scholarly journals Behaviour near extinction for the Fast Diffusion Equation on bounded domains

2012 ◽  
Vol 97 (1) ◽  
pp. 1-38 ◽  
Author(s):  
Matteo Bonforte ◽  
Gabriele Grillo ◽  
Juan Luis Vazquez
Keyword(s):  
Diffusion Equation ◽  
Fast Diffusion ◽  
Bounded Domains ◽  
Fast Diffusion Equation ◽  
Near Extinction

scholarly journals Uniqueness and time oscillating behaviour of finite points blow-up solutions of the fast diffusion equation

2019 ◽  
Vol 150 (6) ◽  
pp. 2849-2870
Author(s):  
Kin Ming Hui
Keyword(s):  
Initial Data ◽  
Diffusion Equation ◽  
Bounded Domain ◽  
Positive Constant ◽  
Blow Up ◽  
Fast Diffusion ◽  
Bounded Domains ◽  
Fast Diffusion Equation

AbstractLet n ⩾ 3 and 0 < m < (n − 2)/n. We extend the results of Vazquez and Winkler (2011, J. Evol. Equ. 11, no. 3, 725–742) and prove the uniqueness of finite points blow-up solutions of the fast diffusion equation ut = Δum in both bounded domains and ℝn × (0, ∞). We also construct initial data such that the corresponding solution of the fast diffusion equation in bounded domain oscillates between infinity and some positive constant as t → ∞.

Optimal rates of convergence to the singular Barenblatt profile for the fast diffusion equation

2016 ◽  
Vol 146 (2) ◽  
pp. 309-324 ◽  
Author(s):  
Marek Fila ◽  
Michael Winkler
Keyword(s):  
Initial Data ◽  
Diffusion Equation ◽  
Asymptotic Behaviour ◽  
Rates Of Convergence ◽  
Fast Diffusion ◽  
Time And Space ◽  
Fast Diffusion Equation ◽  
Optimal Rates Of Convergence ◽  
The Difference ◽  
Near Extinction

We study the asymptotic behaviour of solutions of the fast diffusion equation near extinction. For a class of initial data, the asymptotic behaviour is described by a singular Barenblatt profile. We complete previous results on rates of convergence to the singular Barenblatt profile by describing a new phenomenon concerning the difference between the rates in time and space.

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 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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