Self-similar solutions for a nonlinear radiation diffusion equation

2006 ◽  
Vol 13 (9) ◽  
pp. 092703 ◽  
Author(s):  
Josselin Garnier ◽  
Guy Malinié ◽  
Yves Saillard ◽  
Catherine Cherfils-Clérouin
Keyword(s):  
Diffusion Equation ◽  
Radiation Diffusion ◽  
Nonlinear Radiation ◽  
Self Similar ◽  
Similar Solutions

scholarly journals Global existence and blow-up of generalized self-similar solutions for a space-fractional diffusion equation with mixed conditions

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Farid Nouioua ◽  
Bilal Basti
Keyword(s):  
Global Existence ◽  
Diffusion Equation ◽  
Fixed Point Theorems ◽  
Blow Up ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
Uniqueness Of Solutions ◽  
Space Fractional Diffusion Equation ◽  
Self Similar ◽  
Similar Solutions

Abstract This paper investigates the problem of the existence and uniqueness of solutions under the generalized self-similar forms to the space-fractional diffusion equation. Therefore, through applying the properties of Schauder’s and Banach’s fixed point theorems; we establish several results on the global existence and blow-up of generalized self-similar solutions to this equation.

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.

Self-similar solutions of the non-linear diffusion equation and application to near-critical fluids

1995 ◽  
Vol 218 (3-4) ◽  
pp. 419-436 ◽  
Author(s):  
T. Fröhlich ◽  
S. Bouquet ◽  
M. Bonetti ◽  
Y. Garrabos ◽  
D. Beysens
Keyword(s):  
Diffusion Equation ◽  
Linear Diffusion ◽  
Non Linear ◽  
Self Similar ◽  
Similar Solutions
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