估计
IF 1.5 4区 数学
Evolution Equations and Control Theory Pub Date : 2022-01-01 DOI: 10.3934/eect.2022060
M. D’Abbicco, G. Girardi
{"title":"Decay estimates for a perturbed two-terms space-time fractional diffusive problem","authors":"M. D’Abbicco, G. Girardi","doi":"10.3934/eect.2022060","DOIUrl":"https://doi.org/10.3934/eect.2022060","url":null,"abstract":"","PeriodicalId":48833,"journal":{"name":"Evolution Equations and Control Theory","volume":"338 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82952332","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
Controllability of fractional measure evolution systems with state-dependent delay and nonlocal condition 具有状态相关延迟和非局部条件的分数测度演化系统的可控性
IF 1.5 4区 数学
Evolution Equations and Control Theory Pub Date : 2022-01-01 DOI: 10.3934/eect.2022040
Yongyang Liu, Yansheng Liu
{"title":"Controllability of fractional measure evolution systems with state-dependent delay and nonlocal condition","authors":"Yongyang Liu, Yansheng Liu","doi":"10.3934/eect.2022040","DOIUrl":"https://doi.org/10.3934/eect.2022040","url":null,"abstract":"This paper is concerned with the existence of mild solutions and exact controllability for a class of fractional measure evolution systems with state-dependent delay and nonlocal conditions. We first establish an existence result of mild solutions for the concerned problem by applying an integral equation which is given in terms of probability density and semigroup theory. Then, the exact controllability are obtained by using the fractional calculus theory, Kuratowski measure of noncompactness and Mönch fixed point theorem, without imposing the Lipschitz continuity on nonlinear term. Finally, we give two applications to support the validity of the study.","PeriodicalId":48833,"journal":{"name":"Evolution Equations and Control Theory","volume":"201 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74895335","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
On a beam model with degenerate nonlocal nonlinear damping 具有退化非局部非线性阻尼的梁模型
IF 1.5 4区 数学
Evolution Equations and Control Theory Pub Date : 2022-01-01 DOI: 10.3934/eect.2022048
V. Narciso, F. Ekinci, E. Pişkin
{"title":"On a beam model with degenerate nonlocal nonlinear damping","authors":"V. Narciso, F. Ekinci, E. Pişkin","doi":"10.3934/eect.2022048","DOIUrl":"https://doi.org/10.3934/eect.2022048","url":null,"abstract":"<p style='text-indent:20px;'>This paper contains results about the existence, uniqueness and stability of solutions for the damped nonlinear extensible beam equation</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id=\"FE1\"> begin{document}$ u_{tt}+Delta ^2u-M(|nabla u(t)|^2)Delta u+|Delta u(t)|^{2alpha},|u_t|^{gamma}u_t = 0 mbox{ in } Omega times mathbb{R}^+, $end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>where <inline-formula><tex-math id=\"M1\">begin{document}$ alpha>0 $end{document}</tex-math></inline-formula>, <inline-formula><tex-math id=\"M2\">begin{document}$ gammage 0 $end{document}</tex-math></inline-formula>, <inline-formula><tex-math id=\"M3\">begin{document}$ Omegasubset mathbb{R}^n $end{document}</tex-math></inline-formula> is a bounded domain with smooth boundary <inline-formula><tex-math id=\"M4\">begin{document}$ Gamma = partial Omega $end{document}</tex-math></inline-formula>, and <inline-formula><tex-math id=\"M5\">begin{document}$ M $end{document}</tex-math></inline-formula> is a nonlocal function that represents beam's extensibility term. The novelty of the work is to consider the damping as a product of a degenerate and nonlocal term with a nonlinear function. This work complements the recent article by Cavalcanti et al. [<xref ref-type=\"bibr\" rid=\"b8\">8</xref>] who treated this model with degenerate nonlocal weak (and strong) damping. The main result of the work is to show that for regular initial data the energy associated with the problem proposed goes to zero when <inline-formula><tex-math id=\"M6\">begin{document}$ t $end{document}</tex-math></inline-formula> goes to infinity.</p>","PeriodicalId":48833,"journal":{"name":"Evolution Equations and Control Theory","volume":"94 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79444156","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: 3
Robustness for coupled inclusions with respect to variable exponents 耦合内含物相对于可变指数的鲁棒性
IF 1.5 4区 数学
Evolution Equations and Control Theory Pub Date : 2022-01-01 DOI: 10.3934/eect.2022049
J. Simsen
{"title":"Robustness for coupled inclusions with respect to variable exponents","authors":"J. Simsen","doi":"10.3934/eect.2022049","DOIUrl":"https://doi.org/10.3934/eect.2022049","url":null,"abstract":"<p style='text-indent:20px;'>This work concerns the study of the stability of the solutions and the robustness of the global attractors with respect to the variation of spatially variable exponents for a system with three inclusions. We prove the continuity of the flows and upper semicontinuity of the global attractors.</p>","PeriodicalId":48833,"journal":{"name":"Evolution Equations and Control Theory","volume":"34 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80816481","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
Optimal control for stochastic differential equations and related Kolmogorov equations 随机微分方程及相关Kolmogorov方程的最优控制
IF 1.5 4区 数学
Evolution Equations and Control Theory Pub Date : 2022-01-01 DOI: 10.3934/eect.2022023
Ștefana-Lucia Aniţa
{"title":"Optimal control for stochastic differential equations and related Kolmogorov equations","authors":"Ștefana-Lucia Aniţa","doi":"10.3934/eect.2022023","DOIUrl":"https://doi.org/10.3934/eect.2022023","url":null,"abstract":"&lt;p style='text-indent:20px;'&gt;This paper concerns a stochastic optimal control problem with feedback Markov inputs. The problem is reduced to a deterministic optimal control problem for a Kolmogorov equation where the control for the deterministic problem is of open-loop type. The existence of an optimal control is proved for the deterministic control problem in a particular case. A maximum principle and some first order necessary optimality conditions are derived. Some examples and comments are discussed.&lt;/p&gt;","PeriodicalId":48833,"journal":{"name":"Evolution Equations and Control Theory","volume":"25 5","pages":"0"},"PeriodicalIF":1.5,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138508248","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
Von Karman thermoelastic plates: Existence and nonexistence of global solutions 冯·卡门热弹性板:整体解的存在性与不存在性
IF 1.5 4区 数学
Evolution Equations and Control Theory Pub Date : 2022-01-01 DOI: 10.3934/eect.2022055
{"title":"Von Karman thermoelastic plates: Existence and nonexistence of global solutions","authors":"","doi":"10.3934/eect.2022055","DOIUrl":"https://doi.org/10.3934/eect.2022055","url":null,"abstract":"","PeriodicalId":48833,"journal":{"name":"Evolution Equations and Control Theory","volume":"1 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87848092","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
Existence and robustness results of attractors for partially-damped piezoelectric beams 部分阻尼压电梁吸引子的存在性及鲁棒性结果
IF 1.5 4区 数学
Evolution Equations and Control Theory Pub Date : 2022-01-01 DOI: 10.3934/eect.2022057
M. Freitas, A. Özer, G. Liu, A. Ramos, E. R. N. Fonseca
{"title":"Existence and robustness results of attractors for partially-damped piezoelectric beams","authors":"M. Freitas, A. Özer, G. Liu, A. Ramos, E. R. N. Fonseca","doi":"10.3934/eect.2022057","DOIUrl":"https://doi.org/10.3934/eect.2022057","url":null,"abstract":"","PeriodicalId":48833,"journal":{"name":"Evolution Equations and Control Theory","volume":"114 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74373193","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
A sharp Gagliardo-Nirenberg inequality and its application to fractional problems with inhomogeneous nonlinearity 尖锐的Gagliardo-Nirenberg不等式及其在非齐次非线性分数型问题中的应用
IF 1.5 4区 数学
Evolution Equations and Control Theory Pub Date : 2022-01-01 DOI: 10.3934/eect.2022033
D. Bhimani, H. Hajaiej, S. Haque, Tingjian Luo
{"title":"A sharp Gagliardo-Nirenberg inequality and its application to fractional problems with inhomogeneous nonlinearity","authors":"D. Bhimani, H. Hajaiej, S. Haque, Tingjian Luo","doi":"10.3934/eect.2022033","DOIUrl":"https://doi.org/10.3934/eect.2022033","url":null,"abstract":"The purpose of this paper is threefold. Firstly, we establish a Gagliardo-Nirenberg inequality with optimal constant, which involves a fractional norm and an inhomogeneous nonlinearity. Secondly, as an application of this inequality, we study ground state standing waves to a nonlinear Schrödinger equation (NLS) with a mixed fractional Laplacians and a inhomogeneous nonlinearity, and consider a minimization problem which gives the existence of ground state solutions with prescribed mass. In particular, by making use of this Gagliardo-Nirenberg inequality and its optimal constant, we give a sufficient and necessary condition for the existence results. Finally, we develop local wellposedness theory for NLS with a mixed fractional Laplacians and a inhomogeneous nonlinearity. In the process, we prove Strichartz estimates in Lorentz spaces which may be of independent interest.","PeriodicalId":48833,"journal":{"name":"Evolution Equations and Control Theory","volume":"22 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85619075","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: 7
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