Results 21 to 30 of about 8,017 (310)
Compact global attractors of discrete inclusions [PDF]
Nonlinear Analysis: Theory, Methods & Applications, 2006 Abstract The paper is dedicated to the study of the problem of the existence of compact global attractors of discrete inclusions and to the description of its structure. We consider a family of continuous mappings of a metric space W into itself, and ( W , f i ) i ∈ I is the family of discrete dynamical systems.
D. CHEBAN, MAMMANA, Cristiana
openaire +2 more sources
Global Attractors of Evolutionary Systems [PDF]
Journal of Dynamics and Differential Equations, 2009 An abstract framework for studying the asymptotic behavior of a dissipative evolutionary system $\mathcal{E}$ with respect to weak and strong topologies was introduced in [8] primarily to study the long-time behavior of the 3D Navier-Stokes equations (NSE) for which the existence of a semigroup of solution operators is not known.
openaire +3 more sources
Strong Global Attractors for 3D Wave Equations with Weakly Damping
Abstract and Applied Analysis, 2012 We consider the existence of the global attractor A1 for the 3D weakly damped wave equation. We prove that A1 is compact in (H2(Ω)∩H01(Ω))×H01(Ω) and attracts all bounded subsets of (H2(Ω)∩H01(Ω))×H01(Ω) with respect to the norm of (H2(Ω)∩H01(Ω))×H01(Ω).
Fengjuan Meng
doaj +1 more source
On global attractors of the 3D Navier-Stokes equations
Journal of Differential Equations, 2006 In view of the possibility that the 3D Navier-Stokes equations (NSE) might not always have regular solutions, we introduce an abstract framework for studying the asymptotic behavior of multi-valued dissipative evolutionary systems with respect to two topologies--weak and strong.
Alexey Cheskidov, Ciprian Foiaş
openalex +5 more sources
Attractors for Nonautonomous Parabolic Equations without Uniqueness
International Journal of Differential Equations, 2010 Using the theory of uniform global attractors of multivalued semiprocesses, we prove the existence of a uniform global attractor for a nonautonomous semilinear degenerate parabolic equation in which the conditions imposed on the nonlinearity provide the ...
Cung The Anh, Nguyen Dinh Binh
doaj +1 more source
Advances in Nonlinear Analysis, 2022 This article deals with the degenerate fractional Kirchhoff wave equation with structural damping or strong damping. The well-posedness and the existence of global attractor in the natural energy space by virtue of the Faedo-Galerkin method and energy ...
Yang Wenhua, Zhou Jun
doaj +1 more source
Regularity of Global Attractor for the Reaction-Diffusion Equation
Abstract and Applied Analysis, 2012 By using an iteration procedure, regularity estimates for the linear semigroups, and a classical existence theorem of global attractor, we prove that the reaction-diffusion equation possesses a global attractor in Sobolev space Hk for all k>0, which ...
Hong Luo
doaj +1 more source
Statistical solution and piecewise Liouville theorem for the impulsive discrete Zakharov equations
AIMS Mathematics, 2022 This article studies the discrete Zakharov equations with impulsive effect. The authors first prove that the problem is global well-posed and that the process formed by the solution operators possesses a pullback attractor. Then they establish that there
Binbin Miao, Chongbin Xu, Caidi Zhao
doaj +1 more source
Global Attractor for the Generalized Dissipative KDV Equation with Nonlinearity
International Journal of Mathematics and Mathematical Sciences, 2011 We discuss global attractor for the generalized dissipative KDV equation with nonlinearity under the initial condition u(x,0)=u0(x). We prove existence of a global attractor in space H2(Ω), by using decomposition method with cut-off function and ...
Zai-yun Zhang, Zhen-hai Liu
doaj +1 more source
Data‐driven performance metrics for neural network learning
International Journal of Adaptive Control and Signal Processing, EarlyView., 2023 Summary Effectiveness of data‐driven neural learning in terms of both local mimima trapping and convergence rate is addressed. Such issues are investigated in a case study involving the training of one‐hidden‐layer feedforward neural networks with the extended Kalman filter, which reduces the search for the optimal network parameters to a state ...
Angelo Alessandri +2 more
wiley +1 more source