scholarly journals Existence and uniqueness of solutions for a class of non-linear diffusion equations

1987 ◽  
Vol 27 (2) ◽  
pp. 195-215 ◽  
Author(s):  
Tokuzo Shiga
Keyword(s):  
Existence And Uniqueness ◽  
Diffusion Equations ◽  
Uniqueness Of Solutions ◽  
Linear Diffusion ◽  
Non Linear

scholarly journals Analysis of fractional non-linear diffusion behaviors based on Adomian polynomials

2017 ◽  
Vol 21 (2) ◽  
pp. 813-817 ◽  
Author(s):  
Guo-Cheng Wu ◽  
Dumitru Baleanu ◽  
Wei-Hua Luo
Keyword(s):  
Taylor Expansion ◽  
Numerical Solutions ◽  
Fractional Diffusion ◽  
Diffusion Equations ◽  
Linear Diffusion ◽  
Adomian Polynomials ◽  
Fractional Diffusion Equations ◽  
Non Linear ◽  
Recurrence Formulae ◽  
Diffusion Behaviors

A time-fractional non-linear diffusion equation of two orders is considered to investigate strong non-linearity through porous media. An equivalent integral equation is established and Adomian polynomials are adopted to linearize non-linear terms. With the Taylor expansion of fractional order, recurrence formulae are proposed and novel numerical solutions are obtained to depict the diffusion behaviors more accurately. The result shows that the method is suitable for numerical simulation of the fractional diffusion equations of multi-orders.

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