Evolution Equations & Control Theory最新文献

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Telegraph systems on networks and port-Hamiltonians. Ⅲ. Explicit representation and long-term behaviour 电报系统的网络和港口汉密尔顿。Ⅲ。显性表征和长期行为
Evolution Equations & Control Theory Pub Date : 2021-11-16 DOI: 10.3934/eect.2022016
J. Banasiak, Adam Bloch
{"title":"Telegraph systems on networks and port-Hamiltonians. Ⅲ. Explicit representation and long-term behaviour","authors":"J. Banasiak, Adam Bloch","doi":"10.3934/eect.2022016","DOIUrl":"https://doi.org/10.3934/eect.2022016","url":null,"abstract":"In this paper we present an explicit formula for the semigroup governing the solution to hyperbolic systems on a metric graph, satisfying general linear Kirchhoff's type boundary conditions. Further, we use this representation to establish the long term behaviour of the solutions. The crucial role is played by the spectral decomposition of the boundary matrix.","PeriodicalId":176362,"journal":{"name":"Evolution Equations & Control Theory","volume":"173 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134462190","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Controllability for Schrödinger type system with mixed dispersion on compact star graphs 紧星图上混合色散Schrödinger型系统的可控性
Evolution Equations & Control Theory Pub Date : 2021-09-28 DOI: 10.3934/eect.2022019
R. A. Capistrano-Filho, M. Cavalcante, F. Gallego
{"title":"Controllability for Schrödinger type system with mixed dispersion on compact star graphs","authors":"R. A. Capistrano-Filho, M. Cavalcante, F. Gallego","doi":"10.3934/eect.2022019","DOIUrl":"https://doi.org/10.3934/eect.2022019","url":null,"abstract":"<p style='text-indent:20px;'>In this work we are concerned with solutions to the linear Schrödinger type system with mixed dispersion, the so-called biharmonic Schrödinger equation. Precisely, we are able to prove an exact control property for these solutions with the control in the energy space posed on an oriented star graph structure <inline-formula><tex-math id=\"M1\">begin{document}$ mathcal{G} $end{document}</tex-math></inline-formula> for <inline-formula><tex-math id=\"M2\">begin{document}$ T>T_{min} $end{document}</tex-math></inline-formula>, with</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id=\"FE1\"> begin{document}$ T_{min} = sqrt{ frac{ overline{L} (L^2+pi^2)}{pi^2varepsilon(1- overline{L} varepsilon)}}, $end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>when the couplings and the controls appear only on the Neumann boundary conditions.</p>","PeriodicalId":176362,"journal":{"name":"Evolution Equations &amp; Control Theory","volume":"71 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127403236","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Optimal control of mixed local-nonlocal parabolic PDE with singular boundary-exterior data 具有奇异边界外数据的混合局部-非局部抛物型PDE的最优控制
Evolution Equations &amp; Control Theory Pub Date : 2021-02-18 DOI: 10.3934/eect.2022015
J. Djida, G. Mophou, M. Warma
{"title":"Optimal control of mixed local-nonlocal parabolic PDE with singular boundary-exterior data","authors":"J. Djida, G. Mophou, M. Warma","doi":"10.3934/eect.2022015","DOIUrl":"https://doi.org/10.3934/eect.2022015","url":null,"abstract":"<p style='text-indent:20px;'>We consider parabolic equations on bounded smooth open sets <inline-formula><tex-math id=\"M1\">begin{document}$ {Omega}subset mathbb{R}^N $end{document}</tex-math></inline-formula> (<inline-formula><tex-math id=\"M2\">begin{document}$ Nge 1 $end{document}</tex-math></inline-formula>) with mixed Dirichlet type boundary-exterior conditions associated with the elliptic operator <inline-formula><tex-math id=\"M3\">begin{document}$ mathscr{L} : = - Delta + (-Delta)^{s} $end{document}</tex-math></inline-formula> (<inline-formula><tex-math id=\"M4\">begin{document}$ 0<s<1 $end{document}</tex-math></inline-formula>). Firstly, we prove several well-posedness and regularity results of the associated elliptic and parabolic problems with smooth, and then with singular boundary-exterior data. Secondly, we show the existence of optimal solutions of associated optimal control problems, and we characterize the optimality conditions. This is the first time that such topics have been presented and studied in a unified fashion for mixed local-nonlocal PDEs with singular data.</p>","PeriodicalId":176362,"journal":{"name":"Evolution Equations &amp; Control Theory","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123691716","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Boundedness of solutions in a quasilinear chemo-repulsion system with nonlinear signal production 具有非线性信号产生的拟线性化学排斥系统解的有界性
Evolution Equations &amp; Control Theory Pub Date : 1900-01-01 DOI: 10.3934/eect.2022018
Runlin Hu, Pan Zheng, Zhangqin Gao
{"title":"Boundedness of solutions in a quasilinear chemo-repulsion system with nonlinear signal production","authors":"Runlin Hu, Pan Zheng, Zhangqin Gao","doi":"10.3934/eect.2022018","DOIUrl":"https://doi.org/10.3934/eect.2022018","url":null,"abstract":"<p style='text-indent:20px;'>This paper deals with a quasilinear parabolic-elliptic chemo-repulsion system with nonlinear signal production</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id=\"FE1\"> begin{document}$ begin{eqnarray*} label{1a} left{ begin{split}{} & u_t = nablacdot(phi(u)nabla u)+chinablacdot(u(u+1)^{alpha-1}nabla v)+f(u), & (x,t)in Omegatimes (0,infty), & 0 = Delta v-v+u^{beta}, & (x,t)in Omegatimes (0,infty), end{split} right. end{eqnarray*} $end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>under homogeneous Neumann boundary conditions in a smoothly bounded domain <inline-formula><tex-math id=\"M1\">begin{document}$ Omega subset mathbb{R}^{n}(ngeq1), $end{document}</tex-math></inline-formula> where <inline-formula><tex-math id=\"M2\">begin{document}$ chi,beta>0,alphainmathbb{R}, $end{document}</tex-math></inline-formula> the nonlinear diffusion <inline-formula><tex-math id=\"M3\">begin{document}$ phiin C^{2}([0,infty)) $end{document}</tex-math></inline-formula> satisfies <inline-formula><tex-math id=\"M4\">begin{document}$ phi(u)geq(u+1)^{m} $end{document}</tex-math></inline-formula> with <inline-formula><tex-math id=\"M5\">begin{document}$ minmathbb{R}, $end{document}</tex-math></inline-formula> and the function <inline-formula><tex-math id=\"M6\">begin{document}$ fin C^{1}([0,infty)) $end{document}</tex-math></inline-formula> is a generalized growth term.</p><p style='text-indent:20px;'><inline-formula><tex-math id=\"M7\">begin{document}$ bullet $end{document}</tex-math></inline-formula> When <inline-formula><tex-math id=\"M8\">begin{document}$ fequiv0, $end{document}</tex-math></inline-formula> it is shown that the solution of the above system is global and uniformly bounded for all <inline-formula><tex-math id=\"M9\">begin{document}$ chi,beta>0 $end{document}</tex-math></inline-formula> and <inline-formula><tex-math id=\"M10\">begin{document}$ m,alphainmathbb{R} $end{document}</tex-math></inline-formula>.</p><p style='text-indent:20px;'><inline-formula><tex-math id=\"M11\">begin{document}$ bullet $end{document}</tex-math></inline-formula> When <inline-formula><tex-math id=\"M12\">begin{document}$ fnotequiv0 $end{document}</tex-math></inline-formula> and assume that <inline-formula><tex-math id=\"M13\">begin{document}$ f(u)leq ku-bu^{gamma+1} $end{document}</tex-math></inline-formula> with <inline-formula><tex-math id=\"M14\">begin{document}$ k,b,gamma>0, $end{document}</tex-math></inline-formula> it is proved that the solution of the above system is also global and uniformly bounded for all <inline-formula><tex-math id=\"M15\">begin{document}$ chi,beta>0 $end{document}</tex-math></inline-formula> and <inline-formula><tex-math id=\"M16\">begin{document}$ m,alphainmathbb{R}. $end{document}</tex-math></inline-formula></p>","PeriodicalId":176362,"journal":{"name":"Evolution Equations &amp; Control Theory","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123039453","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Pullback attractors for weak solution to modified Kelvin-Voigt model 修正Kelvin-Voigt模型弱解的回拉吸引子
Evolution Equations &amp; Control Theory Pub Date : 1900-01-01 DOI: 10.3934/eect.2022011
M. Turbin, A. Ustiuzhaninova
{"title":"Pullback attractors for weak solution to modified Kelvin-Voigt model","authors":"M. Turbin, A. Ustiuzhaninova","doi":"10.3934/eect.2022011","DOIUrl":"https://doi.org/10.3934/eect.2022011","url":null,"abstract":"The paper is devoted to the investigation of the qualitative dynamics of weak solutions for the modified Kelvin-Voigt model on the base of the theory of pullback attractors for trajectory spaces. At first, for the studied model, an auxiliary problem is considered, its solvability in the weak sense is proved, and some solution estimates are established. Then, on the base of these estimates, a family of trajectory spaces is determined and the existence of trajectory and minimal pullback attractors for the considered trajectory spaces is proved.","PeriodicalId":176362,"journal":{"name":"Evolution Equations &amp; Control Theory","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132451534","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
Attractors for a class of extensible beams with strong nonlinear damping 一类强非线性阻尼可展梁的吸引子
Evolution Equations &amp; Control Theory Pub Date : 1900-01-01 DOI: 10.3934/eect.2022013
E. Tavares, V. Narciso
{"title":"Attractors for a class of extensible beams with strong nonlinear damping","authors":"E. Tavares, V. Narciso","doi":"10.3934/eect.2022013","DOIUrl":"https://doi.org/10.3934/eect.2022013","url":null,"abstract":"<p style='text-indent:20px;'>We concern to stablish the existence and qualitative properties of the compact global attractor associate to solutions of a class of extensible beam equations with strong nonlinear damping arising from the wave model proposed by Prestel [<xref ref-type=\"bibr\" rid=\"b18\">18</xref>].</p>","PeriodicalId":176362,"journal":{"name":"Evolution Equations &amp; Control Theory","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131907977","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Blow-up of solutions to a viscoelastic wave equation with nonlocal damping 非局部阻尼粘弹性波动方程解的爆破
Evolution Equations &amp; Control Theory Pub Date : 1900-01-01 DOI: 10.3934/eect.2022009
Donghao Li, Hongwei Zhang, Shuo Liu, Qing-Quan Hu
{"title":"Blow-up of solutions to a viscoelastic wave equation with nonlocal damping","authors":"Donghao Li, Hongwei Zhang, Shuo Liu, Qing-Quan Hu","doi":"10.3934/eect.2022009","DOIUrl":"https://doi.org/10.3934/eect.2022009","url":null,"abstract":"<p style='text-indent:20px;'>The viscoelastic wave equation with nonlinear nonlocal weak damping is considered. The local existence of solutions is established. Under arbitrary positive initial energy, a finite-time blow-up result is proved by a new modified concavity method.</p>","PeriodicalId":176362,"journal":{"name":"Evolution Equations &amp; Control Theory","volume":"77 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122927944","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On analytic semigroup generators involving Caputo fractional derivative 涉及Caputo分数阶导数的解析半群生成
Evolution Equations &amp; Control Theory Pub Date : 1900-01-01 DOI: 10.3934/eect.2022014
P. Grabowski
{"title":"On analytic semigroup generators involving Caputo fractional derivative","authors":"P. Grabowski","doi":"10.3934/eect.2022014","DOIUrl":"https://doi.org/10.3934/eect.2022014","url":null,"abstract":"<p style='text-indent:20px;'>Our investigations are motivated by the well - posedness problem of some dynamical models with anomalous diffusion described by the Caputo spatial fractional derivative of order <inline-formula><tex-math id=\"M1\">begin{document}$ alpha in (1, 2) $end{document}</tex-math></inline-formula>. We propose a characterization of an exponentially stable analytic semigroup generator using the inverse operator. This characterization enables us to establish the form of a generator involving the Caputo fractional derivative, under various boundary conditions. In particular, the results simplify those known from literature obtained by means of the fractional Sobolev spaces and some perturbation results. Going further, we show how to construct a control system in factor form, having such a generator as the state operator.</p>","PeriodicalId":176362,"journal":{"name":"Evolution Equations &amp; Control Theory","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115256556","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Well-posedness and stability of non-autonomous semilinear input-output systems 非自治半线性输入输出系统的适定性与稳定性
Evolution Equations &amp; Control Theory Pub Date : 1900-01-01 DOI: 10.3934/eect.2022017
J. Schmid
{"title":"Well-posedness and stability of non-autonomous semilinear input-output systems","authors":"J. Schmid","doi":"10.3934/eect.2022017","DOIUrl":"https://doi.org/10.3934/eect.2022017","url":null,"abstract":"We establish well-posedness results for non-autonomous semilinear input-output systems, the central assumption being the scattering-passivity of the considered semilinear system. Along the way, we also establish global stability estimates. We consider both systems with distributed control and observation and systems with boundary control and observation, and we treat them in a unified manner. Applications are given to nonlinearly controlled collocated systems and to nonlinearly controlled port-Hamiltonian systems.","PeriodicalId":176362,"journal":{"name":"Evolution Equations &amp; Control Theory","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133806639","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Controller and asymptotic autonomy of random attractors for stochastic p-Laplace lattice equations 随机p-拉普拉斯格方程随机吸引子的控制器和渐近自治
Evolution Equations &amp; Control Theory Pub Date : 1900-01-01 DOI: 10.3934/eect.2022010
Li Song, Yangrong Li, Fengling Wang
{"title":"Controller and asymptotic autonomy of random attractors for stochastic p-Laplace lattice equations","authors":"Li Song, Yangrong Li, Fengling Wang","doi":"10.3934/eect.2022010","DOIUrl":"https://doi.org/10.3934/eect.2022010","url":null,"abstract":"A non-autonomous random dynamical system is called to be controllable if there is a pullback random attractor (PRA) such that each fibre of the PRA converges upper semi-continuously to a nonempty compact set (called a controller) as the time-parameter goes to minus infinity, while the PRA is called to be asymptotically autonomous if there is a random attractor for another (autonomous) random dynamical system as a controller. We establish the criteria for ensuring the existence of the minimal controller and the asymptotic autonomy of a PRA respectively. The abstract results are illustrated in possibly non-autonomous stochastic p-Laplace lattice equations with tempered convergent external forces.","PeriodicalId":176362,"journal":{"name":"Evolution Equations &amp; Control Theory","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121387702","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
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