Self-similar singular solution of fast diffusion equation with gradient absorption terms

2007 ◽  
Vol 28 (1) ◽  
pp. 111-118
Author(s):  
Pei-hu Shi ◽  
Ming-xin Wang
Keyword(s):  
Diffusion Equation ◽  
Singular Solution ◽  
Fast Diffusion ◽  
Fast Diffusion Equation ◽  
Self Similar

scholarly journals Non-Self-Similar Dead-Core Rate for the Fast Diffusion Equation with Dependent Coefficient

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Liping Zhu ◽  
Zhengce Zhang
Keyword(s):  
Diffusion Equation ◽  
Single Point ◽  
Fast Diffusion ◽  
Fast Diffusion Equation ◽  
Dead Core ◽  
Core Profile ◽  
Self Similar ◽  
Similar Solutions ◽  
Compactness Arguments ◽  
Core Problem

We consider the dead-core problem for the fast diffusion equation with spatially dependent coefficient and show that the temporal dead-core rate is non-self-similar. The proof is based on the standard compactness arguments with the uniqueness of the self-similar solutions and the precise estimates on the single-point final dead-core profile.

Non-self-similar dead-core rate for the fast diffusion equation with strong absorption

Nonlinearity ◽  
2010 ◽  
Vol 23 (3) ◽  
pp. 657-673 ◽  
Author(s):  
Jong-Shenq Guo ◽  
Chia-Tung Ling ◽  
Philippe Souplet
Keyword(s):  
Diffusion Equation ◽  
Strong Absorption ◽  
Fast Diffusion ◽  
Fast Diffusion Equation ◽  
Dead Core ◽  
Self Similar

scholarly journals Similarity solutions for a quasilinear parabolic equation

1995 ◽  
Vol 37 (2) ◽  
pp. 253-266 ◽  
Author(s):  
Jong-Sheng Guo
Keyword(s):  
Diffusion Equation ◽  
Quasilinear Parabolic Equation ◽  
Similarity Solutions ◽  
Fast Diffusion ◽  
Equation Approach ◽  
Fast Diffusion Equation ◽  
Self Similar ◽  
Similar Solutions ◽  
Quasilinear Parabolic ◽  
Slow Diffusion Equation

AbstractIn this paper, we use an ordinary differential equation approach to study the existence of similarity solutions for the equation u1 = Δ(uα) + θu–β in Rn × (0, ∞) where β > 0, θ ∈ [0, 1}, and n ≥ 1. This includes the slow diffusion equation when α > = 1, and the standard heat equation when α = 1, and the fast diffusion equation when 0 < α < 1. We prove that there are forward self-similar solutions for this equation with initial data of the form c|x|p, where p = 2/(α + β) if θ = 1; p ≥ 0 and 2 + (1 – α)p > 0 if θ = 0, for some positive constant 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
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