The Fast Diffusion Equation with Critical Exponent

2004 ◽  
pp. 169-187
Author(s):  
Victor A. Galaktionov ◽  
Juan Luis Vázquez
Keyword(s):  
Diffusion Equation ◽  
Critical Exponent ◽  
Fast Diffusion ◽  
Fast Diffusion Equation

Asymptotics of the Fast-Diffusion Equation with Critical Exponent

2000 ◽  
Vol 31 (5) ◽  
pp. 1157-1174 ◽  
Author(s):  
Victor A. Galaktionov ◽  
Lambertus A. Peletier ◽  
Juan L. Vazquez
Keyword(s):  
Diffusion Equation ◽  
Critical Exponent ◽  
Fast Diffusion ◽  
Fast Diffusion Equation

scholarly journals The critical exponent for fast diffusion equation with nonlocal source

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Chunxiao Yang ◽  
Linghua Kong ◽  
Yingxue Wu ◽  
Qing Tian
Keyword(s):  
Cauchy Problem ◽  
Diffusion Equation ◽  
Critical Exponent ◽  
Finite Time ◽  
Global Solutions ◽  
Fast Diffusion ◽  
Fast Diffusion Equation ◽  
Nonlocal Source ◽  
Nonlinear Anal ◽  
The Cauchy Problem

Abstract This paper considers the Cauchy problem for fast diffusion equation with nonlocal source $u_{t}=\Delta u^{m}+ (\int_{\mathbb{R}^{n}}u^{q}(x,t)\,dx )^{\frac{p-1}{q}}u^{r+1}$ u t = Δ u m + ( ∫ R n u q ( x , t ) d x ) p − 1 q u r + 1 , which was raised in [Galaktionov et al. in Nonlinear Anal. 34:1005–1027, 1998]. We give the critical Fujita exponent $p_{c}=m+\frac{2q-n(1-m)-nqr}{n(q-1)}$ p c = m + 2 q − n ( 1 − m ) − n q r n ( q − 1 ) , namely, any solution of the problem blows up in finite time whenever $1< p\le p_{c}$ 1 < p ≤ p c , and there are both global and non-global solutions if $p>p_{c}$ p > p c .

scholarly journals A continuum of extinction rates for the fast diffusion equation

2011 ◽  
Vol 10 (4) ◽  
pp. 1129-1147 ◽  
Author(s):  
Michael Winkler ◽  
Juan-Luis Vázquez ◽  
Marek Fila
Keyword(s):  
Diffusion Equation ◽  
Fast Diffusion ◽  
Fast Diffusion Equation ◽  
Extinction Rates

scholarly journals Special asymptotics for a critical fast diffusion equation

2014 ◽  
Vol 7 (4) ◽  
pp. 725-735 ◽  
Author(s):  
Marek Fila ◽  
◽  
Hannes Stuke ◽  
Keyword(s):  
Diffusion Equation ◽  
Fast Diffusion ◽  
Fast Diffusion Equation

scholarly journals Spatial Profile of the Dead Core for the Fast Diffusion Equation with Dependent Coefficient

2011 ◽  
Vol 2011 ◽  
pp. 1-9 ◽  
Author(s):  
Zhengce Zhang ◽  
Biao Wang
Keyword(s):  
Maximum Principle ◽  
Diffusion Equation ◽  
Single Point ◽  
Fast Diffusion ◽  
Spatial Profile ◽  
Fast Diffusion Equation ◽  
Dead Core ◽  
Core Profile ◽  
The Dead ◽  
Core Problem

We consider the dead-core problem for the fast diffusion equation with spatially dependent coefficient and obtain precise estimates on the single-point final dead-core profile. The proofs rely on maximum principle and require much delicate computation.

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