Discrete & Continuous Dynamical Systems - S最新文献

For begin{document}$ C^2 $end{document} cos-type potentials, large coupling constants, and fixed begin{document}$ Diophantine $end{document} frequency, we show that the density of the spectral points associated with the Schrödinger operator is larger than 0. In other words, for every fixed spectral point begin{document}$ E $end{document}, begin{document}$ liminflimits_{epsilonto 0}frac{|(E-epsilon,E+epsilon)bigcapSigma_{alpha,lambdaupsilon}|}{2epsilon} = beta $end{document}, where begin{document}$ betain [frac{1}{2},1] $end{document}. Our approach is a further improvement on the papers [15] and [17].

We study a free boundary problem of a reaction-diffusion equation begin{document}$ u_t = Delta u+f(u) $end{document} for begin{document}$ t>0, |x| under a radially symmetric environment in begin{document}$ mathbb{R}^N $end{document}. The reaction term begin{document}$ f $end{document} has positive bistable nonlinearity, which satisfies begin{document}$ f(0) = 0 $end{document} and allows two positive stable equilibrium states and a positive unstable equilibrium state. The problem models the spread of a biological species, where the free boundary represents the spreading front and is governed by a one-phase Stefan condition. We show multiple spreading phenomena in high space dimensions. More precisely the asymptotic behaviors of solutions are classified into four cases: big spreading, small spreading, transition and vanishing, and sufficient conditions for each dynamical behavior are also given. We determine the spreading speed of the spherical surface begin{document}$ {xin mathbb{R}^N: |x| = h(t)} $end{document}, which expands to infinity as begin{document}$ ttoinfty $end{document}, even when the corresponding semi-wave problem does not admit solutions.

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.

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 begin{document}$ [0, T] $end{document}. That is, if one can observe solution on a convex and connected bounded open set begin{document}$ omega $end{document} in a bounded domain begin{document}$ Omega $end{document} at time begin{document}$ t = T $end{document}, then the norms of solution on begin{document}$ [0,T) $end{document} on begin{document}$ Omega $end{document} are observable. In our discussion, boundary condition is a homogeneous Dirichlet one (hostile boundary condition).

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 begin{document}$ mathcal{H}_infty $end{document} 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.

The aim of this paper is to investigate the existence of weak solutions for the coupled quasilinear elliptic system of gradient type

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}

where begin{document}$ Omega subset mathbb R^N $end{document} is an open bounded domain, begin{document}$ N geq 2 $end{document} and begin{document}$ A(x,t,xi) $end{document}, begin{document}$ B(x,t, {xi}) $end{document} are begin{document}$ mathcal{C}^1 $end{document}–Carathéodory functions on begin{document}$ Omega times mathbb R times { mathbb R}^{N} $end{document} with partial derivatives begin{document}$ A_t = frac{partial A}{partial t} $end{document}, begin{document}$ a = {nabla}_{xi}A $end{document}, respectively begin{document}$ B_t = frac{partial B}{partial t} $end{document}, begin{document}$ b = {nabla}_{{xi}}B $end{document}, while begin{document}$ g_1(x,t,s) $end{document}, begin{document}$ g_2(x,t,s) $end{document} are given Carathéodory maps defined on begin{document}$ Omega times mathbb Rtimes mathbb R $end{document} which are partial derivatives with respect to begin{document}$ t $end{document} and begin{document}$ s $end{document} of a function begin{document}$ G(x,t,s) $end{document}.

We prove that, even if the general form of the terms begin{document}$ A $end{document} and begin{document}$ B $end{document} makes the variational approach more difficult, under suitable hypotheses, the functional related to the problem is b