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Global Existence and Stability of Solutions of Matrix Riccati Equations

✍ Scribed by Jonq Juang

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
97 KB
Volume
258
Category
Article
ISSN
0022-247X

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✦ Synopsis

We consider a matrix Riccati equation containing two parameters c and ␣. The quantity c denotes the average total number of particles emerging from a collision, Ε½ . Ε½ . which is assumed to be conservative i.e., 0c F 1 , and ␣ 0 F ␣ -1 is an Γ„Ε½ . 4 angular shift. Let S s c, ␣ : 0c F 1 and 0 F ␣ -1 . Stability analysis for two steady-state solutions X and X are provided. In particular, we prove that min max Γ„Ε½ .4 X is locally asymptotically stable for S y 1, 0 , while X is unstable for min max Γ„Ε½ .4 S y 1, 0 . For c s 1 and ␣ s 0, X s X is neutral stable. We also show min max Ε½ . that such equations have a global positive solution for c, ␣ g S, provided that the initial value is small and positive.

πŸ“œ SIMILAR VOLUMES

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