HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. Analysis of a linearized poromechanics model for incompressible and nearly incompressible materials Mathieu Barré, Céline Grandmont, Philippe Moireau
它是一个多学科的开放获取档案，用于科学研究文件的存储和传播，无论它们是否出版。这些文件可能来自法国或国外的教学和研究机构，也可能来自公共或私人研究中心。HAL开放多学科档案旨在存放和传播来自法国或外国教育和研究机构、公共或私人实验室的已发表或未发表的研究级科学文件。Analysis of a linearized poromechanics model for不可压缩and是不可压缩的材料(Mathieu划线、celine Grandmont菲利普Moireau
{"title":"Analysis of a linearized poromechanics model for incompressible and nearly incompressible materials","authors":"Mathieu Barré, C. Grandmont, Philippe Moireau","doi":"10.3934/eect.2022053","DOIUrl":"https://doi.org/10.3934/eect.2022053","url":null,"abstract":"HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. Analysis of a linearized poromechanics model for incompressible and nearly incompressible materials Mathieu Barré, Céline Grandmont, Philippe Moireau","PeriodicalId":48833,"journal":{"name":"Evolution Equations and Control Theory","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74377301","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}
This paper is devoted to the null controllability of a cascade system of begin{document}$ m $end{document} coupled backward stochastic heat equations governed by a unique distributed control force, where begin{document}$ mgeq 2 $end{document}. This task is obtained by means of proving a suitable observability estimate for the dual system of the controlled system.
This paper is devoted to the null controllability of a cascade system of begin{document}$ m $end{document} coupled backward stochastic heat equations governed by a unique distributed control force, where begin{document}$ mgeq 2 $end{document}. This task is obtained by means of proving a suitable observability estimate for the dual system of the controlled system.
{"title":"Controllability of a backward stochastic cascade system of coupled parabolic heat equations by one control force","authors":"Mohamed Fadili","doi":"10.3934/eect.2022037","DOIUrl":"https://doi.org/10.3934/eect.2022037","url":null,"abstract":"<p style='text-indent:20px;'>This paper is devoted to the null controllability of a cascade system of <inline-formula><tex-math id=\"M1\">begin{document}$ 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":null,"pages":null},"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}
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.
{"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":null,"pages":null},"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}
This paper contains results about the existence, uniqueness and stability of solutions for the damped nonlinear extensible beam equation
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}^+, $end{document}
where begin{document}$ alpha>0 $end{document}, begin{document}$ gammage 0 $end{document}, begin{document}$ Omegasubset mathbb{R}^n $end{document} is a bounded domain with smooth boundary begin{document}$ Gamma = partial Omega $end{document}, and begin{document}$ M $end{document} is a nonlocal function that represents beam's extensibility term. The novelty of the work is to consider the damping as a product of a degenerate and nonlocal term with a nonlinear function. This work complements the recent article by Cavalcanti et al. [8] who treated this model with degenerate nonlocal weak (and strong) damping. The main result of the work is to show that for regular initial data the energy associated with the problem proposed goes to zero when begin{document}$ t $end{document} goes to infinity.
This paper contains results about the existence, uniqueness and stability of solutions for the damped nonlinear extensible beam equation begin{document}$ 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}^+, $end{document} where begin{document}$ alpha>0 $end{document}, begin{document}$ gammage 0 $end{document}, begin{document}$ Omegasubset mathbb{R}^n $end{document} is a bounded domain with smooth boundary begin{document}$ Gamma = partial Omega $end{document}, and begin{document}$ M $end{document} is a nonlocal function that represents beam's extensibility term. The novelty of the work is to consider the damping as a product of a degenerate and nonlocal term with a nonlinear function. This work complements the recent article by Cavalcanti et al. [8] who treated this model with degenerate nonlocal weak (and strong) damping. The main result of the work is to show that for regular initial data the energy associated with the problem proposed goes to zero when begin{document}$ t $end{document} goes to infinity.
{"title":"On a beam model with degenerate nonlocal nonlinear damping","authors":"V. Narciso, F. Ekinci, E. Pişkin","doi":"10.3934/eect.2022048","DOIUrl":"https://doi.org/10.3934/eect.2022048","url":null,"abstract":"<p style='text-indent:20px;'>This paper contains results about the existence, uniqueness and stability of solutions for the damped nonlinear extensible beam equation</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id=\"FE1\"> begin{document}$ 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":null,"pages":null},"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}
{"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":null,"pages":null},"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}
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":null,"pages":null},"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}
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.
{"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":null,"pages":null},"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}
{"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":null,"pages":null},"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}
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.
{"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":null,"pages":null},"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}
<p style='text-indent:20px;'>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.</p>
{"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":"<p style='text-indent:20px;'>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.</p>","PeriodicalId":48833,"journal":{"name":"Evolution Equations and Control Theory","volume":null,"pages":null},"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}
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