scholarly journals Finite time extinction of solutions to fast diffusion equations driven by linear multiplicative noise

2012 ◽  
Vol 389 (1) ◽  
pp. 147-164 ◽  
Author(s):  
Viorel Barbu ◽  
Giuseppe Da Prato ◽  
Michael Röckner
Keyword(s):  
Finite Time ◽  
Multiplicative Noise ◽  
Diffusion Equations ◽  
Fast Diffusion ◽  
Finite Time Extinction ◽  
Fast Diffusion Equations ◽  
Time Extinction

Poincaré inequalities for linearizations of very fast diffusion equations

Nonlinearity ◽  
2002 ◽  
Vol 15 (3) ◽  
pp. 565-580 ◽  
Author(s):  
J A Carrillo ◽  
C Lederman ◽  
P A Markowich ◽  
G Toscani
Keyword(s):  
Diffusion Equations ◽  
Fast Diffusion ◽  
Poincaré Inequalities ◽  
Poincare Inequalities ◽  
Fast Diffusion Equations

Extinction behaviour for fast diffusion equations with absorption

2001 ◽  
Vol 43 (8) ◽  
pp. 943-985 ◽  
Author(s):  
Raúl Ferreira ◽  
Juan Luis Vazquez
Keyword(s):  
Diffusion Equations ◽  
Fast Diffusion ◽  
Fast Diffusion Equations

scholarly journals Extinction for a Singular Diffusion Equation with Strong Gradient Absorption Revisited

2018 ◽  
Vol 18 (4) ◽  
pp. 785-797
Author(s):  
Razvan Gabriel Iagar ◽  
Philippe Laurençot
Keyword(s):  
Diffusion Equation ◽  
Finite Time ◽  
Extinction Time ◽  
Extinction Rates ◽  
Optimal Decay ◽  
Singular Diffusion ◽  
Finite Time Extinction ◽  
Strong Gradient ◽  
The One ◽  
Time Extinction

AbstractWhen {2N/(N+1)<p<2} and {0<q<p/2}, non-negative solutions to the singular diffusion equation with gradient absorption\partial_{t}u-\Delta_{p}u+|\nabla u|^{q}=0\quad\text{in }(0,\infty)\times% \mathbb{R}^{N}vanish after a finite time. This phenomenon is usually referred to as finite-time extinction and takes place provided the initial condition {u_{0}} decays sufficiently rapidly as {|x|\to\infty}. On the one hand, the optimal decay of {u_{0}} at infinity guaranteeing the occurrence of finite-time extinction is identified. On the other hand, assuming further that {p-1<q<p/2}, optimal extinction rates near the extinction time are derived.

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