Spatially periodic steady-state solutions of a reversible system at strong and subharmonic resonances

1991 ◽  
Vol 48 (1) ◽  
pp. 147-168 ◽  
Author(s):  
Nicholas D. Kazarinoff ◽  
Joseph G.G. Yan
Keyword(s):  
Steady State ◽  
Reversible System ◽  
Spatially Periodic ◽  
Periodic Steady State ◽  
Steady State Solutions ◽  
Subharmonic Resonances

STABILITY OF STEADY-STATE SOLUTIONS IN MULTIDIMENSIONAL COUPLED MAP LATTICES

2004 ◽  
Vol 14 (08) ◽  
pp. 2689-2699
Author(s):  
MIROSLAVA DUBCOVÁ ◽  
DANIEL TURZÍK ◽  
ALOIS KLÍČ
Keyword(s):  
Steady State ◽  
Coupled Map Lattices ◽  
Multidimensional Lattice ◽  
Spatially Periodic ◽  
Spatially Homogeneous ◽  
Periodic Steady State ◽  
The Stability ◽  
Linearized Operator ◽  
Steady State Solutions

Coupled map lattices with multidimensional lattice are considered. A method for the determination of the stability of spatially homogeneous and spatially periodic steady-state solutions is derived. This method is based on the determination of the spectrum of the linearized operator by means of Gelfand transformation of some appropriate Banach algebra. The results are applied to several examples.

STABILITY OF SPATIALLY PERIODIC SOLUTIONS IN COUPLED MAP LATTICES

2003 ◽  
Vol 13 (02) ◽  
pp. 343-356 ◽  
Author(s):  
M. DUBCOVÁ ◽  
A. KLÍČ ◽  
P. POKORNÝ ◽  
D. TURZÍK
Keyword(s):  
Steady State ◽  
Periodic Solutions ◽  
Nonlinear Evolution ◽  
Linear Operators ◽  
Coupled Map Lattices ◽  
Evolution Operators ◽  
Spatially Periodic ◽  
The Stability ◽  
Steady State Solutions ◽  
Theoretical Results

Stability of steady-state solutions of 1-dim coupled map lattices is studied. The stability is determined by the spectrum of linear operators on two-sided sequences of vectors in [Formula: see text] arising as a linearization of the corresponding nonlinear evolution operators. Theoretical results are applied to several examples.

Periodic Steady-state Solutions of a Liquid Film Model via a Classical Method

2018 ◽  
Vol 61 (1) ◽  
pp. 3-15
Author(s):  
Ahmad Alhasanat ◽  
Chunhua Ou
Keyword(s):  
Steady State ◽  
Liquid Film ◽  
Classical Method ◽  
Wave Model ◽  
Integral Form ◽  
Iteration Scheme ◽  
Periodic Steady State ◽  
Steady State Problem ◽  
Steady State Solutions ◽  
Convergence Of The Scheme

AbstractIn this paper, periodic steady-state of a liquid film flowing over a periodic uneven wall is investigated via a classical method. Specifically, we analyze a long-wave model that is valid at the near-critical Reynolds number. For the periodic wall surface, we construct an iteration scheme in terms of an integral form of the original steady-state problem. The uniform convergence of the scheme is proved so that we can derive the existence and the uniqueness as well as the asymptotic formula of the periodic solutions.

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