scholarly journals Finite time extinction for solutions to fast diffusion stochastic porous media equations

2009 ◽  
Vol 347 (1-2) ◽  
pp. 81-84 ◽  
Author(s):  
Viorel Barbu ◽  
Giuseppe Da Prato ◽  
Michael Röckner
Keyword(s):  
Porous Media ◽  
Finite Time ◽  
Fast Diffusion ◽  
Finite Time Extinction ◽  
Porous Media Equations ◽  
Time Extinction

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.

Discontinuous Nonlinearity and Finite Time Extinction

2020 ◽  
Vol 52 (1) ◽  
pp. 894-926
Author(s):  
Jaywan Chung ◽  
Yong-Jung Kim ◽  
Ohsang Kwon ◽  
Xingbin Pan
Keyword(s):  
Finite Time ◽  
Discontinuous Nonlinearity ◽  
Finite Time Extinction ◽  
Time Extinction
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