scholarly journals Small random perturbations of a dynamical system with blow-up

2012 ◽  
Vol 385 (1) ◽  
pp. 150-166 ◽  
Author(s):  
Pablo Groisman ◽  
Santiago Saglietti
Keyword(s):  
Dynamical System ◽  
Blow Up ◽  
Random Perturbations ◽  
Small Random Perturbations

scholarly journals Metastability for small random perturbations of a PDE with blow-up

2018 ◽  
Vol 128 (5) ◽  
pp. 1558-1589 ◽  
Author(s):  
Pablo Groisman ◽  
Santiago Saglietti ◽  
Nicolas Saintier
Keyword(s):  
Blow Up ◽  
Random Perturbations ◽  
Small Random Perturbations

On the equation ut = ∆uα + uβ

1993 ◽  
Vol 123 (2) ◽  
pp. 373-390 ◽  
Author(s):  
Yuan-Wei Qi
Keyword(s):  
Dynamical System ◽  
Blow Up ◽  
Uniqueness Result ◽  
Fast Diffusion ◽  
Negative Solution ◽  
Fast Diffusion Equation ◽  
Infinite Dimensional ◽  
The Cauchy Problem ◽  
Dimensional Dynamical System ◽  
Infinite Dimensional Dynamical System

SynopsisThe Cauchy problem of ut, = ∆uα + uβ, where 0 < α < l and α>1, is studied. It is proved that if 1< β<α + 2/n then every nontrivial non-negative solution is not global in time. But if β>α+ 2/n there exist both blow-up solutions and global positive solutions which decay to zero as t–1/(β–1) when t →∞. Thus the famous Fujita result on ut = ∆u + up is generalised to the present fast diffusion equation. Furthermore, regarding the equation as an infinite dimensional dynamical system on Sobolev space W1,s (W2.s) with S > 1, a non-uniqueness result is established which shows that there exists a positive solution u(x, t) with u(., t) → 0 in W1.s (W2.s) as t → 0.

Small random perturbations of peano phenomena

Stochastics ◽  
1982 ◽  
Vol 6 (3-4) ◽  
pp. 279-292 ◽  
Author(s):  
R. Bafico ◽  
P. Baldi
Keyword(s):  
Random Perturbations ◽  
Small Random Perturbations
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