Discrete & Continuous Dynamical Systems - S最新文献

{"title":"On the density of certain spectral points for a class of $ C^{2} $ quasiperiodic Schrödinger cocycles","authors":"F. Wu, Linlin Fu, Jiahao Xu","doi":"10.3934/dcds.2021201","DOIUrl":"https://doi.org/10.3934/dcds.2021201","url":null,"abstract":"<p style='text-indent:20px;'>For <inline-formula><tex-math id=\"M2\">begin{document}$ C^2 $end{document}</tex-math></inline-formula> cos-type potentials, large coupling constants, and fixed <inline-formula><tex-math id=\"M3\">begin{document}$ Diophantine $end{document}</tex-math></inline-formula> frequency, we show that the density of the spectral points associated with the Schrödinger operator is larger than 0. In other words, for every fixed spectral point <inline-formula><tex-math id=\"M4\">begin{document}$ E $end{document}</tex-math></inline-formula>, <inline-formula><tex-math id=\"M5\">begin{document}$ liminflimits_{epsilonto 0}frac{|(E-epsilon,E+epsilon)bigcapSigma_{alpha,lambdaupsilon}|}{2epsilon} = beta $end{document}</tex-math></inline-formula>, where <inline-formula><tex-math id=\"M6\">begin{document}$ betain [frac{1}{2},1] $end{document}</tex-math></inline-formula>. Our approach is a further improvement on the papers [<xref ref-type=\"bibr\" rid=\"b15\">15</xref>] and [<xref ref-type=\"bibr\" rid=\"b17\">17</xref>].</p>","PeriodicalId":11254,"journal":{"name":"Discrete & Continuous Dynamical Systems - S","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82996723","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}

{"title":"A free boundary problem of nonlinear diffusion equation with positive bistable nonlinearity in high space dimensions I : Classification of asymptotic behavior","authors":"Y. Kaneko, Hiroshi Matsuzawa, Yoshio Yamada","doi":"10.3934/dcds.2021209","DOIUrl":"https://doi.org/10.3934/dcds.2021209","url":null,"abstract":"<p style='text-indent:20px;'>We study a free boundary problem of a reaction-diffusion equation <inline-formula><tex-math id=\"M1\">begin{document}$ u_t = Delta u+f(u) $end{document}</tex-math></inline-formula> for <inline-formula><tex-math id=\"M2\">begin{document}$ t>0, |x|<h(t) $end{document}</tex-math></inline-formula> under a radially symmetric environment in <inline-formula><tex-math id=\"M3\">begin{document}$ mathbb{R}^N $end{document}</tex-math></inline-formula>. The reaction term <inline-formula><tex-math id=\"M4\">begin{document}$ f $end{document}</tex-math></inline-formula> has positive bistable nonlinearity, which satisfies <inline-formula><tex-math id=\"M5\">begin{document}$ f(0) = 0 $end{document}</tex-math></inline-formula> and allows two positive stable equilibrium states and a positive unstable equilibrium state. The problem models the spread of a biological species, where the free boundary represents the spreading front and is governed by a one-phase Stefan condition. We show multiple spreading phenomena in high space dimensions. More precisely the asymptotic behaviors of solutions are classified into four cases: big spreading, small spreading, transition and vanishing, and sufficient conditions for each dynamical behavior are also given. We determine the spreading speed of the spherical surface <inline-formula><tex-math id=\"M6\">begin{document}$ {xin mathbb{R}^N: |x| = h(t)} $end{document}</tex-math></inline-formula>, which expands to infinity as <inline-formula><tex-math id=\"M7\">begin{document}$ ttoinfty $end{document}</tex-math></inline-formula>, even when the corresponding semi-wave problem does not admit solutions.</p>","PeriodicalId":11254,"journal":{"name":"Discrete & Continuous Dynamical Systems - S","volume":"29 3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78883592","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}

{"title":"State bounding for time-delay impulsive and switching genetic regulatory networks with exogenous disturbance","authors":"Jiayuan Yan, Ding-Xue Zhang, Bin Hu, Z. Guan, Xin-Ming Cheng","doi":"10.3934/dcdss.2022004","DOIUrl":"https://doi.org/10.3934/dcdss.2022004","url":null,"abstract":"This paper focuses on the state bounding problem for the time-delay impulsive and switching genetic regulatory networks (ISGRNs) with exogenous disturbances. Firstly, a sufficient criterion for the state bounding is obtained such that all the trajectories of ISGRNs under consideration converge exponentially into a sphere on the basis of an average dwell time (ADT) switching. Besides, globally exponential stability conditions for the considered system are further stated when the exogenous disturbance vanishes. As a special case, the equivalent state bounding criteria are established by using the properties of some special matrices when there exist no impulses at the switching instants in ISGRNs. Finally, an illustrating example is given to demonstrate the derived results. Compared with the existing literatures, the considered genetic regulatory networks (GRNs) have more general structure and the approach adopted in the present paper is more simple than Lyapunov-Krasovskii functional (LKF) approach.","PeriodicalId":11254,"journal":{"name":"Discrete & Continuous Dynamical Systems - S","volume":"44 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82551103","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}

{"title":"Inverse problems on degenerate integro-differential equations","authors":"M. Al Horani, A. Favini, H. Tanabe","doi":"10.3934/dcdss.2022025","DOIUrl":"https://doi.org/10.3934/dcdss.2022025","url":null,"abstract":"<p style='text-indent:20px;'>We study inverse problems on degenerate integro-differential equations without using maximal regularity property. This seems new at all in the related literature. Some applications to concrete partial differential equations are given.</p>","PeriodicalId":11254,"journal":{"name":"Discrete & Continuous Dynamical Systems - S","volume":"21 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78698266","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}

{"title":"Robust adaptive sliding mode tracking control for a rigid body based on Lie subgroups of SO(3)","authors":"Yaobang Ye, Zongyu Zuo, M. Basin","doi":"10.3934/dcdss.2022010","DOIUrl":"https://doi.org/10.3934/dcdss.2022010","url":null,"abstract":"This paper considers the attitude tracking control problem for a rigid body. In order to avoid the complexity and ambiguity associated with other attitude representations (such as Euler angles or quaternions), the attitude dynamics and the proposed control system are represented globally on special orthogonal groups. An adaptive controller based on a Lie subgroup of SO(3) is developed such that the rigid body can track any given attitude command asymptotically without requiring the exact knowledge of the inertia moment. In the presence of external disturbances, the adaptive controller is enhanced with an additional robust sliding mode term by following the same idea within the framework of SO(3). Finally, simulation results are presented to demonstrate efficiency of the proposed controllers.","PeriodicalId":11254,"journal":{"name":"Discrete & Continuous Dynamical Systems - S","volume":"34 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73789546","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}

{"title":"Distributionally robust front distribution center inventory optimization with uncertain multi-item orders","authors":"Yu-Lin Zhang, Lin Han, Xiaotian Zhuang","doi":"10.3934/dcdss.2022006","DOIUrl":"https://doi.org/10.3934/dcdss.2022006","url":null,"abstract":"As a new retail model, the front distribution center (FDC) has been recognized as an effective instrument for timely order delivery. However, the high customer demand uncertainty, multi-item order pattern, and limited inventory capacity pose a challenging task for FDC managers to determine the optimal inventory level. To this end, this paper proposes a two-stage distributionally robust (DR) FDC inventory model and an efficient row-and-column generation (RCG) algorithm. The proposed DR model uses a Wasserstein distance-based distributional set to describe the uncertain demand and utilizes a robust conditional value at risk decision criterion to mitigate the risk of distribution ambiguity. The proposed RCG is able to solve the complex max-min-max DR model exactly by repeatedly solving relaxed master problems and feasibility subproblems. We show that the optimal solution of the non-convex feasibility subproblem can be obtained by solving two linear programming problems. Numerical experiments based on real-world data highlight the superior out-of-sample performance of the proposed DR model in comparison with an existing benchmark approach and validate the computational efficiency of the proposed algorithm.","PeriodicalId":11254,"journal":{"name":"Discrete & Continuous Dynamical Systems - S","volume":"40 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91308482","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}

{"title":"On the time decay for the MGT-type porosity problems","authors":"J. Baldonedo, José R. Fernández, R. Quintanilla","doi":"10.3934/dcdss.2022009","DOIUrl":"https://doi.org/10.3934/dcdss.2022009","url":null,"abstract":"In this work we study three different dissipation mechanisms arising in the so-called Moore-Gibson-Thompson porosity. The three cases correspond to the MGT-porous hyperviscosity (fourth-order term), the MGT-porous viscosity (second-order term) and the MGT-porous weak viscosity (zeroth-order term). For all the cases, we prove that there exists a unique solution to the problem and we analyze the resulting point spectrum. We also show that there is an exponential energy decay for the first case, meanwhile for the second and third case only a polynomial decay is found. Finally, we present some one-dimensional numerical simulations to illustrate the behaviour of the discrete energy for each case.","PeriodicalId":11254,"journal":{"name":"Discrete & Continuous Dynamical Systems - S","volume":"277 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86735683","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}

{"title":"A quantitative strong unique continuation property of a diffusive SIS model","authors":"Taige Wang, Dihong Xu","doi":"10.3934/dcdss.2022024","DOIUrl":"https://doi.org/10.3934/dcdss.2022024","url":null,"abstract":"<p style='text-indent:20px;'>This article is concerned with a strong unique continuation property of solutions for a diffusive SIS (Susceptible - Infected - Susceptible, or SI) model, which belongs to a type of observability inequalities in a time interval <inline-formula><tex-math id=\"M1\">begin{document}$ [0, T] $end{document}</tex-math></inline-formula>. That is, if one can observe solution on a convex and connected bounded open set <inline-formula><tex-math id=\"M2\">begin{document}$ omega $end{document}</tex-math></inline-formula> in a bounded domain <inline-formula><tex-math id=\"M3\">begin{document}$ Omega $end{document}</tex-math></inline-formula> at time <inline-formula><tex-math id=\"M4\">begin{document}$ t = T $end{document}</tex-math></inline-formula>, then the norms of solution on <inline-formula><tex-math id=\"M5\">begin{document}$ [0,T) $end{document}</tex-math></inline-formula> on <inline-formula><tex-math id=\"M6\">begin{document}$ Omega $end{document}</tex-math></inline-formula> are observable. In our discussion, boundary condition is a homogeneous Dirichlet one (hostile boundary condition).</p>","PeriodicalId":11254,"journal":{"name":"Discrete & Continuous Dynamical Systems - S","volume":"53 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80835186","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}

{"title":"Fault detection filtering for continuous-time singular systems under a dynamic event-triggered mechanism","authors":"Q. Zhang, Huaicheng Yan, Jun Cheng, Xisheng Zhan, Kaibo Shi","doi":"10.3934/dcdss.2022023","DOIUrl":"https://doi.org/10.3934/dcdss.2022023","url":null,"abstract":"<p style='text-indent:20px;'>This paper focuses on the problem of fault detection filtering (FDF) for continuous-time singular systems via a dynamic event-triggered mechanism. Firstly, in order to reduce signal transmission and save network resources, a dynamic event-triggered mechanism is adopted. Compared with the static mechanism, the proposed method is more effective on reducing network transmission pressure since a dynamic variable is introduced. Secondly, a novel criterion is derived to guarantee the admissibility of the residual system with a certain <inline-formula><tex-math id=\"M1\">begin{document}$ mathcal{H}_infty $end{document}</tex-math></inline-formula> performance. According to the derived conditions, a new method is given to codesign the desired filter and the event-triggered parameters. Finally, an example is employed to illustrate the validity of the proposed approach.</p>","PeriodicalId":11254,"journal":{"name":"Discrete & Continuous Dynamical Systems - S","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88249060","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}

{"title":"Existence of minimizers for a quasilinear elliptic system of gradient type","authors":"Federica Mennuni, A. Salvatore","doi":"10.3934/dcdss.2022013","DOIUrl":"https://doi.org/10.3934/dcdss.2022013","url":null,"abstract":"<p style='text-indent:20px;'>The aim of this paper is to investigate the existence of weak solutions for the coupled quasilinear elliptic system of gradient type</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id=\"FE1\"> begin{document}$ left{ begin{array}{ll} - {rm div} (a(x, u, nabla u)) + A_t (x, u,nabla u) = g_1(x, u, v) &{rm{ in}} ; Omega , - {rm div} (B(x, v, nabla v)) + B_t (x, v,nabla v) = g_2(x, u, v) &{rm{ in}}; Omega , quad u = v = 0 &{rm{ on}};partialOmega , end{array} right. $end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>where <inline-formula><tex-math id=\"M1\">begin{document}$ Omega subset mathbb R^N $end{document}</tex-math></inline-formula> is an open bounded domain, <inline-formula><tex-math id=\"M2\">begin{document}$ N geq 2 $end{document}</tex-math></inline-formula> and <inline-formula><tex-math id=\"M3\">begin{document}$ A(x,t,xi) $end{document}</tex-math></inline-formula>, <inline-formula><tex-math id=\"M4\">begin{document}$ B(x,t, {xi}) $end{document}</tex-math></inline-formula> are <inline-formula><tex-math id=\"M5\">begin{document}$ mathcal{C}^1 $end{document}</tex-math></inline-formula>–Carathéodory functions on <inline-formula><tex-math id=\"M6\">begin{document}$ Omega times mathbb R times { mathbb R}^{N} $end{document}</tex-math></inline-formula> with partial derivatives <inline-formula><tex-math id=\"M7\">begin{document}$ A_t = frac{partial A}{partial t} $end{document}</tex-math></inline-formula>, <inline-formula><tex-math id=\"M8\">begin{document}$ a = {nabla}_{xi}A $end{document}</tex-math></inline-formula>, respectively <inline-formula><tex-math id=\"M9\">begin{document}$ B_t = frac{partial B}{partial t} $end{document}</tex-math></inline-formula>, <inline-formula><tex-math id=\"M10\">begin{document}$ b = {nabla}_{{xi}}B $end{document}</tex-math></inline-formula>, while <inline-formula><tex-math id=\"M11\">begin{document}$ g_1(x,t,s) $end{document}</tex-math></inline-formula>, <inline-formula><tex-math id=\"M12\">begin{document}$ g_2(x,t,s) $end{document}</tex-math></inline-formula> are given Carathéodory maps defined on <inline-formula><tex-math id=\"M13\">begin{document}$ Omega times mathbb Rtimes mathbb R $end{document}</tex-math></inline-formula> which are partial derivatives with respect to <inline-formula><tex-math id=\"M14\">begin{document}$ t $end{document}</tex-math></inline-formula> and <inline-formula><tex-math id=\"M15\">begin{document}$ s $end{document}</tex-math></inline-formula> of a function <inline-formula><tex-math id=\"M16\">begin{document}$ G(x,t,s) $end{document}</tex-math></inline-formula>.</p><p style='text-indent:20px;'>We prove that, even if the general form of the terms <inline-formula><tex-math id=\"M17\">begin{document}$ A $end{document}</tex-math></inline-formula> and <inline-formula><tex-math id=\"M18\">begin{document}$ B $end{document}</tex-math></inline-formula> makes the variational approach more difficult, under suitable hypotheses, the functional related to the problem is b","PeriodicalId":11254,"journal":{"name":"Discrete & Continuous Dynamical Systems - S","volume":"55 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83929912","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}