March  2003, 9(2): 383-397. doi: 10.3934/dcds.2003.9.383

Discrete admissibility and exponential dichotomy for evolution families

1. 

Department of Mathematics, University of the West Timişoara, Bul. V. Pârvan, Nr. 4, 1900 - Timişoara, Romania

2. 

Faculty of Mathematics and Computer Science, West University of Timişoara, V. Pârvan Blvd. No. 4, 300223 Timişoara, Romania

3. 

Department of Mathematics, University of the West Timişoara, Bul. V. Pârvan, No. 4, 1900 - Timişoara, Romania

Received  August 2001 Revised  March 2002 Published  December 2002

Connections between admissibility and uniform exponential dichotomy of discrete evolution families are studied. Discrete and continuous characterizations for uniform exponential dichotomy of evolution families are given. A new version for a theorem due to Van Minh, Räbiger and Schnaubelt, for the discrete case is obtained.
Citation: Mihail Megan, Adina Luminiţa Sasu, Bogdan Sasu. Discrete admissibility and exponential dichotomy for evolution families. Discrete and Continuous Dynamical Systems, 2003, 9 (2) : 383-397. doi: 10.3934/dcds.2003.9.383
[1]

Godofredo Iommi, Bartłomiej Skorulski. Multifractal analysis for the exponential family. Discrete and Continuous Dynamical Systems, 2006, 16 (4) : 857-869. doi: 10.3934/dcds.2006.16.857

[2]

Éder Rítis Aragão Costa. An extension of the concept of exponential dichotomy in Fréchet spaces which is stable under perturbation. Communications on Pure and Applied Analysis, 2019, 18 (2) : 845-868. doi: 10.3934/cpaa.2019041

[3]

S. Gatti, M. Grasselli, V. Pata, M. Squassina. Robust exponential attractors for a family of nonconserved phase-field systems with memory. Discrete and Continuous Dynamical Systems, 2005, 12 (5) : 1019-1029. doi: 10.3934/dcds.2005.12.1019

[4]

Pierre Fabrie, Cedric Galusinski, A. Miranville, Sergey Zelik. Uniform exponential attractors for a singularly perturbed damped wave equation. Discrete and Continuous Dynamical Systems, 2004, 10 (1&2) : 211-238. doi: 10.3934/dcds.2004.10.211

[5]

Artur Avila, Thomas Roblin. Uniform exponential growth for some SL(2, R) matrix products. Journal of Modern Dynamics, 2009, 3 (4) : 549-554. doi: 10.3934/jmd.2009.3.549

[6]

Jeremy Levesley, Xinping Sun, Fahd Jarad, Alexander Kushpel. Interpolation of exponential-type functions on a uniform grid by shifts of a basis function. Discrete and Continuous Dynamical Systems - S, 2021, 14 (7) : 2399-2416. doi: 10.3934/dcdss.2020403

[7]

Alexandre Nolasco de Carvalho, Stefanie Sonner. Pullback exponential attractors for evolution processes in Banach spaces: Theoretical results. Communications on Pure and Applied Analysis, 2013, 12 (6) : 3047-3071. doi: 10.3934/cpaa.2013.12.3047

[8]

Alexandre Nolasco de Carvalho, Stefanie Sonner. Pullback exponential attractors for evolution processes in Banach spaces: Properties and applications. Communications on Pure and Applied Analysis, 2014, 13 (3) : 1141-1165. doi: 10.3934/cpaa.2014.13.1141

[9]

Pierre Fabrie, Alain Miranville. Exponential attractors for nonautonomous first-order evolution equations. Discrete and Continuous Dynamical Systems, 1998, 4 (2) : 225-240. doi: 10.3934/dcds.1998.4.225

[10]

Alin Pogan, Kevin Zumbrun. Stable manifolds for a class of singular evolution equations and exponential decay of kinetic shocks. Kinetic and Related Models, 2019, 12 (1) : 1-36. doi: 10.3934/krm.2019001

[11]

Christian Pötzsche. Dichotomy spectra of triangular equations. Discrete and Continuous Dynamical Systems, 2016, 36 (1) : 423-450. doi: 10.3934/dcds.2016.36.423

[12]

Zhong-Jie Han, Gen-Qi Xu. Exponential decay in non-uniform porous-thermo-elasticity model of Lord-Shulman type. Discrete and Continuous Dynamical Systems - B, 2012, 17 (1) : 57-77. doi: 10.3934/dcdsb.2012.17.57

[13]

Antoine Perasso. Global stability and uniform persistence for an infection load-structured SI model with exponential growth velocity. Communications on Pure and Applied Analysis, 2019, 18 (1) : 15-32. doi: 10.3934/cpaa.2019002

[14]

Gilbert Peralta. Uniform exponential stability of a fluid-plate interaction model due to thermal effects. Evolution Equations and Control Theory, 2020, 9 (1) : 39-60. doi: 10.3934/eect.2020016

[15]

Sijia Zhang, Shengfan Zhou. Random uniform exponential attractors for Schrödinger lattice systems with quasi-periodic forces and multiplicative white noise. Discrete and Continuous Dynamical Systems - S, 2022  doi: 10.3934/dcdss.2022056

[16]

Yajing Li, Yejuan Wang. The existence and exponential behavior of solutions to time fractional stochastic delay evolution inclusions with nonlinear multiplicative noise and fractional noise. Discrete and Continuous Dynamical Systems - B, 2020, 25 (7) : 2665-2697. doi: 10.3934/dcdsb.2020027

[17]

Daoyi Xu, Weisong Zhou. Existence-uniqueness and exponential estimate of pathwise solutions of retarded stochastic evolution systems with time smooth diffusion coefficients. Discrete and Continuous Dynamical Systems, 2017, 37 (4) : 2161-2180. doi: 10.3934/dcds.2017093

[18]

Arzu Ahmadova, Nazim I. Mahmudov, Juan J. Nieto. Exponential stability and stabilization of fractional stochastic degenerate evolution equations in a Hilbert space: Subordination principle. Evolution Equations and Control Theory, 2022  doi: 10.3934/eect.2022008

[19]

Fedor Nazarov, Kevin Zumbrun. Instantaneous smoothing and exponential decay of solutions for a degenerate evolution equation with application to Boltzmann's equation. Kinetic and Related Models, 2022, 15 (4) : 729-752. doi: 10.3934/krm.2022012

[20]

A. A. Kirillov. Family algebras. Electronic Research Announcements, 2000, 6: 7-20.

2021 Impact Factor: 1.588

Metrics

  • PDF downloads (195)
  • HTML views (0)
  • Cited by (5)

Other articles
by authors

[Back to Top]