Stable stationary solutions induced by spatial inhomogeneity via ?-convergence

1998 ◽  
Vol 29 (1) ◽  
pp. 75-97 ◽  
Author(s):  
Arnaldo Simal Nascimento
Keyword(s):  
Stationary Solutions ◽  
Spatial Inhomogeneity ◽  
Stable Stationary Solutions

scholarly journals Characteristic phenomena in combustion

1997 ◽  
Vol 1 (2) ◽  
pp. 147-159
Author(s):  
Dirk Meinköhn
Keyword(s):  
State Space ◽  
Reaction Diffusion ◽  
Stationary Solutions ◽  
The State ◽  
State Variable ◽  
Finite Dimensional ◽  
Dimensional State Space ◽  
Singularity Order ◽  
The Relationship ◽  
Stable Stationary Solutions

For the case of a reaction–diffusion system, the stationary states may be represented by means of a state surface in a finite-dimensional state space. In the simplest example of a single semi-linear model equation given. in terms of a Fredholm operator, and under the assumption of a centre of symmetry, the state space is spanned by a single state variable and a number of independent control parameters, whereby the singularities in the set of stationary solutions are necessarily of the cuspoid type. Certain singularities among them represent critical states in that they form the boundaries of sheets of regular stable stationary solutions. Critical solutions provide ignition and extinction criteria, and thus are of particular physical interest. It is shown how a surface may be derived which is below the state surface at any location in state space. Its contours comprise singularities which correspond to similar singularities in the contours of the state surface, i.e., which are of the same singularity order. The relationship between corresponding singularities is in terms of lower bounds with respect to a certain distinguished control parameter associated with the name of Frank-Kamenetzkii.

SPATIAL DISORDER OF CELLULAR NEURAL NETWORKS — WITH BIASED TERM

2002 ◽  
Vol 12 (03) ◽  
pp. 525-534 ◽  
Author(s):  
JUNG-CHAO BAN ◽  
SONG-SUN LIN ◽  
CHENG-HSIUNG HSU
Keyword(s):  
Neural Networks ◽  
Stationary Solutions ◽  
Cellular Neural Networks ◽  
One Dimensional ◽  
Spatial Entropy ◽  
Stable Stationary Solutions

This study describes the spatial disorder of one-dimensional Cellular Neural Networks (CNN) with a biased term by applying the iteration map method. Under certain parameters, the map is one-dimensional and the spatial entropy of stable stationary solutions can be obtained explicitly as a staircase function.

scholarly journals Corotation Solutions in the Elliptic Asteroidal Problem with Stokes Drag

1992 ◽  
Vol 152 ◽  
pp. 355-358
Author(s):  
C. Beaugé ◽  
S. Ferraz-Mello
Keyword(s):  
Restricted Problem ◽  
Stationary Solutions ◽  
Numerical Results ◽  
Stokes Drag ◽  
Elliptic Restricted Problem ◽  
Stable Stationary Solutions

We have searched for stable stationary solutions of the resonant elliptic restricted problem of three bodies with Stokes drag. Results for the 1/2 external Jovian resonance are shown as example, including a comparison with numerical results of an N-body simulation.

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